GMATGuruNY posted a reply to Henry eats X scones in X percent of the time it takes Rachel in the Problem Solving forum
“Let X=8 and Y=4. Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. Since Henry eats X=8 scones in 8% of the time it takes Rachel to eat Y=4 scones -- 10 minutes, according to the prompt -- the time for Henry to eat 8 scones = 8% of 10 minutes = (8/100)(10) = 4/5 ...”
Yesterday
Brent@GMATPrepNow posted a reply to Henry eats X scones in X percent of the time it takes Rachel in the Problem Solving forum
“Let''s use the INPUT-OUTPUT approach. Let''s assign some values of X and Y so that they satisfy the information in the question. Let X = 25. This means Henry eats 25 scones in 25 percent of the time it takes Rachel to eat Y scones Let Y = 100. This means Henry eats 25 scones in 25 percent of ...”
Yesterday
Brent@GMATPrepNow posted a reply to Roger wants to arrange three of his five books on his in the Problem Solving forum
“I''m not crazy about this question. The official answer suggests that, although 2 books are DUPLICATES, they''re still considered DIFFERENT. Here''s what I mean: Let''s let D and d represent the two duplicate books. Let, A, B and C represent the other three books. The official answer ...”
Yesterday
Brent@GMATPrepNow posted a reply to The three-digit positive integer n can be written as ABC, in in the Data Sufficiency forum
“IMPORTANT point: The VALUE of a 3-digit integer xyz is 100x + 10y + z Example: 723 = (7)(100) + (2)(10) + 3 Target question: What is the remainder when n is divided by 37? Statement 1: A + B/10 + C/100 = B + C/10 + A/100 Multiply both sides by 100 to get: 100A + 10B + C = 100B + 10C + ...”
Yesterday
Brent@GMATPrepNow posted a reply to If x, y are integers, is x^2+x+y an odd integer? in the Data Sufficiency forum
“ Given: x and y are integers Target question: Is x² + x + y an odd integer? This is a good candidate for rephrasing the target question. Take x² + x + y and factor the first two terms to get: x(x + 1) + y Notice that x and x+1 are CONSECUTIVE INTEGERS, which means one value is ODD and ...”
Yesterday
fskilnik@GMATH posted a reply to If x, y are integers, is x^2+x+y an odd integer? in the Data Sufficiency forum
“$$x,y\,\,{\rm{ints}}\,\,\,\left( * \right)$$ $${{\text{x}}^{\text{2}}} + x + y\,\, = \,\,\underbrace {x\left( {x + 1} \right)}_{\left( * \right)\,\,{\text{even}}} + y\,\,\mathop = \limits^? \,\,\,{\text{odd}}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,y\,\,\mathop = \limits^? ...”
Yesterday
fskilnik@GMATH posted a reply to Twenty people at a meeting were born during the month of in the Problem Solving forum
“$$? = 1 - P\left( {\underbrace {{\rm{all}}\,\,20\,\,{\rm{different}}\,\,{\rm{birthday}}\,\,{\rm{dates}}}_{{\rm{unfavorable}}}} \right)$$ $${\rm{Total}}:\,\,30 \cdot 30 \cdot \ldots \cdot 30 = {30^{20}}\,\,\,{\rm{equiprobable}}\,\,{\rm{possibilities}}\,\,\,$$ $${\rm{unfavorable}} = \,\,30 \cdot ...”
Yesterday
fskilnik@GMATH posted a reply to An assembly line produces 40 cogs per hour until an initial in the Problem Solving forum
“$$? = {{\# \,\,{\rm{cogs}}} \over {\# \,\,{\rm{hours}}}}$$ Trivial application of UNITS CONTROL, one of the most powerful tools of our method! $${V_1} = {{40\,\,{\rm{cogs}}} \over {{\rm{1}}\,\,{\rm{h}}}}\,\,\,{\rm{for}}\,\,\,60\,\,{\rm{cogs}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{T_1}\,\,\, = ...”
Yesterday
fskilnik@GMATH posted a reply to Which of the following CANNOT result in an integer? A. The in the Problem Solving forum
“$$?\,\,:\,\,\,{\rm{cannot}}\,\,{\rm{be}}\,\,{\rm{integer}}$$ $$\left( {\rm{A}} \right)\,\,\,\left( {0 \cdot 0} \right) \div {1^{ - 1}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{A}} \right)\,\,\,{\rm{refuted}}$$ $$\left( {\rm{B}} \right)\,\,\,0 \div 7\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( ...”
Yesterday
fskilnik@GMATH posted a reply to A rectangular wall has dimensions of 800 by 300. If the wall in the Problem Solving forum
“Trivial application of UNITS CONTROL, one of the most powerful tools of our method! (We assume the units length is centimeters, just for didactic reasons.) $$?\,\,\, = \,\,\,800 \cdot 300\,\,{\rm{c}}{{\rm{m}}^2}\,\,\left( {{{1\,\,{\rm{tile}}} \over {12\, \cdot 25\,\,{\rm{c}}{{\rm{m}}^2}}}} ...”
Yesterday
GMATGuruNY posted a reply to A rectangular wall has dimensions of 800 by 300. If the wall in the Problem Solving forum
“number of tiles = (wall area)/(tile area) = (800*300)/(25*12) = 32*25 = 800. The correct answer is E.”
Yesterday
GMATGuruNY posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“Consider the following equation: 7x + 5y = 70. If x and y are nonnegative integers, the following solutions are possible: x=10, y=0 x=5, y=7 x=0, y=14. Notice the following: The value of x changes in increments of 5 (the coefficient for y). The value of y changes in increments of ...”
Yesterday
Brent@GMATPrepNow posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”
Yesterday
GMATGuruNY posted a reply to The cost of a square slab is proportional to its thickness a in the Data Sufficiency forum
“x is directly proportional to y implies the following: x/y = k. x = ky. In each case, k is a CONSTANT. The cost of a square slab is proportional to its thickness and also proportional to the square of its length. Thus: c = k * T * L². What is the cost of a square slab that is 3 meters ...”
Yesterday
GMATGuruNY posted a reply to Thomasville tree planting in the Critical Reasoning forum
“species may be singular or plural. Passage: Planting trees primarily from the species that turns out to have the best record of survival will assure downtown Thomasville of an abundant tree population 20 years from now. Here, the verb attributed to species is turns. Since turns is singular, ...”
January 14, 2019
Brent@GMATPrepNow posted a reply to Three machines have equal constant work rates. It takes h + in the Problem Solving forum
“ It takes h + 3 hours to produce 360 toys when 2 machines work together So, during those h + 3 hours, EACH machine makes 180 toys So, ONE machine can produce 180 toys in h + 3 hours rate = output/time So, we can write: rate of ONE machine = 180/(h + 3) It takes h hours to produce 360 toys ...”
January 14, 2019
GMATGuruNY posted a reply to Three machines have equal constant work rates. It takes h + in the Problem Solving forum
“(number of machines)(number of hours) = number of toys that are produced. In the prompt above, the blue values are THE SAME. Implication: 2 machines take h+3 hours to produce the same number of toys as 3 machines in 2 hours: 2(h+3) = 3h 2h + 6 = 3h 6 = h. Since 3 machines produce 360 toys ...”
January 14, 2019
fskilnik@GMATH posted a reply to Is a > b - c? in the Data Sufficiency forum
“$$a\,\,\mathop > \limits^? \,\,b - c$$ $$\left( 1 \right)\,\,\,a\,\, > \,\,\left| {c - b} \right|\,\,\, = \,\,\,\left| {b - c} \right|\,\,\,\, \ge \,\,\,b - c\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,$$ $$\left( 2 \right)\,\, \Rightarrow \,\,\left( 1 ...”
January 14, 2019
fskilnik@GMATH posted a reply to To furnish a room in model home, an interior decorator is to in the Problem Solving forum
“$$? = T$$ $$C\left( {T,2} \right) \cdot \underbrace {C\left( {5,2} \right)}_{ = \,\,10} = 150\,\,\,\,\, \Rightarrow \,\,\,\,\,C\left( {T,2} \right) = 15$$ $${{T\left( {T - 1} \right)} \over 2} = 15\,\,\,\,\,\,\mathop \Rightarrow \limits^{T\, > \,0} \,\,\,\,\,\,? = T = 6$$ This solution ...”
January 14, 2019
fskilnik@GMATH posted a reply to Three machines have equal constant work rates. It takes h + in the Problem Solving forum
“$$1\,\,{\rm{mach}}\,\,\, \to \,\,\,{{?\,\,{\rm{toys}}} \over {1\,\,{\rm{hour}}}}$$ $$\left. \matrix{ 2\,\,{\rm{mach}}\,\,\, \to \,\,\,{{360\,\,{\rm{toys}}} \over {h + 3\,\,{\rm{hours}}}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,1\,\,{\rm{mach}}\,\,\, \to \,\,\,{{180\,\,{\rm{toys}}} \over {h + ...”
January 14, 2019
GMATGuruNY posted a reply to If Jay has 99 problems, in how many ways can he select k of in the Data Sufficiency forum
“Rule: nCr = nC(n-r) Examples: 5C2 = 5C(5-2) = 5C3. 10C3 = 10C(10-3) = 10C7. 99C5 = 99C(99-5) = 99C94. Statement 2: Jay can select k-1 of his problems in 4851 different ways. Since 4851 is relatively small, test small values for k-1. Case 1: k-1 = 2 From 99 problems, the number of ...”
January 14, 2019
fskilnik@GMATH posted a reply to If set S consists of the numbers 1, 5, -2, 8, and n, is 0 &l in the Data Sufficiency forum
“$$S = \left\{ { - 2,1,5,8} \right\} \cup \left\{ n \right\}$$ $$?\,\,\,:\,\,\,0 < n < 7$$ $$\left( 1 \right)\,\,\,{\rm{Med}}\left( S \right) < 5\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,n = 0\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle ...”
January 13, 2019
fskilnik@GMATH posted a reply to m is a multiple of 13. Is mn a multiple of 195? in the Data Sufficiency forum
“$$m = 13K,\,\,K\,\,{\mathop{\rm int}} \,\,\,\,\,\left( * \right)$$ $$\frac{{m \cdot n}}{{3 \cdot 5 \cdot 13}}\,\,\mathop = \limits^? \,\,\operatorname{int} \,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\boxed{\,\,\frac{{m \cdot n}}{{3 \cdot 5}}\,\,\,\mathop = ...”
January 13, 2019
fskilnik@GMATH posted a reply to Patricia builds two triangles, each with 30 feet of wood. in the Problem Solving forum
“$$x + y + z = 30\,\,\,\,\,\left( {\Delta \,\,{\rm{lengths}}\,\,{\rm{positive}}\,\,{\rm{ints}}\,\,{\rm{,}}\,\,\,x\,\,{\rm{base}}} \right)$$ $$?\,\,\, = \,\,\,\,{{x\,\,\,\left( {x\,\,\max } \right)} \over {x\,\,\,\,\left( {{S_\Delta }\max } \right)\,\,\,}}\,\,\,\mathop = \limits^{\left( * \right)} ...”
January 13, 2019
fskilnik@GMATH posted a reply to There is a total of 120 marbles in a box, each of which is in the Problem Solving forum
“$$? = {{\# \left( {{\rm{red}}\,\,{\rm{or}}\,\,{\rm{blue}}} \right)} \over {\,120\,\,{\rm{equiprobables}}\,}}$$ $$\# \left( {{\rm{red}}\,\,{\rm{or}}\,\,{\rm{blue}}} \right)\,\,\, = \,\,\,120\,\, - \,\,\# \left( {{\rm{white}}\,\,{\rm{or}}\,\,{\rm{green}}} \right) = 120 - \left This solution follows ...”
January 13, 2019
fskilnik@GMATH posted a reply to Carlos runs a lap around the track in x seconds. His second in the Problem Solving forum
“$$?\,\,\,:\,\,\,\,\,\,f\left( x \right)\,\,\,{{\min } \over {{\rm{lap}}}}$$ $$\eqalign{ & {1^{{\rm{st}}}}\,{\rm{lap}}\,\,\,\, \to \,\,\,\,\,\,\,x\,\,\sec \cr & {2^{{\rm{nd}}}}\,{\rm{lap}}\,\,\,\, \to \,\,\,\,\,\left( {x + 5} \right)\,\,\sec \,\,\,\,\, \cr & ...”
January 13, 2019
fskilnik@GMATH posted a reply to If an integer n is to be chosen at random from the integers in the Problem Solving forum
“$$?\,\,\, = \,\,\,{{{?_{\,{\rm{temp}}}}\,\,\,\,\left( {{\rm{favorable}}\,\,{\rm{remainders}}} \right)} \over {8\,\,\,\,\left( {{\rm{equiprobable}}\,\,{\rm{remainders}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{division}}\,\,{\rm{by}}\,\,{\rm{8}}} \right)}}$$ $$\left. \matrix{ n\,\, \in \,\,\left\{ ...”
January 13, 2019
fskilnik@GMATH posted a reply to At a certain fruit stand, the price of each apple is 40 in the Problem Solving forum
“$$? = b\,\,\left( {{\rm{back}}} \right)$$ $$10 \to 10 - b\,\,{\rm{fruits}}\,\,\,\left\{ \matrix{ \,{\rm{apples}}\,\, = a\,\,{\rm{units}}\,\,,\,\,40\,\,{\rm{cents}}\,\,{\rm{each}} \hfill \cr \,{\rm{oranges}}\,\,{\rm{ = }}\,\,10 - a\,\,\, \to \,\,\,{\rm{10}} - b - ...”
January 13, 2019
GMATGuruNY posted a reply to A tank has two water pumps Alpha and Beta and one drain Gamm in the Problem Solving forum
“Let x = 2 hours, y = 3 hours and z = 4 hours. Let the tank = 12 gallons. Since Alpha takes 2 hours to fill the 12-gallon tank, Alpha''s rate = w/t = 12/2 = 6 gallons per hour. Since Beta takes 3 hours to fill the 12-gallon tank, Beta''s rate = w/t = 12/3 = 4 gallons per hour. Since Gamma takes ...”
January 13, 2019
Brent@GMATPrepNow posted a reply to There is a total of 120 marbles in a box, each of which is in the Problem Solving forum
“...the probability that it So, 1/4 of the 120 marbles are white. In other words, there are 30 white marbles. ...the probability that it So, 1/3 of the 120 marbles are green . In other words, there are 40 green marbles. Altogether, there are 70 marbles that are EITHER white or green. ...”
January 12, 2019
Brent@GMATPrepNow posted a reply to To furnish a room in model home, an interior decorator is to in the Problem Solving forum
“Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables) So, 150 = (# of ways to select 2 chairs)(# of ways to select 2 tables) # of ways to select 2 chairs 5 tables, choose 2 of them. Since the order of the selected chairs does not matter, we can use ...”
January 11, 2019
GMATGuruNY posted a reply to To furnish a room in model home, an interior decorator is to in the Problem Solving forum
“Since 150 combinations are possible, we get: (number of ways to choose 2 chairs)(number of ways to choose 2 tables) = 150. From 5 chairs, the number of ways to choose 2 = 5C2 = (5*4)/(2*1) = 10. Thus: (10)(number of ways to choose 2 tables) = 150 number of ways to choose 2 tables = 150/10 = ...”
January 11, 2019
GMATGuruNY posted a reply to Carlos runs a lap around the track in x seconds. His second in the Problem Solving forum
“Let x = 5 seconds for the first lap, implying 10 seconds for the second lap, 3 seconds for the third lap, and a total of 18 seconds for all 3 laps. (18 seconds)/(3 laps) = (6 seconds)/(1 lap) = 1/10 minute per lap. The correct answer must yield a value of 1/10 when x=5. Only D works: (x+1)/60 ...”
January 11, 2019
GMATGuruNY posted a reply to Every day in the morning Ross cycles for 2 hours. He always in the Problem Solving forum
“The information in red is irrelevant. Only the following facts matter: Ross travels onward at a rate of 1 mile every 12 minutes. He travels home for twice the onward distance at half the onward speed. Onward speed = 1 mile per 12 minutes = 5 miles per 60 minutes = 5 mph. Let the onward ...”
January 11, 2019
GMATGuruNY posted a reply to At a certain fruit stand, the price of each apple is 40 in the Problem Solving forum
“The original total cost of the 10 pieces of fruit = 10*56 = 560. According to the answers, after 1, 2, 3, 4, or 5 oranges are removed -- so that 9, 8, 7, 6, or 5 pieces of fruit remain -- the average cost per piece decreases to 52. Since the original total cost is a multiple of 10, and the price ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to At a certain fruit stand, the price of each apple is 40 in the Problem Solving forum
“It turns out that the cost per apple is irrelevant. Here''s why: The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents So, (total value of all 10 pieces of fruit)/10 = 56 cents This means, total value of all 10 pieces of fruit = 560 cents How many oranges must Mary put ...”
January 11, 2019
fskilnik@GMATH posted a reply to If Jay has 99 problems, in how many ways can he select k of in the Data Sufficiency forum
“Let me solve a "different" problem. In the end, I am sure you will understand the solution to the original problem throughly! $$? = C\left( {7,k} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = k\,}$$ $$\left( 1 \right)\,\,\,C\left( {7,k + 1} \right) = ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to A librarian has a set of ten books, including four different in the Problem Solving forum
“Take the task of arranging the 10 books and break it into stages. Stage 1: Arrange the 4 books about Abe Lincoln in a row We can arrange n objects in n! ways. So, we can arrange the 4 books in 4! ways IMPORTANT: Now we''ll "glue" the 4 Abe Lincoln books together to form 1 SUPER ...”
January 11, 2019
Brent@GMATPrepNow posted a reply to By what percent is 25 greater than 15? in the Problem Solving forum
“An alternative approach is to test the answer choices First, however, we can eliminate some answer choices by first testing an easy value: 50% Is 25 50% greater than 15? Well, 50% of 15 = 7.5 So, 50% greater than 15 = 15 + 7.5 = 22.5 22.5 is too small (we need to get 25), so we need a ...”
January 11, 2019
fskilnik@GMATH posted a reply to x, y and z are the sides of the triangle shown and h is its in the Data Sufficiency forum
“$$x + y + z\,\,\mathop > \limits^? \,\,\,1$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ \,x\mathop > \limits^{\left( * \right)} \,\,\,h = {1 \over 2} \hfill \cr \,z\mathop > \limits^{\left( * \right)} \,\,\,h = {1 \over 2} \hfill \cr y > 0 \hfill \cr} ...”
January 11, 2019
fskilnik@GMATH posted a reply to In the xy-plane, a circle has center (0,0) and radius 5. Is in the Data Sufficiency forum
“$$\left( {r,s} \right)\,\,\,\mathop \in \limits^? \,\,\,\left\{ {\,\left( {x,y} \right)\,\,:\,\,{{\left( {x - 0} \right)}^2} + {{\left( {y - 0} \right)}^2} \leqslant {5^2}\,} \right\}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,\,{r^2} + {s^2}\,\,\,\mathop \leqslant \limits^? ...”
January 11, 2019
fskilnik@GMATH posted a reply to By what percent is 25 greater than 15? in the Problem Solving forum
“$$15\,\,\mathop \to \limits^{?\,\, = \,\,\Delta \% } \,\,25$$ $$? = {{25 - 15} \over {15}} = {2 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\left( {\rm{E}} \right)$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
January 11, 2019
fskilnik@GMATH posted a reply to A librarian has a set of ten books, including four different in the Problem Solving forum
“$$?\,\,\,:\,\,\,\# \,\,\,{\rm{possibilities}}\,{\rm{,}}\,\,{\rm{Abe}}\,\,{\rm{books}}\;\,{\rm{together}}$$ $$10\,\,{\rm{different}}\,\,{\rm{books,}}\,\,{\rm{4}}\,\,{\rm{about}}\,{\rm{Abe}}\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,1\,\,{\rm{multiple - block}}\,\,\,\left( ...”
January 11, 2019
fskilnik@GMATH posted a reply to n is a product of 6 distinct prime numbers. m!/n is an integ in the Problem Solving forum
“$$\left. \matrix{ n = {p_1} \cdot {p_2} \cdot \ldots \cdot {p_6}\,\,\,{\rm{primes}}\,\,{\rm{and}}\,\,{\rm{distincts}}\,\,\, \hfill \cr {{m!} \over n} = {\mathop{\rm int}} \hfill \cr ? = m\,\,\min \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{Take}}\,\,\left( ...”
January 11, 2019
fskilnik@GMATH posted a reply to A class consists of 12 girls and 20 boys. One quarter of the in the Problem Solving forum
“$$? = P\left( {{\rm{girl}}\,{\rm{and}}\,\,{\rm{not}}\,\,{\rm{blue}}} \right)$$ $$20\,{\rm{boys}}\,\,\,{\rm{and}}\,\,\,12\,\,{\rm{girls}}\,\,\,\left\{ \matrix{ \,{1 \over 4}\left( {12} \right) = 3\,\,{\rm{girls}}\,\,{\rm{blue}} \hfill \cr \,9\,\,\,{\rm{girls}}\,\,{\rm{not}}\,\,{\rm{blue}} ...”
January 11, 2019
GMATGuruNY posted a reply to This year, x people won an Olympic medal for water in the Problem Solving forum
“Let x = the product of the two denominators in the prompt = 3*4 = 12. Since 1/3 won a medal for swimming, the number who won a medal for swimming = (1/3)(12) = 4. Since 1/4 of the medal winners for swimming also won a medal for diving, the number who won both a medal for swimming and a medal for ...”
January 10, 2019
fskilnik@GMATH posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum
“$$? = f + 13c\,\,\,\,\leftThe constant fee (f) and the minute-charge (c) will be considered in CENTS. (Amounts in cents are always integers!) $$\left\{ \matrix{ \,f + 10c = 290 \hfill \cr \,f + 16c = 440 \hfill \cr} \right.\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + ...”
January 10, 2019
fskilnik@GMATH posted a reply to Given that x ≠ 5, is x>{1/(x-5)^2} in the Data Sufficiency forum
“$$x\,\,\mathop > \limits^? \,\,\frac{1}{{{{\left( {x - 5} \right)}^2}}}\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,x{{\left( {x - 5} \right)}^2}\,\,\mathop > \limits^? \,\,1\,\,\,{\text{with}}\,\,{\text{x}} \ne {\text{5}}\,\,}$$ $$\left( 1 \right)\,\,\,x > 0\left\{ \matrix{ ...”
January 10, 2019
Brent@GMATPrepNow posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum
“Let C = price of connection fee Let M = the price PER MINUTE A 10-minute call costs $2.90 We can write: C + 10M = 2.90 A 16-minute call costs $4.40. We can write: C + 16M = 4.40 How much does a 13-minute call cost? So far, we have: C + 10M = 2.90 C + 16M = 4.40 ONE (slower) ...”
January 10, 2019
fskilnik@GMATH posted a reply to This year, x people won an Olympic medal for water in the Problem Solving forum
“$$x\,\,\left( {{\rm{water}}} \right)\,\,\left\{ \matrix{ \,{x \over 3}\,\,\left( {{\rm{swim}}} \right)\,\,\, \to \,\,\,\left\{ \matrix{ \,{1 \over 4}\left( {{x \over 3}} \right)\,\,\left( {{\rm{swim}}\,\,{\rm{\& }}\,\,{\rm{dive}}} \right) \hfill \cr \,{3 \over 4}\left( {{x \over 3}} ...”
January 10, 2019
fskilnik@GMATH posted a reply to (7+43+7-43)^2 is equal to which of the following? in the Problem Solving forum
“$$? = {\left( {\sqrt {7 + 4\sqrt 3 } + \sqrt {7 - 4\sqrt 3 } } \right)^2} = {\left( {A + B} \right)^2}$$ $${A^2} = 7 + 4\sqrt 3 $$ $${B^2} = 7 - 4\sqrt 3 $$ $$2AB = 2\sqrt {\left( {7 + 4\sqrt 3 } \right)\left( {7 - 4\sqrt 3 } \right)} = 2\sqrt {{7^2} - {{\left( {4\sqrt 3 } \right)}^2}} = ...”
January 10, 2019
fskilnik@GMATH posted a reply to 17^27 has a units digit of: in the Problem Solving forum
“$$? = \left\langle {{{17}^{27}}} \right\rangle = \left\langle {{7^{27}}} \right\rangle $$ $$\left\langle {{7^4}} \right\rangle = \left\langle {{7^2} \cdot {7^2}} \right\rangle = \left\langle {\left\langle {{7^2}} \right\rangle \cdot \left\langle {{7^2}} \right\rangle } \right\rangle = 1$$ ...”
January 10, 2019
Brent@GMATPrepNow posted a reply to At the end of the first quarter, the share price of a in the Problem Solving forum
“Let $100 = share price at the beginning of the year At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. So, $120 = share price at the end of the first quarter At the end of the second quarter, the share ...”
January 10, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency Video #1: Introduction to GMAT Data Sufficiency Video: https://www.youtube.com/watch?v=3MaEqnSnK-s Cheers, Brent”
January 10, 2019
Brent@GMATPrepNow posted a reply to 17^27 has a units digit of: in the Problem Solving forum
“Look for a pattern 17^1 = 17 17^2 = (17)(17) = ---9 17^3 = (17)(17^2) = (17)(---9) = ----3 17^4 = (17)(17^3) = (17)(---3) = ----1 17^5 = (17)(17^4) = (17)(---1) = ----7 NOTICE that we''re back to where we started. 17^5 has units digit 7, and 17^1 has units digit 7 So, at this point, ...”
January 10, 2019
GMATGuruNY posted a reply to (7+43+7-43)^2 is equal to which of the following? in the Problem Solving forum
“√3 ≈ 1.7. 7 + 4√3 ≈ 7 + (4)(1.7) = 13.8. 7 - 4√3 ≈ 7 - (4)(1.7) = 0.2. Thus, the given expression can be approximated as follows: (√13.8 + √0.2)² = a little more than 13.8. Only D is viable. The correct answer is D.”
January 10, 2019
GMATGuruNY posted a reply to PLease help me with the concept! in the Sentence Correction forum
“Offhand, I cannot cite an official SC that violates the rule discussed above.”
January 10, 2019
GMATGuruNY posted a reply to What is the greatest possible area of a triangular region in the Problem Solving forum
“Given two sides of a triangle, the greatest possible area will be achieved if the two sides form a RIGHT ANGLE and serve as the triangle''s base and height. For the problem above, I posted an illustrated solution here: ...”
January 9, 2019
fskilnik@GMATH posted a reply to What is the greatest possible area of a triangular region in the Problem Solving forum
“https://i.ibb.co/zfXsqRV/09-Jan19-3x.gif $$?\,\,\, = \,\,{S_{\Delta ABC}}\,\,\max $$ Let C be the center of the circle with unitary radius. Without loss of generality, we may (and will) assume point A is one unit at the right of point C (as shown in the figure on the left). For the last ...”
January 9, 2019
fskilnik@GMATH posted a reply to What is the difference between the sum of all even integers in the Problem Solving forum
“$${S_A}\,\,\, = \,\,\,2 + 4 + 6 + \ldots + 50$$ $${S_B}\,\,\, = \,\,\,\left( {50 + 2} \right) + \left( {50 + 4} \right) + \left( {50 + 6} \right) + \ldots + \left( {50 + 50} \right)\,\,\, = \,\,\,{S_A} + 25 \cdot 50$$ $$?\,\,\, = \,\,\,{S_B} - {S_A}\,\,\, = \,\,\,25 \cdot 50\,\,\, = ...”
January 9, 2019
fskilnik@GMATH posted a reply to If x and y are positive, is x > y? in the Data Sufficiency forum
“$$x,y\,\, > 0\,$$ $$x\,\mathop > \limits^? \,\,y$$ $$\left( 1 \right)\,\,2x > 3y\,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,2} \,\,\,\,\,\,x\,\, > \,\,{3 \over 2}y\,\,\,\mathop > \limits^{\left( * \right)} \,\,\,y\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} ...”
January 9, 2019
fskilnik@GMATH posted a reply to Emily keeps 12 different pairs of shoes (24 individual shoes in the Problem Solving forum
“$$\left. \matrix{ {\rm{Total}}\,\,:\,\,\,C\left( {24,2} \right) = {{24 \cdot 23} \over 2} = 12 \cdot 23\,\,{\rm{equiprobable}}\,\,{\rm{pairs}}\,\,\,\, \hfill \cr {\rm{Favorable:}}\,\,\,12\,\,{\rm{real}}\,\,{\rm{pairs}}\,\,\left( {{\rm{matches}}} \right) \hfill \cr} \right\}\,\,\,\,\,\, ...”
January 9, 2019
Brent@GMATPrepNow posted a reply to The water from one outlet, flowing at a constant rate, can f in the Problem Solving forum
“One approach is to assign a NICE NUMBER to the volume of the swimming pool. This number will work well with the two pieces of information (fill pool in 9 hours and fill pool in 5 hours). So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant ...”
January 9, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive, is x > y? in the Data Sufficiency forum
“Target question: Is x > y? This is a good candidate for rephrasing the target question. Since y is POSITIVE, we can safely take the inequality x > y and divide both sides by y to get: x/y > 1 REPHRASED target question: Is x/y > 1? Aside: Here’s a video with tips on rephrasing ...”
January 9, 2019
Brent@GMATPrepNow posted a reply to Emily keeps 12 different pairs of shoes (24 individual shoes in the Problem Solving forum
“P(dog selects matching pair) = P(dog chooses ANY sock 1st AND 2nd sock matches the 1st sock) = P(dog chooses ANY sock 1st) x P(2nd sock matches the 1st sock) = 24/24 x 1/23 = 1/23 Answer: C Cheers, Brent”
January 9, 2019
GMATGuruNY posted a reply to Stock - Number of shares V ------------------- 68 W ------- in the Problem Solving forum
“Original range = (greatest number of shares) - (smallest number of shares) = 112-45 = 67. After 24 shares of Y are purchased, new Y = 94+24 = 118. After 20 shares of X are sold, new X = 56-20 = 36. New range = (new greatest number of shares) - (new smallest number of shares) = 118-36 = 82. ...”
January 9, 2019
GMATGuruNY posted a reply to On a certain Monday, Carlos drove to work at an average in the Problem Solving forum
“When the SAME DISTANCE is traveled at two different speeds, the average speed for the entire trip will be CLOSER TO THE LOWER SPEED than to the higher speed. The reason: The portion traveled at the lower speed takes LONGER. Since more time is spent at the lower speed than at the higher speed, the ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to On a certain Monday, Carlos drove to work at an average in the Problem Solving forum
“Average speed = (TOTAL distance)/TOTAL travel time)Carlos drove to work at an average speed of 50 miles per hour Time = distance/speed So, travel time TO work = d/50 hours Carlos drove home from work at an average speed of 70 miles per hour So, travel time FROM work = d/70 hours So, TOTAL ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to How many integers between in the Problem Solving forum
“He spent 40% (of the $35) on chicken feed. 40% of $35 = $14. So, he spent $14 on chicken feed. He got a 20% discount on the chicken feed. In other words, he paid 80% of the original price. So, let C = original price of chicken feed. We can write 80% of C = $14 Or we can write 0.8C = $14 ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to On Monday, the opening price of a certain stock was $100 in the Problem Solving forum
“On Monday, the opening price of a certain stock was $100 per share and its closing price was $110 per share. On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday, We can say that the stock LOST 10% of its value. OR we can say that the stock RETAINED 90% ...”
January 8, 2019
GMATGuruNY posted a reply to A department manager distributed a number of pens, pencils, in the Data Sufficiency forum
“Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively. Since 2+3+4 = 9, the total number of pens + pencils + pads must be a multiple of 9. No way to determine the exact number of staff members. INSUFFICIENT. Statement 2: ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to A department manager distributed a number of pens, pencils, in the Data Sufficiency forum
“Jay''s solution is great. I just wanted to mention that this question hinges largely on the fact that the number of pens, pencils, and pads that each staff member receives MUST HAVE INTEGER VALUES. So, for example, if statement 1 were different and statement 2 read "The manager ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to In 1982 and 1983, Company B's operating expenses were $12.0 in the Problem Solving forum
“The profit in 1982 = 15.6 - 12.0 = $3.6 million The profit in 1983 = 18.8 - 14.0 = $4.8 million Percent change = (100)(new - old)/old = (100)(4.8 - 3.6)/3.6 = (100)(1.2)/(3.6) = (100)(1/3) = 33 1/3% Answer: D Cheers, Brent”
January 8, 2019
Brent@GMATPrepNow posted a reply to x is a positive integer, and the units digits of both (x+2)^ in the Problem Solving forum
“Another approach is to test the answer choices A. If the units digit of x is 1, is it the case that units digits of both (x+2)² and (x-2)² is 9? Well, (x+2)² = (1+2)² = 9. Works! To test (x-2)², let''s let x = 11. We get: (11-2)² = 9² = 81. NO GOOD ELIMINATE A B. If the units digit ...”
January 8, 2019
GMATGuruNY posted a reply to Because natural gas is composed mostly of methane in the Sentence Correction forum
“Both of the following are viable: Vehicles powered by natural gas emit less of certain pollutants than those burning gasoline or diesel fuel. Vehicles powered by ndatural gas emit less of certain pollutants than do those burning gasoline or diesel fuel. The inclusion of do is optional. With or ...”
January 8, 2019
GMATGuruNY posted a reply to If the graph of y = x^2 + ax + b passes through the points ( in the Data Sufficiency forum
“What is the value of n-m? (m,0) and (n,0) are the two points where y=0 and the graph intersects the x-axis. Thus, m and n are the x-intercepts of the graph. Since m < n, n-m > 0. Question rephrased: What is the positive difference between the x-intercepts? Statement 1: 4b = a²-4 Test ...”
January 8, 2019
GMATGuruNY posted a reply to If x is integer and 3 | x |+x < 4, what is the value of x in the Data Sufficiency forum
“3|x| < 4-x Case 1: Signs unchanged 3x < -x 4x < 4 x < 1 Case 2: Signs changed in the absolute value 3(-x) < 4-x -2x < 4 x > -2 Question stem, rephrased: If x is an integer such that -2 < x < 1, what is the value of x? Statement 1: x < 0 Here, x must ...”
January 8, 2019
fskilnik@GMATH posted a reply to If the graph of y = x^2 + ax + b passes through the points ( in the Data Sufficiency forum
“$$? = n - m$$ $$n > m\,\,\,{\rm{are}}\,\,{\rm{the}}\,\,{\rm{roots}}\,\,{\rm{of}}\,\,{\rm{the}}\,\,{\rm{equation}}\,\,\,{x^2} + ax + b = 0\,\,\,\,\left( * \right)\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{sum/product}}} \,\,\,\,\,\,\,\,\left\{ \matrix{ \,m + n = - a \hfill \cr \,mn = b ...”
January 8, 2019
fskilnik@GMATH posted a reply to If x is integer and 3 | x |+x < 4, what is the value of x in the Data Sufficiency forum
“$$3\left| x \right| + x < 4\,\,\,\,\,,\,\,\,\,x\,\,{\mathop{\rm int}} $$ $$? = x$$ $$\left( 1 \right)\,\,\,x < 0\,\,\,\,\, \Rightarrow \,\,\,\,3\left( { - x} \right) + x < 4\,\,\,\,\, \Rightarrow \,\,\,\, - 2x < 4\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\left( { - 2} \right)} ...”
January 8, 2019
fskilnik@GMATH posted a reply to What is the value of 25*8÷50÷2 in the Problem Solving forum
“$$?\,\,\, = \,\,\,25 \cdot 8 \div 50 \div 2\,\,\, = \,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
January 8, 2019
fskilnik@GMATH posted a reply to x is a positive integer, and the units digits of both (x+2)^ in the Problem Solving forum
“$$x \ge 1\,\,{\mathop{\rm int}} $$ $$? = \left\langle x \right\rangle \,\,\,\,\,\left( {{\rm{units}}\,\,{\rm{digit}}\,\,{\rm{of}}\,\,x} \right)$$ $$\left. \matrix{ \left\langle {{{\left( {x + 2} \right)}^2}} \right\rangle = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {x + 2} \right\rangle ...”
January 8, 2019
Brent@GMATPrepNow posted a reply to In 1991, the price of a house was 80% of its original price. in the Problem Solving forum
“I''d typically assign a "nice" value to the original price, and then follow the steps that Mitch demonstrated. Alternatively, we can solve the question algebraically In 1991, the price of a house was 80% of its original price. Let x = the original price So, 0.8x = the 1991 price ...”
January 7, 2019
Brent@GMATPrepNow posted a reply to If triangle ABC is an isosceles triangle, what is ∠ABC? in the Data Sufficiency forum
“Target question: What is ∠ABC? Given: Triangle ABC is an isosceles triangle So, ∆ABC has 2 equal angles Statement 1: ∠CAB = 45 degrees Since ∆ABC has 2 equal angles, there are two possible triangles that satisfy statement 1: Case a: ∠CAB = 45, ∠BCA = 45 and ∠ABC = 90. ...”
January 7, 2019
Brent@GMATPrepNow posted a reply to If f(a*b) = f(a) + f(b), what is the value of f(1)? in the Problem Solving forum
“To generalize Mitch''s and Fabio''s solutions, notice that, as long as we can get f(1) involved in the process, we''ll arrive at answer choice C every time. Notice that k = 1*k Since f(a*b) = f(a) + f(b), we can write: f(1*k) = f(1) + f(k) Simplify: f(k) = f(1) + f(k) Subtract f(k) from both ...”
January 7, 2019
GMATGuruNY posted a reply to In 1991, the price of a house was 80% of its original price. in the Problem Solving forum
“Let the original price = 100. 1991 price = 80% of 100 = 80. 1992 price = 60% of 100 = 60. Percent decrease from 80 to 60 = (Difference/Larger) * 100 = (20/80) * 100 = 25. The correct answer is B.”
January 7, 2019
GMATGuruNY posted a reply to The main ingredient in a certain prescription drug capsule c in the Problem Solving forum
“Each capsule contains 600 milligrams of ingredient. 10⁶ milligrams = 1 kilogram. 1 kilogram of ingredient = 500 dollars. To determine the cost per capsule, we must use the relationships above to convert 600 milligrams into dollars: (600 milligrams) * (1 kilogram)/(10⁶ milligrams) * ...”
January 7, 2019
GMATGuruNY posted a reply to The numbers of women is singular or plural? in the Sentence Correction forum
“percent may serve as a NOUN. Of the students in the class, eighty percent passed the test. Here, eighty percent is a NOUN serving as the subject of passed. twice is a MODIFIER. It cannot serve as the subject of a sentence. Of the students in the class, twice passed the test. The sentence ...”
January 7, 2019
fskilnik@GMATH posted a reply to Is x^2 + 9 prime? in the Data Sufficiency forum
“$${x^2} + 9\,\,\,\mathop = \limits^? \,\,\,{\rm{prime}}$$ $$\left( 1 \right)\,\,\,x\,\,{\rm{odd}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{x^2} + 9\,\, \ge \,\,\,10\,\,\,{\rm{and}}\,\,{\rm{even}}\,\,\,\,\,\left( {{\rm{also}}\,\,{\rm{when}}\,\,x \le - 1} \right)\,\,\,\,\,\,\, \Rightarrow ...”
January 7, 2019
fskilnik@GMATH posted a reply to If x and y are nonzero integers, is in the Data Sufficiency forum
“$$x,y\,\, \ne 0\,\,\,{\rm{ints}}\,\,\,\left( * \right)$$ $$\frac{1}{{\frac{1}{x} + \frac{1}{y}}}\,\,\mathop > \limits^? \,\,\frac{1}{{\frac{1}{{xy}}}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\boxed{\,\,\,\,\frac{{xy}}{{y + x}}\,\,\,\mathop > \limits^? \,\,\,xy\,\,\,}$$ $$\left( 1 ...”
January 7, 2019
GMATGuruNY posted a reply to If f(a*b) = f(a) + f(b), what is the value of f(1)? in the Problem Solving forum
“Let a=1 and b=2. Plugging a=1 and b=2 into f(ab) = f(a) + f(b), we get: f(1*2) = f(1) + f(2) f(2) = f(1) + f(2) 0 = f(1). The correct answer is C.”
January 7, 2019
fskilnik@GMATH posted a reply to If a/b > 4, is a > 8? in the Data Sufficiency forum
“$${a \over b} > 4$$ $$a\,\,\mathop > \limits^? \,\,8$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ \,b > 2 \hfill \cr \,{a \over b} > 4 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a\,\,\, = \,\,\,b \cdot {a \over b}\,\,\, > \,\,\,2 \cdot 4\,\,\, = ...”
January 7, 2019
fskilnik@GMATH posted a reply to In 1991, the price of a house was 80% of its original price. in the Problem Solving forum
“$$?\,\,\,:\,\,\,\Delta \% = \frac{{{P_{92}} - {P_{91}}}}{{{P_{91}}}}\,\,\,\,\,\,\,\left( {\Delta \% < 0} \right)$$ $$\left. \matrix{ {P_{91}} = {4 \over 5}P \hfill \cr {P_{92}} = {3 \over 5}P\,\,\, \hfill \cr} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\Delta \% = {{ - {1 \over 5}P} ...”
January 7, 2019
fskilnik@GMATH posted a reply to The main ingredient in a certain prescription drug capsule c in the Problem Solving forum
“Perfect opportunity for UNITS CONTROL, one of the most powerful tools of our method! $${\text{licit}}\,\,{\text{converters}}\,\,:\,\,\,\frac{{\$ ...”
January 7, 2019
fskilnik@GMATH posted a reply to If f(a*b) = f(a) + f(b), what is the value of f(1)? in the Problem Solving forum
“$$f\left( {ab} \right) = f\left( a \right) + f\left( b \right)\,\,\,\,\,\left( * \right)$$ $$? = f\left( 1 \right)$$ $$f\left( 1 \right) = f\left( {1 \cdot 1} \right)\mathop = \limits^{\left( * \right)} f\left( 1 \right) + f\left( 1 \right)$$ $$f\left( 1 \right) = 2 \cdot f\left( 1 ...”
January 7, 2019
Brent@GMATPrepNow posted a reply to After her birthday, Fiona had D dollars in gift money. in the Problem Solving forum
“Another approach is to use algebra. After her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard. If Fiona SPENT 3/5 of D dollars, then 2/5 of D dollars REMAINED In other words, the amount remaining at the end of the day = 2D/5 dollars The next day, ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to After her birthday, Fiona had D dollars in gift money. in the Problem Solving forum
“One option is to WORK BACKWARDS The next day, she spent 1/3 of what was left on a movie passcard, and then finally put the last $80 in the bank. If she spent 1/3 of her money on a movie passcard, then 2/3 of her money remained (which she put in the bank). This means 2/3 of her money = $80 We ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to A retailer sells only radios and clocks. If she currently ha in the Data Sufficiency forum
“ Given: A retailer sells only radios and clocks, and she currently has 44 total items in inventory. Target question: How many radios are there in the inventory Statement 1: The retailer has more than 28 radios in inventory There are several scenarios that satisfy statement 1. Here are ...”
January 6, 2019
Brent@GMATPrepNow posted a reply to Number Properties in the Data Sufficiency forum
“The error is highlighted above in blue. if a>0 we will have the answer as YES is ALMOST true. The only time it''s not true is when a = 1 If a = 1, then the answer is NO. We can verify this using either the original inequality or the rephrased inequality. Take "Is a + 1/a > ...”
January 6, 2019
GMATGuruNY posted a reply to A store sells erasers for 0.23$ per piece and pencil for in the Data Sufficiency forum
“Consider the following equation: 5x + 7y = 70. If x and y are nonnegative integers, the following solutions are possible: x=0, y=10 x=7, y=5 x=14, y=0. Notice the following: The value of x changes in increments of 7 (the coefficient for y). The value of y changes in increments of 5 (the ...”
January 6, 2019
GMATGuruNY posted a reply to the mixture to make the ratio of milk and water in the new m in the Problem Solving forum
“The ratio of milk and water in a mixture is 2:1, Let milk = 2 liters and water = 1 liter. Some quantity of water is added to the mixture to make the ratio of milk and water in the new mixture 1:2. Since the resulting amount of water must be double the original 2 liters of milk, the resulting ...”
January 6, 2019
GMATGuruNY posted a reply to Little Texas Drilling Company has three wells, each producin in the Problem Solving forum
“Given the answer choices, the prompt should read as follows: A''s rate = (1 barrel)/(2 minutes) * (60 minutes)/(1 hour) = 30 barrels per hour. B''s rate = (1 barrel)/(3 minutes) * (60 minutes)/(1 hour) = 20 barrels per hour. C''s rate = (1 barrel)/(15 minutes) * (60 minutes)/(1 hour) = 15 ...”
January 6, 2019
GMATGuruNY posted a reply to If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many in the Problem Solving forum
“|a-b| = the distance between a and b |a+b| = |a-(-b)| = the distance between a and -b y = |2 + x| - |2 – x| y = |x+2| - |x-2| y = |x-(-2)| - |x-2| y = the subtraction of two distances: (distance between x and -2) - (distance between x and 2) On the number line: ...”
January 5, 2019
GMATGuruNY posted a reply to Seven cars of seven different models are going to park in in the Problem Solving forum
“Let the 7 cars be A, B, C, D, P, Q and S. Since P and Q must occupy adjacent positions, consider PQ a single element in the arrangement. The number of ways to arrange the 6 elements A, B, C, D, PQ and S = 6! = 720. In 1/2 of these arrangements, S will be to the LEFT of PQ. In the ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to A store sells erasers for 0.23$ per piece and pencil for in the Data Sufficiency forum
“This question illustrates a common trap on the GMAT. As Jay has shown, with statement 2, we''re able to write the equation 23x + 11y = 170 , and in high school we learned that, if we''re given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to A barn is enclosed in the shape of a 6-sided figure; all in the Data Sufficiency forum
“This Date Sufficiency question is almost identical to the following Problem Solving question, which requires us to find the actual area: http://www.beatthegmat.com/plz-explain-t270003.html Cheers, Brent”
January 5, 2019
Brent@GMATPrepNow posted a reply to In the rectangular coordinate system above, the area of in the Problem Solving forum
“Let''s draw a rectangle around the triangle (as shown below) and then subtract from the rectangle''s area (28) the areas of the 3 right triangles that surround the triangle in question. We get the following: http://s13.postimage.org/a47qx0j8j/triangle_in_coordinate_plane_2.jpg So, the area ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to What is the perimeter of quadrilateral Q? in the Data Sufficiency forum
“Target question: What is the perimeter of quadrilateral Q? If we recognize that each statement alone is not sufficient, we can jump straight to...... Statements 1 and 2 combined There are several quadrilaterals satisfy BOTH statements. Here are two: Case a: Q is a rectangle with width 1 ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to The price of a consumer good increased by p% in the Problem Solving forum
“Let $100 be the original price The price of a consumer good increased by p% during 2012 p% = p/100, so a p% INCREASE is the same a multiplying the original price by 1 + p/100 So, the new price = ($100)(1 + p/100) The price then decreased by 12% during 2013 A 12% DECREASE is the same a ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to The number of students who attend a school could be divided in the Problem Solving forum
“The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. This tells us that the TOTAL number of students is a multiple of 10, 12 and 16 What is the minimum number of students that could attend the school? ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to Set K consists of a finite number of consecutive odd in the Data Sufficiency forum
“Target question: What is the value of y - x? Given: Set K consists of a finite number of consecutive odd integers Statement 1: The average (arithmetic mean) of set K is –36 There''s a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to The value of (10^8-10^2)/(10^7-10^3) is closest to which in the Problem Solving forum
“Since the answer choices are so spread out, we can be quite aggressive with out estimation. First, 10⁸ - 10² can be rounded to 10⁸ Is this reasonable? Well, 10⁸ equals 100,000,000, so subtracting 10² (aka 100) from 100,000,000 still leaves us with approximately 100,000,000 ...”
January 5, 2019
GMATGuruNY posted a reply to Which of the following must be non-negative? in the Problem Solving forum
“D: (a-0.9)(a-0.9) = (a-0.9)². The square of a value cannot be negative. The correct answer is D.”
January 5, 2019
GMATGuruNY posted a reply to Machine M and Machine N working alone at their constant rate in the Data Sufficiency forum
“Statement 1: Case 1: N = 4000 nails per hour, M = 2000 nails per hour Since N''s rate = 4000 nails per hour, the time for N to produce 8000 nails = 8000/4000 = 2 hours. Since M''s rate = 2000 nails per hour, the time for M to produce 6000 nails = 6000/2000 = 3 hours. In this case, M works longer ...”
January 5, 2019
Brent@GMATPrepNow posted a reply to Each of the 25 balls in a certain box is either red, blue, in the Data Sufficiency forum
“Target question: What is the value of P(white or even)? To solve this, we need P(A or B) = P(A) + P(B) - P(A & B) So, P(white or even) = P(white) + P(even) - P(white & even) Statement 1: P(white & even) = 0 We can add this to our probability equation to get: P(white or even) = ...”
January 4, 2019
GMATGuruNY posted a reply to Each of the 25 balls in a certain box is either red, blue, in the Data Sufficiency forum
“Let: W = the total number of white marbles. E = the total number of even marbles. WE = the total number of white even marbles. Statement 1: Thus, WE = 0. No way to determine the value of W or E. INSUFFICIENT. Statement 2: Implication: W-E = (0.2)(25) = 5. Case 1: W=10, E=5, WE=0 ...”
January 4, 2019
GMATGuruNY posted a reply to Allison always leaves her office at 5.00pm and reaches her in the Data Sufficiency forum
“Statement 2: Brittany always leaves the hotel at exactly 5.30pm. To see the situation more clearly, plug in a value for the distance between the hotel and the office. Let the distance = 6 miles. Since Allison takes 1 hour -- from 5 to 6pm -- to travel the entire distance, Alison''s rate = d/t = ...”
January 4, 2019
fskilnik@GMATH posted a reply to Is x/y < 0? in the Data Sufficiency forum
“$$\frac{x}{y}\,\,\mathop < \limits^? \,\,0$$ $$\left( 1 \right)\,\,{x^4}{y^5} < 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x \ne 0\,\,\,{\rm{and}}\,\,\,y < 0\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1, - 1} \right)\,\,\,\,\, \Rightarrow ...”
January 4, 2019
Brent@GMATPrepNow posted a reply to The profit from the sale of a certain appliance increases, in the Data Sufficiency forum
“Target question: Did the profit exceed $4 million on sales of 380,000 units? Given: The profit from the sale of a certain appliance increases, though not proportionally, with the number of units sold. IMPORTANT: This means that we CANNOT make any "good" assumptions about the ...”
January 4, 2019
fskilnik@GMATH posted a reply to What is the largest value of non-negative integer N for in the Problem Solving forum
“$$N \geqslant 0\,\,\operatorname{int} \,\,{\text{such}}\,\,{\text{that}}\,\,\,\frac{{50!}}{{{{10}^N}}} = \operatorname{int} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\boxed{\,N \geqslant 0\,\,\operatorname{int} ...”
January 4, 2019
fskilnik@GMATH posted a reply to In a sports club, 6 players are divided into 3 teams of 2 pl in the Problem Solving forum
“Mitch has a good point. We will follow his suggestion. $$?\,\,\,:\,\,\,\# \,\,{\rm{pairs}}\,\,{\rm{among}}\,\,6\,\,{\rm{people}}$$ $${\rm{If}}\,\,{\rm{teams}}\,\,\left( {{\rm{pairs}}} \right)\,\,A,B,C\,\,{\rm{are}}\,\,{\rm{distinguishable:}}$$ $$\underbrace {C\left( {6,2} ...”
January 4, 2019
fskilnik@GMATH posted a reply to If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ? in the Problem Solving forum
“$$\left. \matrix{ y = 2\left( {k + 1} \right) \hfill \cr ?\,\,:\,\,\,4\left( {{1 \over y}} \right) = {4 \over y}\,\, = f\left( k \right)\,\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = {4 \over {2\left( {k + 1} \right)}} = {2 \over {k + 1}}$$ This solution ...”
January 4, 2019
GMATGuruNY posted a reply to If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ? in the Problem Solving forum
“Let k=0, implying that y = 2 + 2*0 = 2. Plugging y=2 into 1/y + 1/y + 1/y + 1/y, we get: 1/2 + 1/2 + 1/2 + 1/2 = 2. The correct answer must yield a value of 2 when k=0. Only B works: 2/(1+k) = 2/(1+0) = 2. The correct answer is B.”
January 4, 2019
Brent@GMATPrepNow posted a reply to If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ? in the Problem Solving forum
“Given: y = 2 + 2k Rewrite as: y/1 = (2 + 2k)/1 Flip both fractions to get: 1/y = 1/(2 + 2k) So, 1/y + 1/y + 1/y + 1/y = 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) = 4/(2 + 2k) = 4/(2)(1 + k) = 2/(1 + k) Answer: B Cheers, Brent”
January 4, 2019
Brent@GMATPrepNow posted a reply to Is x/y < 0? in the Data Sufficiency forum
“Target question: Is x/y < 0? Statement 1: (x^4)(y^5) < 0 There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = -1. Notice that (x^4)(y^5) = (1^4)(-1^5) = (1)(-1) = -1, which is less than 0. In this case, x/y = 1/(-1) = -1. So, the answer to ...”
January 4, 2019
GMATGuruNY posted a reply to OG Verbal 2016-SC# 63 in the Sentence Correction forum
“In my previous response, I provided links to three official examples. This construction seems viable.”
January 4, 2019
GMATGuruNY posted a reply to OG Verbal 2016-SC# 63 in the Sentence Correction forum
“It is possible for back-to-back modifiers joined solely by a comma to have the same referent. Three examples: http://www.beatthegmat.com/the-hognose-snake-puts-on-an-impressive-bluff-t93558.html http://www.beatthegmat.com/parallelism-issue-t96011.html ...”
January 4, 2019
GMATGuruNY posted a reply to In a sports club, 6 players are divided into 3 teams of 2 pl in the Problem Solving forum
“The usage of the term arrangements is misleading. The prompt seems intended to ask the following: The first player selected can be paired with any of the 5 other players. Thus, the number of options for the first player selected = 5. At this point, 4 players remain. The next player ...”
January 4, 2019
Brent@GMATPrepNow posted a reply to If 4+ 1n = 55n, what is the value of n? in the Problem Solving forum
“GIVEN: √(4 + 1/n) = 5√(5/n) Square both sides to get: (5)(5)√(5/n)√(5/n) Simplify right side again: 4 + 1/n = 25(5/n) Simplify right side: 4 + 1/n = 125/n Multiply both sides by n to get: 4n + 1 = 125 Subtract 1 from both sides to get: 4n = 124 Solve: n = 124/4 =31 Answer: A ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to On a construction site, 16 of the men wear helmets, and 19 in the Data Sufficiency forum
“I thought I''d point out that Jay''s approach is also known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of construction worker, and the two ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to If the average of four numbers is 35, how many of the in the Data Sufficiency forum
“Target question: How many of the numbers are less than 35? Given: The average of four numbers is 35 All this tells us is that the SUM of the 4 numbers is 140 (since 140/4 = 35) Given the limited amount of information, it''s likely that the correct answer is C or E Statement 1: None of ...”
January 3, 2019
GMATGuruNY posted a reply to This morning, a certain sugar container was full. Since then in the Data Sufficiency forum
“The determine the percent decrease, we need to know the RATIO between the remaining amount of sugar after cookie-making and the original amount of sugar. Statement 1: Case 1: Remaining sugar after cookie-making = 10 pounds Since the remaimning amount of sugar would need to increase by 30% to ...”
January 3, 2019
GMATGuruNY posted a reply to Is x/y < 0? in the Data Sufficiency forum
“Question stem, rephrased: Do x and y have different signs? Statement 1: |x+y| < |x|+|y| Since an absolute value cannot be negative, both sides here are NONNEGATIVE, enabling us to safely square the inequality: (|x+y|)²< (|x|+|y|)² x² + y² + 2xy < x² + y² + 2|x||y| xy < ...”
January 3, 2019
GMATGuruNY posted a reply to If the average of four numbers is 35, how many of the in the Data Sufficiency forum
“Sum of the 4 numbers = (quantity)(average) = 4*35 = 140. Statement 1: None of the numbers are exactly 3 To save time, check whether it''s possible to get different answers to the question stem while also satisfying Statement 2. Case 1: 0, 33, 33, 74 --> sum = 0+33+33+74 = 140 In this ...”
January 3, 2019
GMATGuruNY posted a reply to If a car traveled from Townsend to Smallville at an average in the Data Sufficiency forum
“Statement 1: The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. Case 1: Distance between Townsend and Smallville = 80 miles Time to travel from Townsend to Smallville at a speed of 40 mph = 80/40 = 2 hours. Time to travel from Smallville to Townsend = ...”
January 3, 2019
fskilnik@GMATH posted a reply to If m and n are positive integers such that m>n, what is t in the Data Sufficiency forum
“Important: the solution presented below assumes a reasonable quantitative maturity. (If you do not have that, I recommend the excellent step-by-step presentation offered by Brent above.) $$\eqalign{ & m > n \ge 1\,\,\,{\rm{ints}}\,\,\,\left( * \right) \cr & {m^{\rm{2}}} - ...”
January 3, 2019
fskilnik@GMATH posted a reply to Is x/y < 0? in the Data Sufficiency forum
“$${x \over y}\,\,\mathop < \limits^? \,\,0\,\,\,\,\left( {y \ne 0} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,xy\,\,\mathop < \limits^? \,\,0\,\,\,\,,\,\,\,{\rm{with}}\,\,y \ne 0$$ $$\left( 1 \right)\,\,\,\,\left| {x + y} \right|\,\,\, < \,\,\,\left| x \right| + \left| y ...”
January 3, 2019
fskilnik@GMATH posted a reply to Alice, Benjamin, and Carol each try independently to win a c in the Problem Solving forum
“$$? = P\left( {A \cap B \cap \overline C } \right) + P\left( {A \cap C \cap \overline B } \right) + P\left( {B \cap C \cap \overline A } \right)$$ $$\left( * \right)\,\,\left\{ \matrix{ \,P\left( {A \cap B \cap \overline C } \right) = {1 \over 5} \cdot {3 \over 8} \cdot {5 \over 7} = {{15} \over ...”
January 3, 2019
fskilnik@GMATH posted a reply to If 4+ 1n = 55n, what is the value of n? in the Problem Solving forum
“$$? = n$$ $$\sqrt {{{4 \cdot n} \over n} + {1 \over n}} = 5\,\,\sqrt {{5 \over n}} \,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,\,{{4n + 1} \over n} = {{25 \cdot 5} \over n}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,4n = 125 - 1\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = n = {{120 + 4} ...”
January 3, 2019
GMATGuruNY posted a reply to On each lab that René completed he received either 100 in the Data Sufficiency forum
“Let x = the number of 100-point labs and y = the number of 85-point labs. Question stem, rephrased: What is the value of x? Statement 1: 100x + 85y = 1140 20x + 17y = 228 The value in blue implies the following: Since 20x will have a units digit of 0, 17y must have a UNITS DIGIT OF 8. ...”
January 3, 2019
GMATGuruNY posted a reply to Absolute value in the Problem Solving forum
“Alternate approach: Since an absolute value cannot be negative -- implying that the right side of the equation must be NONNEGATIVE -- we know that x≥0. If x²-6=x, we get: x²-x-6=0 (x-3)(x+2) = 0 Only the factor in green implies a nonnegative option for x: x-3=0 x=3. The correct ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to Absolute value in the Problem Solving forum
“A quick approach is to simply test the answer choices A) -2 No good. The absolute value of something cannot be negative B) 0 Plug in to get |0² - 6| = 0. Doesn''t work. C) 1 Plug in to get |1² - 6| = 1. Doesn''t work. D) 3 Plug in to get |3² - 6| = 3. WORKS!!! Answer: D Cheers, ...”
January 3, 2019
Brent@GMATPrepNow posted a reply to If m and n are positive integers such that m>n, what is t in the Data Sufficiency forum
“ Given: m and n are positive integers such that m > n Target question: What is the remainder when m² – n² is divided by 21? Statement 1: The remainder when (m + n) is divided by 21 is 1 There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 12 and ...”
January 2, 2019
Brent@GMATPrepNow posted a reply to If x + y is not equal to 0. What is the value of (ax + ay)/( in the Data Sufficiency forum
“Target question: What is the value of (ax + ay)/(x + y)? This is a good candidate for rephrasing the target question. Take the expression: (ax + ay)/(x + y) Factor the numerator to get: a(x + y)/(x + y) Simplify the fraction to get: a Since (ax + ay)/(x + y) = a, we can rephrase the target ...”
January 2, 2019
Brent@GMATPrepNow posted a reply to Can n be expressed as the difference of 2 prime numbers? in the Data Sufficiency forum
“Target question: Can n be expressed as the difference of 2 prime numbers? Statement 1: (n-17)(n-21) = 0 This tells us that EITHER n = 17 OR n = 21 IMPORTANT: Upon seeing that n can equal one of two values, some students will incorrectly conclude that statement 1 is not sufficient. However, ...”
January 2, 2019
fskilnik@GMATH posted a reply to Can n be expressed as the difference of 2 prime numbers? in the Data Sufficiency forum
“$$n\,\,\mathop = \limits^? \,\,{p_1} - {p_2}\,\,\,\,\left( {{p_1} \,,\, {p_2}\,\,{\rm{primes}}} \right)$$ $$\left( 1 \right)\,\,\,n = 17\,\,\,{\rm{or}}\,\,\,n = 21\,\,\,\,\left\{ \matrix{ \,n = 17 = 19 - 2\,\,\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr ...”
January 2, 2019
fskilnik@GMATH posted a reply to What is the value of the integer n? in the Data Sufficiency forum
“$$? = n\,\,\,\,\left( {n\,\,{\mathop{\rm int}} } \right)$$ $$\left( 1 \right)\,\,n \in \left\{ {3,7} \right\}\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
January 2, 2019
fskilnik@GMATH posted a reply to If 2x+y=3 and 4x^2-4xy+y^2=1, what is the value of xy? in the Problem Solving forum
“$$? = xy$$ $${\left( {2x - y} \right)^2} = 4{x^2} - 4xy + {y^2} = 1\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,2x - y = \pm 1$$ $$\left\{ \matrix{ \,2x + y = 3 \hfill \cr \,2x - y = 1 \hfill \cr} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,x = 1\,\,\,\,\, ...”
January 2, 2019
fskilnik@GMATH posted a reply to Which of the following could be the area of a regular hexago in the Problem Solving forum
“$$?\,\,\,:\,\,\,{\rm{possible}}\,\,S\, = \,{\rm{regular}}\,\,{\rm{hexagon}}\,\,{\rm{area}}\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
January 2, 2019
fskilnik@GMATH posted a reply to (x^8y^2+x^2y^8)/(x^2+y^2)=? in the Problem Solving forum
“Let´s explore a particular case and proceed with the "filtering" (i.e., refuting alternatives that do not match the target)! $$? = {{{x^8}{y^2} + {x^2}{y^8}} \over {{x^2} + {y^2}}}\,\,$$ $${\left. {{{{x^8}{y^2} + {x^2}{y^8}} \over {{x^2} + {y^2}}}\,\,} \right|_{\,\left( {x,y} \right) = ...”
January 2, 2019
GMATGuruNY posted a reply to What is the units digit of the number z? in the Data Sufficiency forum
“The usage of number implies that we should consider NON-INTEGER values. Both statements are satisfied by z=18.1 and z=19.1 Since the units digit of z can be different values, the two statements combinecd are INSUFFICIENT. The correct answer is E.”
January 2, 2019
Brent@GMATPrepNow posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”
January 1, 2019
Brent@GMATPrepNow posted a reply to What is the value of the integer n? in the Data Sufficiency forum
“Target question: What is the value of the integer n? Statement 1: n is a prime factor of 21 21 = (3)(7) So, EITHER n = 3 OR n = 7 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: n is a factor of 49 49 has three positive factors: 1, ...”
January 1, 2019
Brent@GMATPrepNow posted a reply to If 2x+y=3 and 4x^2-4xy+y^2=1, what is the value of xy? in the Problem Solving forum
“This question becomes a lot easier if we recognize that (2x + y)² = 4x² + 4xy + y² (which is VERY similar to 4x² - 4xy + y²) Here''s what I mean: Take 2x + y = 3 and square both sides to get: (2x + y)² = 3² Simplify both sides to get: 4x² + 4xy + y²= 9 We now have two (quite ...”
January 1, 2019
GMATGuruNY posted a reply to Is √(x+1)^2=x+1 ? in the Data Sufficiency forum
“√(a²) = |a|. Question stem, rephrased: Is |x+1| = x+1? The answer will be YES if x+1 is NONNEGATIVE: x+1≥0 x≥-1. Question stem, rephrased again: Is x≥-1? Statement 1: x=0 or x=2. Since x≥-1 in both cases, the answer to the question stem is YES. SUFFICIENT. Statement 2: ...”
December 31, 2018
GMATGuruNY posted a reply to If f(x)=1-(1/x), then f(f(f(x)))=? in the Problem Solving forum
“Let x=2 and apply the function three times: f(2) = 1 - 1/2 = 1/2. f(1/2) = 1 - 1/(1/2) = -1. f(-1) = 1 - (1/-1) = 2. The correct answer must yield a value of 2 when x=2. Only A works. The correct answer is A.”
December 31, 2018
GMATGuruNY posted a reply to Singular or Plural Verb with None in the Sentence Correction forum
“Any BAG taken on the subway IS subject to search by the police. Any BAGS taken on the subway ARE subject to search by the police. In each of these sentences, any is a MODIFIER describing the subject in blue. In the first sentence, the verb (is) is SINGULAR to match the singular subject in blue. ...”
December 31, 2018
GMATGuruNY posted a reply to Brady, Charlie, and Daryl play on the same baseball team. Th in the Data Sufficiency forum
“Statement 1: No information about Charlie or Daryl. INSUFFICIENT. Statement 2: For every 2 home run hits made by Charlie and Daryl combined, Brady made 4 home run hits, implying that Brady made 4 of every 6 home run hits: 4/6 = 2/3. SUFFICIENT. The correct answer is B.”
December 31, 2018
Brent@GMATPrepNow posted a reply to Given four rods of length 1 meter, 3 meters, 5 meters, and 7 in the Problem Solving forum
“IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . . DIFFERENCE between A and B < length of third side < SUM of A and B Let''s focus on this part: length of third side < SUM of A and B We can also say that the length of LONGEST side must be less than the SUM of ...”
December 31, 2018
Brent@GMATPrepNow posted a reply to Brady, Charlie, and Daryl play on the same baseball team. Th in the Data Sufficiency forum
“ Given: Brady, Charlie, and Daryl play on the same baseball team. Target question: The number of home runs hit by Brady in a particular season is what fraction of the total home runs hit by the three players in that season? This is a good candidate for rephrasing the target question. Let ...”
December 31, 2018
Brent@GMATPrepNow posted a reply to What is the 1st term in sequence S ? (1) The 3rd term in S in the Data Sufficiency forum
“Target question: What is the 1st term in sequence S ? Statement 1: The 3rd term in S is 2 Since we''re not given any information about the NATURE of the sequence, there''s no way to answer the target question with certainty. So, statement 1 is NOT SUFFICIENT Statement 2: The 2nd term in ...”
December 31, 2018
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Here''s our video on Weighted Averages video: https://www.youtube.com/watch?v=B7J6lr_qBG4 Cheers, Brent”
December 31, 2018
GMATGuruNY posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill r in the Problem Solving forum
“Downhill speed - uphill speed = (x+10) - (x-8) = 18. Implication: The downhill speed is 18 mps greater than the uphill speed. We can PLUG IN THE ANSWERS, which represent the downhill speed. Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER ...”
December 31, 2018
fskilnik@GMATH posted a reply to Inequalities in the GMAT Math forum
“It´s not. Your mistake is the implication show in red. $$\left( {x;y} \right) = \left( {{1 \over 4};{1 \over 3}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x > {y^2}\,\,\,{\rm{true}} \hfill \cr \,x > y\,\,\,\,\,{\rm{false}} \hfill \cr} \right.\,\,$$ Regards, Fabio.”
December 30, 2018
fskilnik@GMATH posted a reply to Inequalities in the GMAT Math forum
“$$x\,\,\mathop > \limits^? \,\,y$$ $$\left( {1 + 2} \right)\,\,\,\,{x^2} < y < \sqrt x \,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x;y} \right) = \left( {{1 \over 4};{1 \over 3}} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to Marcia's bucket can hold a maximum of how many liters of wat in the Data Sufficiency forum
“Target question: Marcia''s bucket can hold a maximum of how many liters of water? In other words, what is the TOTAL CAPACITY of Marcia''s bucket? Statement 1: The bucket currently contains 9 liters of water. Not enough info to determine the TOTAL CAPACITY of Marcia''s bucket. Since we ...”
December 30, 2018
fskilnik@GMATH posted a reply to Marcia's bucket can hold a maximum of how many liters of wat in the Data Sufficiency forum
“$$? = C\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 30, 2018
fskilnik@GMATH posted a reply to If the original price of an item in a retail store is marked in the Data Sufficiency forum
“$$1\,\, \le m,d\,\, \le \,\,99\,\,\,\,\,{\rm{ints}}$$ $$P\,\,\,\, \to \,\,\,\,\left( {1 + {m \over {100}}} \right)P\,\,\,\, \to \,\,\,\,\left( {1 - {d \over {100}}} \right)\left( {1 + {m \over {100}}} \right)P\,\,\,\,\,\,\,\,\,\,\,\,\leftThis solution follows the notations and rationale taught in ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to In a stack of boards at a lumber yard, the 20th board counti in the Problem Solving forum
“Let''s start from the bottom and work our way up: We''ll start with the 16th board counting from the bottom of the stack Right BELOW that 16th board, we have a board that we''ll call Larry. So, Larry is the 15th board counting from the bottom of the stack. So, starting from the bottom and ...”
December 30, 2018
GMATGuruNY posted a reply to Two dogsled teams raced across a 300 mile course in Wyoming. in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent B''s speed. When the correct answer is plugged in, B''s time - A''s time = 3 hours. For each team: Time = distance/speed = 300/speed. B: B''s speed = 15 mph, implying that A''s speed = 15+5 = 20 mph In this case, B''s time - A''s time = 300/15 - ...”
December 30, 2018
GMATGuruNY posted a reply to In a stack of boards at a lumber yard, the 20th board counti in the Problem Solving forum
“1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 = 16 20 = 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 In the rendering above: The red values represent the number of boards when counting from the TOP. The blue values represent the number of boards when counting from the ...”
December 30, 2018
GMATGuruNY posted a reply to If the original price of an item in a retail store is marked in the Data Sufficiency forum
“Let the original price = 100. Then the markup = (m/100)*100 = m. The resulting price = 100+m. The subsequent discount = d/100*(100+m) = d + md/100 Thus, the total percent change = percent increase - percent decrease = m - d - md/100. For the final price to be greater than the original price, ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to Overlapping Sets in the Data Sufficiency forum
“I thought I''d point out that Manasa3190''s approach is known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of people, and the two characteristics are: ...”
December 30, 2018
fskilnik@GMATH posted a reply to If a certain positive integer is divided by 9, the remainder in the Data Sufficiency forum
“$$N \ge 1\,\,{\mathop{\rm int}} \,\,\,\left( * \right)$$ $$N = 9M + 3\,\,,\,\,\,M\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} $$ $$N = 5K + R\,\,,\,\,\,K\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} $$ $$0 \le R\,\,\,{\mathop{\rm int}} \le 4$$ $$? = R$$ ...”
December 30, 2018
fskilnik@GMATH posted a reply to Is x + y > 0 ? (1) x - y > 0 (2) x^2 - y^2 > 0 in the Data Sufficiency forum
“$$x + y\,\,\mathop > \limits^? \,\,0$$ $$\left( 1 \right)\,\,x > y\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0, - 1} ...”
December 30, 2018
Brent@GMATPrepNow posted a reply to Car X left Town T (RATE PROBLEM, Need Help) in the Problem Solving forum
“IMPORTANT: Let''s use HOURS throughout our solution, and then convert hours to minutes at the end. When car Y had traveled for z HOURS, car Y had traveled 23 miles more that car X had from the time that car X left Town T. z = car Y''s travel time in HOURS So, z + 3/10 = car X''s travel time in ...”
December 28, 2018
GMATGuruNY posted a reply to Mark has fewer than 9 coins. Each coin is either a quarter in the Data Sufficiency forum
“Statement 1: To MINIMIZE the number of coins so that a sum of 170 cents is yielded by at most 8 coins, we must MAXIMIZE the number of quarters. Since 7*25 = 175 cents, the number of quarters must be less than 7. 170 cents will be yielded by 6 quarters (totaling 150 cents) and 2 dimes (totaling 20 ...”
December 28, 2018
fskilnik@GMATH posted a reply to If x^2+y^2=2xy, then (x+y)/(2x-y)=? in the Problem Solving forum
“$$? = {{x + y} \over {2x - y}}$$ $${x^2} + {y^2} = 2xy\,\,\,\left( * \right)$$ Important: x=0 (or y=0) implies (by (*)) that both x and y are equal to zero, what is impossible (because 2x-y is implicitly different from zero). Conclusion: we may (and will) admit that x and y are nonzero. ...”
December 27, 2018
GMATGuruNY posted a reply to Pumping alone at their respective constant rates, one inlet in the Problem Solving forum
“Let the tank = 36 gallons. Since the first pipe takes 3 hours to fill 1/2 the tank -- and (1/2)(36) = 18 gallons -- the rate for the first pipe = w/t =18/3 = 6 gallons per hour. Since the second pipe takes 6 hours to fill 2/3 of the tank -- and (2/3)(36) = 24 gallons -- the rate for the second ...”
December 27, 2018
GMATGuruNY posted a reply to Solution A is 20% salt and Solution B is 80% salt. If you in the Problem Solving forum
“Since the desired salt percentage -- 50% -- is HALFWAY between the salt percentages for A and B (20% and 80%), the resulting solution must contain equal amounts of A and B. The correct answer is C.”
December 27, 2018
GMATGuruNY posted a reply to If the ratio of the price of 1 kilogram Camembert cheese to in the Data Sufficiency forum
“What is the value of T-C? Statement 1: T:B = 4:5. To combine T:B = 4:5 and C:B = 5:8, the element common to both ratios -- B -- must be represented by the SAME VALUE in each: T:B = 4:5 = 32:40. C:B = 5:8 = 25:40. Combining the two ratios, we get: C:T:B = 25:32:40. Case 1: T=32 and C=25, ...”
December 26, 2018
fskilnik@GMATH posted a reply to A bigger circle (with center A) and a smaller circle (with c in the Data Sufficiency forum
“\(1) Sufficient. Please follow the arguments below looking at the image attached. \(2) Insufficient. We present the GEOMETRIC BIFURCATION in the image attached. https://i.ibb.co/Zh47W85/26-Dec18-4z.gif This solution follows the notations and rationale taught in the GMATH method. ...”
December 26, 2018
GMATGuruNY posted a reply to In a village of 100 households, 75 least one DVD player, 80 in the Problem Solving forum
“Let D = DVD owners, C = cellphone owners, and M = MP3 owners. T = D + C + M - (DC + DM + CM) - 2(DCM). The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS. When we add together everyone in D, everyone in C, and everyone in M: Those in exactly 2 of the groups (DC + DM + ...”
December 26, 2018
GMATGuruNY posted a reply to A certain punch contains grape juice, orange juice, and in the Problem Solving forum
“The sum of the parts of the ratio = 2+3+7 = 12. Thus -- of every 12 ounces -- 2 ounces are grape juice, 3 ounces are orange juice, and 7 ounces are pineapple juice. Since grape juice constitutes 2 of every 12 ounces, the amount of grape juice is equal to 2/12 of the total: (2/12)(156) = 2*13 = ...”
December 26, 2018
fskilnik@GMATH posted a reply to If n is a positive integer, is in the Data Sufficiency forum
“Beautiful problem, Max. Congrats! $$n \geqslant 1\,\,\,\operatorname{int} $$ $$\sqrt {n + 1} \,\,\,\mathop = \limits^? \,\,{\text{even}}\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\boxed{\,\,n + 1\,\,\,\mathop = \limits^? \,\,\,{{\left( {{\text{even}}} ...”
December 26, 2018
fskilnik@GMATH posted a reply to If m and n are positive integers, is m + n an odd number? in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 26, 2018
fskilnik@GMATH posted a reply to The sum of 4 different odd integers is 64. What is the value in the Data Sufficiency forum
“$$\sum\nolimits_{4\,\,{\rm{different}}\,\,{\rm{odds}}} {\,\, = \,\,\,64\,\,\,\,\left( * \right)} $$ $$? = \,\,{\rm{max}}\,\,{\rm{among}}\,\,{\rm{them}}$$ $$\left( 1 \right)\,\,\,{\rm{consecutive}}\,\,{\rm{and}}\,\,{\rm{sum}}\,\,64\,\,\,\left( {{\rm{from}}\,\,\left( * \right)} ...”
December 26, 2018
GMATGuruNY posted a reply to If x is a factor of positive integer y, then which of the fo in the Problem Solving forum
“Strategy: Try to show that four of the answer choices do NOT have to be positive. Case 1: x=1 and y=1 In this case, A, B and D are not positive. Eliminate A, B and D. Case 2: x=1 and y=2 In this case, C is not positive. Eliminate C. The correct answer is E.”
December 26, 2018
fskilnik@GMATH posted a reply to If x is a factor of positive integer y, then which of the fo in the Problem Solving forum
“$$y \ge 1\,\,{\mathop{\rm int}} $$ $$x\,\,{\mathop{\rm int}} \,\,\,,\,\,\,{y \over x} = {\mathop{\rm int}} \,\,\,\left( * \right)$$ $$?\,\,\,:\,\,\,{\rm{positive}}\,\,\left( {{\rm{always}}} \right)$$ $$\left( {\rm{A}} \right)\,\,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,1} ...”
December 26, 2018
GMATGuruNY posted a reply to The sum of 4 different odd integers is 64. What is the value in the Data Sufficiency forum
“Statement 1: Since the numbers are EVENLY SPACED, median = sum/count: 64/4 = 16. Since the median = 16, the 4 odd integers must be as follows: 13, 15, 17, 19. Thus, the greatest of the 4 odd integers = 19. SUFFICENT. Statement 2: The 4 odd integers yielded by Statement 1 -- 13, 15, 17, 19 ...”
December 26, 2018
fskilnik@GMATH posted a reply to If a certain coin is flipped, it has probability 1/2 of land in the Problem Solving forum
“$$? = P\left( {{\text{at}}\,\,{\text{least}}\,\,{\text{1}}\,\,{\text{tail}}\,\,{\text{in}}\,\,{\text{4}}\,\,{\text{landings}}} \right)$$ $$?\,\,\, = \,\,\,1 - P\left( {{\text{only}}\,\,{\text{heads}}} \right)\,\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,1 - {\left( {\frac{1}{2}} \right)^4} ...”
December 26, 2018
fskilnik@GMATH posted a reply to A set of 15 different integers has median of 25 and a range in the Problem Solving forum
“WLOG (without loss of generality) we may assume that: $$a = {x_1} < {x_2} < \ldots < {x_7} < {x_8} = 25 < {x_9} < \ldots < {x_{14}} < {x_{15}} = a + 25\,\,\,\,\,{\text{ints}}$$ Considering this powerful structure, the problem is trivialized: $$?\,\, = \,\,\left( {a + ...”
December 25, 2018
GMATGuruNY posted a reply to If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? in the Problem Solving forum
“Every test-taker should know the following quadratic identities: (x+y)² = x² + y² + 2xy (x-y)² = x² + y² - 2xy (x+y)(x-y)² = x² - y² Substituting x²+y²=28 and xy=11 into (x+y)² = x² + y² + 2xy, we get: (x+y)² = 28 + 2*11 = 50. The correct answer is C. An alternate ...”
December 25, 2018
GMATGuruNY posted a reply to There are 10 books on a shelf: 5 English books, 3 Spanish bo in the Problem Solving forum
“P(2 different languages) = 1 - P(2 of the same language). Case 1: P(2 English books are selected) P(1st book is English) = 5/10. (Of the 10 books, 5 are English.) P(2nd book is English) = 4/9. (Of the 9 remaining books, 4 are English.) To combine these probabilities, we multiply: 5/10 * 4/9 = ...”
December 25, 2018
fskilnik@GMATH posted a reply to There are 10 books on a shelf: 5 English books, 3 Spanish bo in the Problem Solving forum
“$$10\,\,{\rm{books}}\,\,{\rm{in}}\,\,3\,\,{\rm{langs}}\,\,\,\left\{ \matrix{ 5\,\,{\rm{engl}} \hfill \cr {\rm{3}}\,\,{\rm{span}} \hfill \cr 2\,\,{\rm{port}} \hfill \cr} \right.$$ $$? = P\left( {{\rm{2}}\,{\rm{langs}}\,\,{\rm{in}}\,\,{\rm{2}}\,\,{\rm{extractions}}} \right)$$ ...”
December 25, 2018
fskilnik@GMATH posted a reply to If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? in the Problem Solving forum
“$$? = {\left( {x + y} \right)^2}$$ $$\left\{ \matrix{ {x^2} + {y^2} = 28 \hfill \cr 2xy = 2 \cdot 11 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,? = 28 + 2 \cdot 11 = 50$$ This solution follows the notations and rationale taught in the ...”
December 25, 2018
fskilnik@GMATH posted a reply to f(x) is the greatest prime factor of x. If n is a positive i in the Data Sufficiency forum
“$$1 \leqslant n\,\,\operatorname{int} \leqslant 9\,\,\,\,\,\left( * \right)$$ $$? = n\,$$ $$\left( 1 \right)\,\,\,{\text{max}}\,\,{\text{prime}}\,\,{\text{factor}}\,\,{\text{of}}\,\,n\,\,{\text{equals}}\,\,\,5\,\,\,\,\left( {{\text{ = ...”
December 24, 2018
fskilnik@GMATH posted a reply to If x and y are positive integers, what is the remainder when in the Data Sufficiency forum
“$$x,y\,\, \ge 1\,\,\,{\rm{ints}}$$ $${x^y} = 10M + R$$ $$M,R\,\,{\mathop{\rm int}} \,\,\,,\,\,\,0 \le R\,\, \le 9$$ $$? = R\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,?\,\,\,:\,\,\,{\text{units}}\,\,{\text{digit}}\,\,{\text{of}}\,\,{x^y}\,\,\,}\,$$ $$\left( 1 \right)\,\,{x^y} = ...”
December 24, 2018
GMATGuruNY posted a reply to If the farmer sells 75 of his chickens, his stock of feed wi in the Problem Solving forum
“Total amount of feed = (number of chickens)(number of days). The number of chickens is INVERSELY PROPORTIONAL to the number of days. If the number of chickens DOUBLES, then the feed will last for 1/2 the number of days. If the number of chickens TRIPLES, then the feed will last for 1/3 the ...”
December 24, 2018
fskilnik@GMATH posted a reply to If 0 < x < 2 and 0 < y < 2 on the xy-plane, what in the Problem Solving forum
“https://i.ibb.co/bgYXq46/24-Dec18-4v.gif $$? = {{{S_{\Delta OAB}}} \over {{S_{{\rm{square}}}}}}\,\,\,\,\,\,\,\left( {{\rm{geometric}}\,\,{\rm{probability}}} \right)$$ $$A = \left( {0,1} \right)\,\,,\,\,B = \left( {1,0} \right)$$ $$? = {{\,\,{{1 \cdot 1} \over 2}\,\,} \over {2 \cdot 2}} = {1 ...”
December 24, 2018
fskilnik@GMATH posted a reply to 120 tickets are to be evenly distributed to n people. If n in the Problem Solving forum
“The calculation shown in red is wrong and our focus need NOT be taken among the alternative choices only. Regards, Fabio.”
December 24, 2018
fskilnik@GMATH posted a reply to Number Properties in the Data Sufficiency forum
“$$z,f\,\,\mathop > \limits^? \,\,0\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 24, 2018
fskilnik@GMATH posted a reply to Set P consists of all the multiples of 4 from 12 to 52, incl in the Data Sufficiency forum
“$$P = \left\{ {12,16,20,24, \ldots ,52} \right\}\,\,\,\,\,\,\leftThe correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 24, 2018
fskilnik@GMATH posted a reply to If the farmer sells 75 of his chickens, his stock of feed wi in the Problem Solving forum
“$$\left( {\# {\rm{chicken}}} \right)\left( {\# days} \right) = {\rm{constant}}$$ $$? = x = \# {\rm{chicken}}$$ $$\left\{ \matrix{ \left( {x - 75} \right)\left( {d + 20} \right) = \left( {x + 100} \right)\left( {d - 15} \right)\,\,\,\,\left( {\rm{I}} \right) \hfill \cr \left( {x - 75} ...”
December 24, 2018
fskilnik@GMATH posted a reply to Three circles with radii of 2 cm, 3 cm and 5 cm, respective in the Problem Solving forum
“The correct answer is (B). https://preview.ibb.co/dhQD9f/19-Nov18-5z.gif Regards, Fabio.”
December 24, 2018
fskilnik@GMATH posted a reply to A plane traveled k miles in its first 96 minutes of flight in the Problem Solving forum
“Let´s use UNITS CONTROL, one of the most powerful tools of our method! $$? = {{\left( {k + 300} \right)\,\,{\rm{miles}}} \over {\left( {96 + t} \right)\,\,\min }}\,\,\,\left( {{{60\,\,\min } \over {1\,\,{\rm{h}}}}} \right)\,\,\,\,\, = \,\,\,\,\,{{60\left( {k + 300} \right)} \over {96 + ...”
December 24, 2018
fskilnik@GMATH posted a reply to On the most recent test in stats class, Jamal scored x point in the Problem Solving forum
“$$? = x$$ $$\left\{ \matrix{ 2 \cdot 89 = J + C = x + C \hfill \cr 2 \cdot 79 = R + C = 73 + C \hfill \cr} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,2 \cdot \left( {89 - 79} \right) = x - 73$$ $$? = 73 + 20 = 93\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( ...”
December 24, 2018
Brent@GMATPrepNow posted a reply to A shipping company has four empty trucks that will head out in the Problem Solving forum
“Take the task of shipping the 4 boxes and break it into stages. Let''s call the 4 boxes A, B, C and D Stage 1: Select a truck to ship box A in There are 4 trucks from which to choose, so we can complete stage 1 in 4 ways Stage 2: Select a truck to ship box B in There are 4 trucks ...”
December 24, 2018
Brent@GMATPrepNow posted a reply to resolution in the Data Sufficiency forum
“ Given: A quorum of at least half the 20 directors must pass the resolution by at least a two-thirds majority Target question: At a meeting of the board of directors, did resolution X pass or fail?  Statement 1: Ten directors voted for the resolution.  KEY: We don''t know how many ...”
December 23, 2018
Brent@GMATPrepNow posted a reply to a data from gmat forum in the Data Sufficiency forum
“ Given: Every student at the Performing Arts Academy must take at least one of the two drama courses offered, Classical Theater or Improvisation. 15% of the students who take Classical Theater also take Improvisation Let''s use the Every student at the Performing Arts Academy must take at least ...”
December 23, 2018
Brent@GMATPrepNow posted a reply to Tough Rate problem in the Data Sufficiency forum
“ Given: At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. Target question: If seventy people are standing in line, will all of their presents be wrapped after one hour? Statement 1: Each person in ...”
December 23, 2018
GMATGuruNY posted a reply to While driving on a highway, Harry and Ron crossed checkpoint in the Problem Solving forum
“9am-10am: Since Harry reaches checkpoint P at 9am -- and travels at rate of 30 mph -- from 9am to 10am Harry travels 30 miles beyond checkpoint P. Thus, when Ron reaches checkpoint P at 10am, he is 30 miles behind Harry. Checkpoint Q: When people compete, SUBTRACT THEIR RATES. Every hour Ron ...”
December 23, 2018
fskilnik@GMATH posted a reply to Is the range of the integers 6, 3, y, 4, 5, and x greater in the Data Sufficiency forum
“$$A = \left\{ {3,4,5,6} \right\} \cup \left\{ {x,y} \right\}\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 23, 2018
fskilnik@GMATH posted a reply to If mn ≠ 0, is m > n? in the Data Sufficiency forum
“$$m,n\,\, \ne 0$$ $$m\mathop > \limits^? n$$ $$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,\left( {m,n} \right) = \left( { - ...”
December 23, 2018
fskilnik@GMATH posted a reply to What is the smallest integer n such that 2^8 is a factor of in the Problem Solving forum
“$$?\,\,\,:\,\,\,n \ge 0\,\,{\rm{int}}\,\,\,{\rm{min}}\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,{{n!} \over {{2^8}}} = {\mathop{\rm int}} $$ $${{n!} \over {{2^8}}} = {\mathop{\rm int}} \,\,\,\,\, \Leftrightarrow \,\,\,\,n!\,\,{\rm{has}}\,\,\left( {{\rm{at}}\,\,{\rm{least}}} ...”
December 23, 2018
Brent@GMATPrepNow posted a reply to Two trees have a combined height of 60 feet, and the taller in the Problem Solving forum
“Let y = the height of the shorter tree The taller tree is x times the height of the shorter tree. Ho So, yx = the height of the taller tree The two trees have a combined height of 60 feet We can write: y + yx = 60 How tall is the shorter tree, in terms of x? We must solve the equation ...”
December 22, 2018
Brent@GMATPrepNow posted a reply to Two water pumps, working simultaneously at their respective in the Problem Solving forum
“Let''s pick some nice numbers that adhere to the given information. ...the constant rate of one pump was 1.5 times the constant rate of the other So, the fast pump has a pumping rate that''s 1.5 faster then the slow pump. So, let''s say the SLOW pump pumps at 2 gallons per hour This means ...”
December 22, 2018
fskilnik@GMATH posted a reply to In how many ways can the letters D, I, G, I, T be arranged in the Problem Solving forum
“$$?\,\,\,:\,\,\,{\rm{\# }}\,\,\,{\rm{permutations}}\,\,{\rm{Is}}\,\,{\rm{apart}}$$ $${\rm{all}}\,\,{\rm{permutations}}\,\,{\rm{with}}\,\,{\rm{repetition}} = {{5!} \over {2!}} = 5 \cdot 4 \cdot 3 = 60$$ $${\rm{all}}\,\,{\rm{permutations}}\,\,{\rm{with}}\,\,{\rm{Is}}\,\,{\rm{together}} = 4! = 24$$ ...”
December 22, 2018
Brent@GMATPrepNow posted a reply to Fractions/Ratios in the Data Sufficiency forum
“ Given: There are two types of rolls on a counter, plain rolls and seeded rolls. Let P = # of plain rolls Let S = # of seeded rolls Target question: What is the value of P + S? Statement 1: The ratio of the number of seeded rolls on the counter to the number of plain rolls on the ...”
December 21, 2018
Brent@GMATPrepNow posted a reply to Five friends - Ross, Phoebe, Chandler, Joey and Monica - in the Problem Solving forum
“Take the task of feeding the 5 friends and break it into stages. We’ll begin with the most restrictive stage(s). Stage 1: Select a pizza for Phoebe Since Phoebe will only eat Margherita pizza, there''s only 1 pizza we can serve her. So, we can complete stage 1 in 1 way Stage 2: ...”
December 21, 2018
GMATGuruNY posted a reply to Work/Rate in the Data Sufficiency forum
“Let J = the number of hours that John works. Since John assembles 3 chairs per hour, the number of chairs assembled by John = 3J. Let L = the number of hours that Larry works. Since Larry assembles 4 chairs per hour, the number of chairs assembled by Larry = 4L. Since John and Larry work a total ...”
December 21, 2018
GMATGuruNY posted a reply to Five friends - Ross, Phoebe, Chandler, Joey and Monica - in the Problem Solving forum
“Number of options for Phoebe = 1. (Must be Margherita.) Number of options for Ross = 3. (Of the 4 remaining pizzas, any but Hawaiian.) Number of options for Chandler = 3. (Any of the 3 remaining pizzas.) Number of options for Joey = 2. (Either of the 2 remaining pizzas.) Number of options for ...”
December 21, 2018
Brent@GMATPrepNow posted a reply to A list kept at Town Hall contains that town's average daily in the Data Sufficiency forum
“Target question: Does this month have 30 or 31 days? IMPORTANT: Notice that the question does not ask "How many days are in this month?" If that were the case, then we''d have to consider February. Instead, the question is ruling out February by basically telling us that the month in ...”
December 20, 2018
fskilnik@GMATH posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum
“$$S\,\,:\,\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right)$$ $$? = {a_{105}}$$ $$\left( 1 \right)\,\,{a_1} = - 8\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {{a_1},{a_2}, \ldots ,{a_{120}}} \right) = \left( { - 8, - 8, \ldots , - 8} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,?\, = ...”
December 20, 2018
fskilnik@GMATH posted a reply to If the remainder when positive integer x is divided by 7 is in the Data Sufficiency forum
“$$x \ge 1\,\,{\mathop{\rm int}} \,\,\,\left( * \right)$$ $$x = 7M + 4\,\,\,,\,\,M\mathop \ge \limits^{\left( * \right)} 0\,\,\,{\mathop{\rm int}} $$ $$? = x$$ $$\left( 1 \right)\,\,x < 50\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 4\,\,\,\,\, \hfill \cr \,{\rm{Take}}\,\,x = 4 + 7 = ...”
December 20, 2018
fskilnik@GMATH posted a reply to A geometric sequence is one in which the ratio of any term in the Problem Solving forum
“Important: the fact that a,b,c,d is a given GP in that order guarantees, implicitly, that a,b, c and d are not zero. Think about that! $$\left( {\rm{I}} \right)\,\,\,\,{{ck} \over {dk}} = {{bk} \over {ck}} = {{ak} \over {bk}}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{c \over d} = {b \over c} = {a ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to In how many ways can the letters D, I, G, I, T be arranged in the Problem Solving forum
“One approach is to count all possible arrangements (that may or may not break the given rule) and then subtract all outcomes the break the rule. Here''s another approach. Take the task of arranging the 5 letters and break it into stages. Stage 1: Arrange the 3 CONSONANTS (D, G and T) in a ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to Inequalities in the GMAT Math forum
“Target question: Is x² > y²? Statement 2: x > y There are several values of x and y that satisfy statement 2. Here are two: Case a: x = 2 and y = 1. In this case, x² = 4 and y² = 1. So, the answer to the target question is YES, x² IS greater than y² Case b: x = -2 and y = -3. ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum
“Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to Two dice, each with six sides numbered 1 through 6, are toss in the Problem Solving forum
“P(both dice will come up with either a 1 or a 2) = P(1st die is 1 or 2 AND 2nd die is 1 or 2) = P(1st die is 1 or 2) x P(2nd die is 1 or 2) = 2/6 x 2/6 = 1/3 x 1/3 = 1/9 Answer: C Cheers, Brent”
December 20, 2018
Brent@GMATPrepNow posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom apart in the Problem Solving forum
“A fast and easy approach is to assign a "nice" value to the monthly rent of a ONE-bedroom apartment. Let''s say the rent on a ONE-bedroom apartment is $100 per month A two-bedroom apartment costs 50% more to rent than a one-bedroom apartment 50% of $100 = $50 So, the rent on a ...”
December 20, 2018
fskilnik@GMATH posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom apart in the Problem Solving forum
“$$? = x$$ Trivial application of UNITS CONTROL, one of the most powerful tools of our method: $$\left. \matrix{ {\rm{one - bed}}\,\,\,:\,\,\,\,{{\$ \,\,2d} \over {1\,\,{\rm{month}}\,}}\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,12\,\,{\rm{months}}\,\,\,\left( {{{\$ \,\,2d} \over ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to If the remainder when positive integer x is divided by 7 is in the Data Sufficiency forum
“Target question: What is the value of x? Given: If the remainder when positive integer x is divided by 7 is 4 When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For ...”
December 20, 2018
GMATGuruNY posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom apart in the Problem Solving forum
“Let the monthly rent for a one-bedroom apartment = $2, implying that the monthly rent for a two-bedroom apartment = 2 + (50% of 2) = 2 + 1 = $3. Since the monthly rent for a one-bedroom apartment = $2, the total amount required to rent a one-bedroom apartment for 12 months = 2*12 = 24. If Alex ...”
December 20, 2018
fskilnik@GMATH posted a reply to (0.0004)(0.000005)/200,000 is equal to which of the followin in the Problem Solving forum
“Hi, Max! You certainly mean: = (10^-9)/(10^5) = 10^-14 Regards, Fabio.”
December 20, 2018
fskilnik@GMATH posted a reply to Is |m-n|=|m|-|n| ? in the Data Sufficiency forum
“$$\left| {m - n} \right|\,\,\mathop = \limits^? \,\,\left| m \right| - \left| n \right|$$ $$\left( 1 \right)\,\,m - n = 0\,\,\,\, \Rightarrow \,\,\,\,\left| {m - n} \right| = \left| 0 \right| = 0\,\,\,\mathop = \limits^{m = n} \,\,\,\left| m \right| - \left| m \right|\,\,\,\, \Rightarrow ...”
December 20, 2018
fskilnik@GMATH posted a reply to 120 tickets are to be evenly distributed to n people. If n in the Problem Solving forum
“$${\rm{Each}}\,\,{\rm{person}}:\,\,{{120} \over n}\,\,\left( {{\mathop{\rm int}} } \right)\,\,\,{\rm{tickets}}$$ $$2 \le n \le 119\,\,{\mathop{\rm int}} $$ $$? = {n_{\max }}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{\rm{max}}\,\,{\rm{divisor}}\,\,{\rm{of}}\,\,120\,\,{\rm{less}}\,\,{\rm{that}}\,\,120$$ ...”
December 20, 2018
fskilnik@GMATH posted a reply to Two dice, each with six sides numbered 1 through 6, are toss in the Problem Solving forum
“$$?\,\,:\,\,{\rm{prob}}\,\,{\rm{just}}\,\,1,2$$ $$\left( {{1^{{\rm{st}}}},\,\,{2^{{\rm{nd}}}}} \right)\,\,\,\,\left\{ \matrix{ \,{\rm{total}}\,\,\,:\,\,6 \cdot 6\,\,{\rm{equiprobable}}\,\, \hfill \cr \,{\rm{favor}}\,\,:\,\,4\,\,\leftThis solution follows the notations and rationale taught in ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to The value of a share was 25% less in the 2nd quarter over in the Problem Solving forum
“Let''s assign a nice value to the share value in the 1st quarter. Let''s say the share value in the 1st quarter = $100 The value of a share was 25% less in the 2nd quarter over the 1st quarter . . . So, the share value in the 2nd quarter = $100 - (25% of $100) = $100 - $25 = $75 . . . ...”
December 20, 2018
Brent@GMATPrepNow posted a reply to The usual price of a bagel was reduced during a sale. How in the Data Sufficiency forum
“Target question: How much money could be saved by purchasing 10 bagels at the sale price rather than at the usual price? Statement 1: The usual price for a bagel is $0.50 per bagel. Since there''s no information about the SALE price, there''s no way to calculate the amount saved. Since we ...”
December 20, 2018
GMATGuruNY posted a reply to absolute value in the Problem Solving forum
“The CRITICAL POINTS are where the expressions inside the absolute values are equal to 0. x+5 = 0 when x=-5. Substituting x=-5 into y = |x+5|-|x-5|, we get: y = |-5+5| - |-5-5| = 0-10 = -10. x-5 = 0 when x=5. Substituting x=5 into y = |x+5|-|x-5|, we get: y = |5+5| - |5-5| = 10-0 = ...”
December 19, 2018
GMATGuruNY posted a reply to One woman and one man can build a wall together in two hours in the Problem Solving forum
“One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. Since replacing 1 man with 2 girls does not change the amount of time required to complete the job, 1 man is the equivalent of 2 ...”
December 19, 2018
fskilnik@GMATH posted a reply to One woman and one man can build a wall together in two hours in the Problem Solving forum
“https://i.ibb.co/XpsQyWd/19-Dec18-6j.gif This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 19, 2018
Brent@GMATPrepNow posted a reply to One woman and one man can build a wall together in two hours in the Problem Solving forum
“One approach is to determine the size of the job One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. The part in blue tells us that 2 girls have the same output as 1 man. ...”
December 19, 2018
fskilnik@GMATH posted a reply to absolute value in the Problem Solving forum
“Alternate way: https://i.ibb.co/HpZcMqb/19-Dec18-5b.gif There are 21 integers between -10 and 10, both of them included (see blue interval). It´s done! This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
December 19, 2018
fskilnik@GMATH posted a reply to absolute value in the Problem Solving forum
“$$?\,\,\,:\,\,\,\# \,\,\,{\rm{integer}}\,\,{\rm{values}}\,\,{\rm{for}}\,\,\,y = \left| {x + 5} \right| - \left| {x - 5} \right|$$ $$\left( {\rm{i}} \right)\,\,\,x \le - 5\,\,\,\,\, \Rightarrow \,\,\,\,\,y = - \left( {x + 5} \right) - \left( {5 - x} \right) = - 10\,\,\,\,\,\, \Rightarrow ...”
December 19, 2018
fskilnik@GMATH posted a reply to At garage sale, all of the prices of the items sold were in the Problem Solving forum
“A simple drawing does the trick! https://i.ibb.co/Xb0N80B/19-Dec18-4b.gif \This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
December 19, 2018
Brent@GMATPrepNow posted a reply to Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 in the Data Sufficiency forum
“When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Target question: Is x > 0 ? Statement 1: |x+3| < ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to In the xy-plane, what is the y-intercept of line l? in the Data Sufficiency forum
“Target question: What is the y-intercept of line L? IMPORTANT: When I scan the two statements, I see that they are strongly related. If the x-intercept is -1/3 (as per statement 2), the slope of the line is GUARANTEED to be 3 times its y-intercept (as per statement 1). Here''s why... ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to At garage sale, all of the prices of the items sold were in the Problem Solving forum
“The price of the radio was the 15th highest price So, there were 14 items that were more expensive than the radio. In other words, if we listed all of the prices in ascending order, we''d get something like: ........... radio, X, X, X, X, X, X, X, X, X, X, X, X, X, X The price of the radio ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to A certain company charges $6 per package to ship packages in the Problem Solving forum
“Let x = the weight of the package (in pounds) So, the shipping cost = $6 + 2x We''re told the shipping cost is $38. So, we can write: 6 + 2x = 38 Subtract 6 from both sides: 2x = 32 Solve: x = 32/2 = 16 Answer: A Cheers, Brent”
December 19, 2018
Brent@GMATPrepNow posted a reply to Is x/y>1? in the Data Sufficiency forum
“Target question: Is x/y > 1? Statement 1: x > y Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is YES, x/y IS greater than 1 Case b: x = ...”
December 19, 2018
Brent@GMATPrepNow posted a reply to How many 4-digit numbers greater than 3,000 have the digits: in the Problem Solving forum
“Take the task of creating 4-digit numbers and break it into stages. We’ll begin with the most restrictive stage. Stage 1: Select the first digit (to go in the thousands place) Since the 4-digit number must be GREATER THAN 3000, the first digit must be greater than or equal to 3 This means ...”
December 19, 2018
fskilnik@GMATH posted a reply to At a certain university, the ratio of the number of teaching in the Problem Solving forum
“$$t\,\,({\rm{ta}})\,\,,\,\,s\,\,\left( {{\rm{student}}} \right)\,\,\,\, \ge \,\,1\,\,\,{\rm{ints}}\,\,\,\,\,\,\left( * \right)$$ $${t \over s} > {3 \over {80}}\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,{s_{\,\max }}\,\,\,{\rm{when}}\left( {{\rm{for}}} \right)\,\,\,t = 5$$ $$\frac{5}{s} > ...”
December 19, 2018
GMATGuruNY posted a reply to At garage sale, all of the prices of the items sold were in the Problem Solving forum
“Since the radio = 15th highest price, 14 prices are HIGHER: RADIO-----14 higher prices-----> Since the radio = the 20th lowest price, 19 prices are LOWER: <-----19 lower prices-----RADIO-----14 higher prices----> Total number of items = 19 + RADIO + 14 = 34. The correct answer is ...”
December 19, 2018
fskilnik@GMATH posted a reply to A one-million dollar inheritance was divided among five in the Data Sufficiency forum
“$$A \leqslant B \leqslant C \leqslant D \leqslant E\,\,\,\,\,\,\left( \$ \right)$$ $$A + B + C + D + E = {10^6}$$ $$A,B,C,D,E\,\,\,\, \leqslant \,\,\,30\% \left( {{{10}^6}} \right)$$ $$? = E$$ $$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {A;B;C;D;E} \right) = ...”
December 18, 2018
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Shortcut for quickly dividing by 5 in your head Video: https://www.youtube.com/watch?v=fK29jTSJOi8 Cheers, Brent”
December 18, 2018
fskilnik@GMATH posted a reply to Automobile A is traveling at two-thirds the speed that in the Data Sufficiency forum
“Excellent opportunity for the k technique, one of our powerful tools when dealing with ratios! $$A = {2 \over 3}B\,\,\,\,\,\mathop \Rightarrow \limits^{B\,\, \ne \,\,0} \,\,\,\,\,{A \over B} = {2 \over 3}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,A = 2k \hfill \cr \,B = 3k \hfill ...”
December 18, 2018
fskilnik@GMATH posted a reply to A restaurant serves only tacos and enchiladas. If 60% of all in the Data Sufficiency forum
“$$? = x\,\,\,\,\left( {{\rm{see}}\,\,{\rm{figure}}} \right)$$ https://i.ibb.co/wgnGqhv/18-Dec18-4x.gif $$\left( 1 \right)\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 18, 2018
fskilnik@GMATH posted a reply to x and y are positive integers. Is y an even integer? in the Data Sufficiency forum
“$$x,y\,\, \ge 1\,\,{\rm{ints}}$$ $$y\,\,\mathop = \limits^? \,\,{\rm{even}}$$ $$\left( 1 \right)\,\,y = \underbrace {x\left( {x + 1} \right)}_{{\rm{even}}\,\,\,\left( {x\,\,{\mathop{\rm int}} } \right)} - 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\,\,\,$$ ...”
December 18, 2018
fskilnik@GMATH posted a reply to Is x > 0 ? (1) |x+3| < 4 (2) |x-3| < 4 in the Data Sufficiency forum
“$$x\,\mathop > \limits^? \,\,0$$ $$\,\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,x = 0.5\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, ...”
December 18, 2018
Brent@GMATPrepNow posted a reply to At a certain university, the ratio of the number of teaching in the Problem Solving forum
“We can solve this using equivalent ratios We''re comparing teaching assistants/number of students Let x = number of students possible We can write: 5/x = 3/80 Cross multiply to get: 3x = (5)(80) Simplify: 3x = 400 Solve: x = 400/3 = 133 1/3 = 133.3333 Since 134 students would exceed ...”
December 18, 2018
Brent@GMATPrepNow posted a reply to Automobile A is traveling at two-thirds the speed that in the Data Sufficiency forum
“ Given: Automobile A is traveling at two-thirds the speed that Automobile B is traveling. Let A = Car A''s speed Let B = Car B''s speed So, we can write: A = (2/3)B Target question: What is the value of A? Statement 1: If both automobiles increased their speed by 10 miles per hour, ...”
December 18, 2018
GMATGuruNY posted a reply to x and y are positive integers. Is y an even integer? in the Data Sufficiency forum
“The product of two consecutive integers is always EVEN: 1*2 = 2 2*3 = 6 3*4 = 12 Statement 1: y+2 = x² + x y+2 = x(x+1) y+2 = product of 2 consecutive integers y+2 = EVEN y = EVEN - 2 y = EVEN - EVEN y = EVEN SUFFICIENT. Statement 2: No information about y. INSUFFICIENT. The ...”
December 18, 2018
GMATGuruNY posted a reply to (0.0004)(0.000005)/200,000 is equal to which of the followin in the Problem Solving forum
“I believe that the answer choices should appear as shown below: The blue values below cancel out, leaving only the red values: (4 * 10¯⁴)(5 * 10¯⁶) / (20 * 10⁴) = 10¯¹⁰/10⁴ = 10¯¹⁴. The correct answer is B.”
December 18, 2018
fskilnik@GMATH posted a reply to (0.0004)(0.000005)/200,000 is equal to which of the followin in the Problem Solving forum
“$$? = {{4 \cdot {{10}^{ - 4}} \cdot 5 \cdot {{10}^{ - 6}}} \over {2 \cdot {{10}^5}}} = 10 \cdot {10^{ - 15}} = {10^{ - 14}}$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
December 18, 2018
GMATGuruNY posted a reply to Sanjana jogged uphill for a while at an average speed of 3 m in the Problem Solving forum
“This is a MIXTURE problem. Two speeds (3 mph and 8 mph) are combined to form a mixture with an average speed of 4 mph. To determine how much time must be spent at each speed, we can use ALLIGATION. Let U = the uphill speed and D = the downhill speed. Step 1: Plot the 3 speeds on a number ...”
December 18, 2018
fskilnik@GMATH posted a reply to Pam and Robin each roll a pair of fair, six-sided dice. What in the Problem Solving forum
“Very nice problem! $$? = {{\# \,\,{\rm{favorables}}} \over {\# \,\,{\rm{total}}\,\,\left( {{\rm{equiprobables}}} \right)}}$$ $$\# \,\,{\rm{total}}\,\,\left( {{\rm{equiprobables}}} \right) = {6^2} \cdot {6^2}\,\,\,\,\left( ...”
December 17, 2018
fskilnik@GMATH posted a reply to If every boy in a kindergarten class buys a soda and every g in the Problem Solving forum
“$$\left. \matrix{ g\,\,\, = \,\,\# \,\,{\rm{of}}\,\,{\rm{girls}} \hfill \cr b\,\,\, = \,\,\# \,\,{\rm{of}}\,\,{\rm{boys}}\,\,{\rm{ = }}\,\,\,g + k\,\, \hfill \cr} \right\}\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,\,k\,\,\,\,,\,\,\,k \ge 1\,\,\,{\mathop{\rm int}} \,\,\,\,\,\left( {b > g} ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to If every boy in a kindergarten class buys a soda and every g in the Problem Solving forum
“Let B = # of boys in kindergarten Let G = # of girls in kindergarten Let J = price (in CENTS) of ONE juice box Let S = price (in CENTS) of ONE soda If every boy in a kindergarten class buys a soda and every girl in the same class buys a juice box, the class will spend 1¢ less in total than it ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to Sanjana jogged uphill for a while at an average speed of 3 m in the Problem Solving forum
“You could also try testing the answer choices. Cheers, Brent”
December 17, 2018
Brent@GMATPrepNow posted a reply to If 3x + 12 = 21, then x + 4 = A. 3 B. 4 C. 5 D. 7 E. 9 in the Problem Solving forum
“One option is to first solve the equation, 3x + 12 = 21, for x, and then determine the value of x+4. Alternatively, we can factor the left side to get: 3(x + 4) = 21 Now divide both sides by 3 to get: x + 4 = 7 Answer: D Cheers, Brent”
December 17, 2018
Brent@GMATPrepNow posted a reply to If a, b & c are integers, is abc odd? in the Data Sufficiency forum
“Some important rules: #1. (ODD)(ODD) = ODD #2. (ODD)(EVEN) = EVEN #3. (EVEN)(EVEN) = EVEN Given: a, b & c are integers Target question: Is abc odd? Statement 1: ab is odd This tells us that a and b are both odd. However, we have no information about c. Consider these two ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to In the coordinate plane, the y-intercept of the line k is eq in the Problem Solving forum
“One approach is to choose some values that meet the given information. In the coordinate plane, the y-intercept of the line k is equal to twice its slope. Okay, so let''s say the y-intercept of line k is 6. We get: https://i.imgur.com/qJ5GeRQ.png Since the y-intercept (6) is TWICE the ...”
December 17, 2018
fskilnik@GMATH posted a reply to [x] is the greatest integer less than or equal to x. <x&a in the Data Sufficiency forum
“$$? = x$$ $$\left( 1 \right)\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 17, 2018
GMATGuruNY posted a reply to If 2 and 17 are factors of positive integer n, then which of in the Problem Solving forum
“2 and 17 have no factors in common. Since n must be divisible by both 2 and 17 -- and 2*17 = 34 -- n must be a MULTIPLE OF 34. Thus, n must be divisible by I. Eliminate any answer choice that does not include I. Eliminate B and E. If n=34, then n is not divisible by II or III. Eliminate any ...”
December 17, 2018
fskilnik@GMATH posted a reply to After multiplying a positive integer A, which has n digits, in the Problem Solving forum
“$$\left. \matrix{ A = \,\,\underbrace {\underline {} \,\,\underline {} \,\,\underline {} \,\, \ldots \,\,\underline {} }_{n\,\,{\rm{digits}}}\,\,\,\, \ge 1\,\,{\mathop{\rm int}} \hfill \cr A \cdot \left( {n + 2} \right) = \underbrace {\underline {n + 1} \,\,\underline {n + 1} \,\,\underline ...”
December 17, 2018
GMATGuruNY posted a reply to Seven students are trying out for the school soccer team, on in the Problem Solving forum
“To keep track of the number of options for each position, draw a TREE. Start with the MOST RESTRICTED position, which is SWEEPER. If Sweeper = 3, then Goalie = 5. If Sweeper = 4, then Fullback = 2. Here''s the tree so far: http://s11.postimage.org/laxnlsbof/soccer_half_tree.jpg Now complete ...”
December 17, 2018
fskilnik@GMATH posted a reply to Seven students are trying out for the school soccer team, on in the Problem Solving forum
“$$\left. \matrix{ {\rm{Full}}\,\,\,{\rm{:}}\,\,\,\,{\rm{2}}\,\,{\rm{students}}\,\,\left( {A,B} \right) \hfill \cr {\rm{Swee}}\,\,\,{\rm{:}}\,\,\,{\rm{2}}\,\,{\rm{students}}\,\,\left( {C,D} \right) \hfill \cr {\rm{Goal}}\,\,\,{\rm{:}}\,\,\,{\rm{3}}\,\,{\rm{students}}\,\,\left( {E,F,G} ...”
December 17, 2018
fskilnik@GMATH posted a reply to If 2 and 17 are factors of positive integer n, then which of in the Problem Solving forum
“$$n \ge 1\,\,{\mathop{\rm int}} $$ $$\left\{ \matrix{ {n \over 2} = {\mathop{\rm int}} \hfill \cr {n \over {17}} = {\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,$$ $$?\,\,\,:\,\,\,{n \over {\,{\rm{I}}\,{\rm{,}}\,{\rm{II}}\,{\rm{,}}\,{\rm{III}}\,}}\,\,\,\mathop = \limits^? ...”
December 17, 2018
fskilnik@GMATH posted a reply to In the coordinate plane, the y-intercept of the line k is eq in the Problem Solving forum
“$$k\,\,\,:\,\,\,y = ax + 2a\,\,\,\,\,\,\left( {a \ne 0} \right)\,\,\,\,\,\,\left( * \right)$$ $$?\,\,\,\,:\,\,\,{x_p}\,\,{\rm{when}}\,\,y = 0$$ $$\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,\,\,0 = a\left( {{x_p} + 2} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{a \ne 0} \,\,\,\,\,\,\,? = ...”
December 17, 2018
Brent@GMATPrepNow posted a reply to Sanjana jogged uphill for a while at an average speed of 3 m in the Problem Solving forum
“Let''s start with a "Word Equation" (distance traveled uphill) + (distance traveled downhill) = TOTAL DISTANCE Let t = the time spent jogging UPHILL (in hours) The total travel time = 40 minutes = 2/3 HOURS So, 2/3 - t = the time spent jogging DOWNHILL (in hours) Distance = ...”
December 16, 2018
Brent@GMATPrepNow posted a reply to If one manual weighs 400 grams, how many kilograms does a in the Problem Solving forum
“Since the answer choices are VERY SPREAD APART, we can be quite aggressive with our ESTIMATION. (400 grams)(50 manuals) = 20,000 grams = 20 KILOgrams So, the answer is approximately 20 Answer: C Cheers, Brent”
December 16, 2018
fskilnik@GMATH posted a reply to Three circles are drawn within triangle ABC such that no two in the Data Sufficiency forum
“Let´s go straight to (1+2) to PROVE the insufficiency through a GEOMETRIC BIFURCATION : https://i.ibb.co/QpNzhg7/16-Dec18-4z.gif This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 16, 2018
fskilnik@GMATH posted a reply to A mixture of oil, water, and vinegar contains 10% oil. After in the Data Sufficiency forum
“$${\text{Before: x}}\,\,{\text{liters}}\,\,\,\,\left\{ \begin{gathered} {\text{oil}}\,\,:0.1x\,\,{\text{liters}} \hfill \\ water\,\,:\,\,k\left( {0.9x} \right)\,\,{\text{liters}} \hfill \\ vinegar\,\,:\,\,\,\left( {1 - k} \right)\left( {0.9x} \right)\,\,{\text{liters}}\,\, \hfill \\ ...”
December 16, 2018
fskilnik@GMATH posted a reply to What is the value of integer x? in the Data Sufficiency forum
“$$? = x\,\,\left( {{\mathop{\rm int}} } \right)$$ $$\left( 1 \right)\,\,\,\,\left| {x - 1} \right| = \left| {x + 1} \right|\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,dist\left( {x,1} \right) = dist\left( {x, - 1} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = 0\,\,\,\,\,\,\, \Rightarrow ...”
December 16, 2018
GMATGuruNY posted a reply to In a network of car dealerships, a group of d sales director in the Data Sufficiency forum
“A group...EACH has a team. The wording above does not convey a logical meaning. When each serves as an adverb, it cannot refer to a singular noun such as a group. When each serves as an adverb, it may refer only to a PLURAL noun. The prompt seems intended to convey the following: Since ...”
December 16, 2018
fskilnik@GMATH posted a reply to At a certain supplier, a machine of type A costs $20,000 and in the Problem Solving forum
“Money values will be presented in thousands of dollars. $$\left\{ \matrix{ \,A\,\,\, \to \,\,\,\,{\rm{each}}\,\,::\,\,\$ 20\,\,\,,\,\,\,{\rm{\$ 4}}\,\,{\rm{down}}\,\,{\rm{and}}\,\,{\rm{\$ 16}}\,\,{\rm{at}}\,\,{\rm{40\% }} \hfill \cr \,B\,\,\, \to \,\,\,\,{\rm{each}}\,\,::\,\,\$ ...”
December 16, 2018
fskilnik@GMATH posted a reply to In an office of eleven people, everyone but Lauren each in the Problem Solving forum
“$$\left\{ \matrix{ \,{\rm{Lauren}} \hfill \cr \,{\rm{10}}\,\,{\rm{others}}\,\, \to \,\,\,{\rm{\$ }}d\,\,{\rm{each}} \hfill \cr} \right.\,\,\,\,\,\,\,;\,\,\,\,\,\,\$ g\,\,{\rm{gift}}$$ $$? = {{\,{\rm{total}}\,\,{\rm{refund}}\,\,\leftThis solution follows the notations and rationale taught in ...”
December 16, 2018
fskilnik@GMATH posted a reply to When the positive integer x is divided by 9, the remainder in the Problem Solving forum
“$$x \ge 1\,\,\,{\mathop{\rm int}} \,\,\,\left( * \right)$$ $$\left\{ \matrix{ 3x = 9J + R\,, \hfill \cr 0 \le R\,\,{\mathop{\rm int}} \,\le 8\,\,\,,\,\,J\,\,\mathop \ge \limits^{\left( * \right)} \,\,0\,\,\,{\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,? = R$$ ...”
December 16, 2018
GMATGuruNY posted a reply to If one manual weighs 400 grams, how many kilograms does a in the Problem Solving forum
“48 manuals * (400 grams)/(1 manual) * (1 kilogram)/(1000 grams) = (48*400)/1000 = 192/10 = 19.2 kilograms.”
December 16, 2018
GMATGuruNY posted a reply to When the positive integer x is divided by 9, the remainder in the Problem Solving forum
“Let x=5, since dividing 5 by 9 yields a remainder of 5: 5/9 = 0 R5. When 3x=15 is divided by 9, we get: 15/9 = 1 R6. The correct answer is E.”
December 16, 2018
GMATGuruNY posted a reply to The main ingredient in a certain prescription drug capsule in the Problem Solving forum
“Each capsule contains 600 milligrams of ingredient. 10⁶ milligrams = 1 kilogram. 1 kilogram of ingredient = 500 dollars. To determine the cost per capsule, we must use the relationships above to convert 600 milligrams into dollars: (600 milligrams) * (1 kilogram)/(10⁶ milligrams) * (500 ...”
December 15, 2018
GMATGuruNY posted a reply to Each Machine of type A has 3 steel parts and 2 chrome parts. in the Problem Solving forum
“(3 steel parts in each type A machine) + (4 steel parts in each type B machine) = 20 steel parts: 3A + 4B = 20 3A = a multiple of 3 less than 20. Options for 3A: 3, 6, 9, 12, 15, 18 4B = a multiple of 4 less than 20. Options for 4B: 4, 8, 12, 16 Only the two values in blue yield a sum ...”
December 15, 2018
Brent@GMATPrepNow posted a reply to Madge paid A dollars for R bananas. Dean paid B dollars for in the Data Sufficiency forum
“ Given: Madge paid A dollars for R bananas. Dean paid B dollars for S bananas. Target question: Which one of them paid a higher price-per-banana? Statement 1: B > A This tells us that Dean PAID more than Madge paid. However, we don''t know HOW MANY bananas each person bought. ...”
December 15, 2018
Brent@GMATPrepNow posted a reply to Jason's salary and Karen's salary were each p percent in the Data Sufficiency forum
“Target question: What is the value of p? Given: Jason''s salary and Karen''s salary were each p percent greater in 1998 than in 1995. IMPORTANT: If my 1998 salary is p percent greater than my 1995 salary, then: 1998 salary = (1 + p/100)(1995 salary) For example, if my 1998 salary is 7 percent ...”
December 15, 2018
Brent@GMATPrepNow posted a reply to If w + 2x = 150, 2w + 3y = 100, and x + 3z = 50, what is the in the Problem Solving forum
“GIVEN: w + 2x = 150 2w + 3y = 100 x + 3z = 50 If we add all 3 equations, we get: 3w + 3x + 3y + 3z = 300 Divide both sides by 3 to get: w + x + y + z = 100 Answer: D Cheers, Brent”
December 15, 2018
fskilnik@GMATH started following OfficialGMAT
December 14, 2018
GMATGuruNY posted a reply to Did Jeff record more sales revenue this month than Dan did? in the Data Sufficiency forum
“Statement 1: For every $100 commission that Dan earns, Jeff earns $120 in commission. Since the commission rates for Dan and Jeff are unknown, no way to determine whether Jeff recorded more sales revenue than Dan. INSUFFICIENT. Statement 2: Since Jeff''s sales and Dan''s sales can be any ...”
December 14, 2018
GMATGuruNY posted a reply to If sets A and B have the same number of terms, is the standa in the Data Sufficiency forum
“Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased: Do the values in set A deviate more from the mean than the do ...”
December 14, 2018
fskilnik@GMATH posted a reply to If sets A and B have the same number of terms, is the standa in the Data Sufficiency forum
“$$\# A = \# B$$ $${\sigma _A}\mathop > \limits^? {\sigma _B}$$ $$\left( 1 \right)\,\,{R_A} > {R_B}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{A = }}\left\{ {0,1} \right\}\,,\,\,B = \left\{ {0,0} \right\}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr ...”
December 14, 2018
fskilnik@GMATH posted a reply to Seven small circles of radius 2 are cut from the large circl in the Problem Solving forum
“https://i.ibb.co/RgxtS5T/14-Dec18-3v.gif $$? = \pi \cdot {6^2} - 7 \cdot \pi \cdot {2^2} = 8\pi $$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
December 14, 2018
fskilnik@GMATH posted a reply to When n is a positive integer, is n / 4 an integer? in the Data Sufficiency forum
“$$n \ge 1\,\,{\mathop{\rm int}} $$ $${n \over 4}\,\,\mathop = \limits^? \,\,{\rm{int}}$$ $$\left( {1 + 2} \right)\,\,\,\mathop \Leftrightarrow \limits^{n\,\,{\mathop{\rm int}} } \,\,n\,\,{\rm{even}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{n = 2}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle ...”
December 14, 2018
GMATGuruNY posted a reply to Is (y−10)^2>(x+10)^2? ----Veritas in the Data Sufficiency forum
“x² < y² can be rephrased as follows: |x| < |y| Thus, the question stem can be rephrased as follows: Is |x+10| < |y-10|? |a-b| = the distance between a and b |a+b| = |a-(-b)| = the distance between a and -b Thus, the question stem can be further rephrased as follows: Is the ...”
December 14, 2018
fskilnik@GMATH posted a reply to Is (y−10)^2>(x+10)^2? ----Veritas in the Data Sufficiency forum
“VERY nice problem. Please note we will use two different rephrasings (one for each (1) and (2) alone, the other for (1+2)): $${\left( {y - 10} \right)^2}\,\,\mathop > \limits^? \,\,{\left( {x + 10} \right)^2}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ \matrix{ \,\left| {y - 10} ...”
December 13, 2018
fskilnik@GMATH posted a reply to If A is the center of the circle shown above and AB = BC in the Problem Solving forum
“ABCD is a rhombus (all sides same length), hence each diagonal bisects the angles at its extremities. From the fact that angle ABC measures 60 degrees (triangle ABC is equilateral), ? = x = 60/2 = 30 degrees. This solution follows the notations and rationale taught in the GMATH ...”
December 13, 2018
Brent@GMATPrepNow posted a reply to If A is the center of the circle shown above and AB = BC in the Problem Solving forum
“First recognize that all radii (indicated with BLUE lines) have equal length https://i.imgur.com/iz8ur0Z.png Since BC and CD are both equal to the radius AB, we can see that all BLUE lines have equal length https://i.imgur.com/mF0UxTp.png This means the 2 blue triangles are EQUILATERAL ...”
December 13, 2018
fskilnik@GMATH posted a reply to How many subsets of {1,2,3,4,5,6,7,8} contain at least one p in the Problem Solving forum
“Very nice problem, Max. Congrats! $$\left. \matrix{ \matrix{ {\underline {\,\,\,1\,\,\,} } \cr {{\rm{yes/no}}} \cr } \,\,\,\,\matrix{ {\underline {\,\,\,2\,\,\,} } \cr {{\rm{yes/no}}} \cr } \,\,\, \ldots \,\,\,\,\matrix{ {\underline {\,\,\,7\,\,\,} } \cr ...”
December 13, 2018
GMATGuruNY posted a reply to Three congruent circles overlap in such a way that each circ in the Problem Solving forum
“The statement above is incorrect. https://i.postimg.cc/jL1NMjTL/three-congruent-circles-shaded-region.png The shaded region encompassing the equilateral triangle is not a circle.”
December 13, 2018
Brent@GMATPrepNow posted a reply to If m and n are positive integers, is mn an even number? in the Data Sufficiency forum
“Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is mn an even number? Given: m and n are positive integers Statement 1: m/n is an even number. ...”
December 13, 2018
Brent@GMATPrepNow posted a reply to What distance did Jane travel? in the Data Sufficiency forum
“Target question: What distance did Jane travel? Statement 1: Bill traveled 40 miles in 40 minutes. No info about Jane Statement 1 is NOT SUFFICIENT Statement 2: Jane traveled at the same average rate as Bill We don''t know Bill''s speed (rate) Statement 2 is NOT SUFFICIENT ...”
December 13, 2018
fskilnik@GMATH posted a reply to If m and n are positive integers, is mn an even number? in the Data Sufficiency forum
“$$m,n\,\, \ge \,\,1\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$ $$mn\,\,\,\mathop = \limits^? \,\,\,{\text{even}}\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\boxed{\,?\,\,\,:\,\,\,m\,\,{\text{or}}\,\,n\,\,{\text{even}}\,\,}$$ $$\left( 1 \right)\,\,{m \over n} = ...”
December 13, 2018
fskilnik@GMATH posted a reply to What distance did Jane travel? in the Data Sufficiency forum
“$$? = {\text{dist}}\,\,{\text{Jane}}$$ $$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,{\rm{Take:}}\,\,{\rm{total}}\,\,{\rm{Jane}}\,\,{\rm{time}}\,\,40\min \,\,{\rm{and}}\,\,\,\,\,?\,\,\, = \,\,\,40\,\,{\rm{miles}}\,\, \hfill \cr ...”
December 13, 2018
fskilnik@GMATH posted a reply to A city council will select 2 of 9 available firefighters and in the Problem Solving forum
“$$? = C\left( {9,2} \right) \cdot 6 = \frac{{9 \cdot 8}}{2} \cdot 6 = \underleftrightarrow {3 \cdot 8 \cdot \left( {10 - 1} \right) = 240 - 24} = 216\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\text{D}} \right)$$ This solution follows the notations and rationale taught in the GMATH method. ...”
December 13, 2018
fskilnik@GMATH posted a reply to Three congruent circles overlap in such a way that each circ in the Problem Solving forum
“https://i.ibb.co/gydQZsf/13-Dec18-4z.gif $$? = {S_{\Delta {\rm{equil}}}} + \,\,3 \cdot \,{S_{{\rm{blue}}}}$$ $${S_{\Delta {\rm{equil}}}} = {{{r^{\,2}}\sqrt 3 } \over 4}\,\,\,\mathop = \limits^{r\, = \,8} \,\,16\sqrt 3 $$ $${S_{{\rm{blue}}}} = {{60} \over {360}}\left( {\pi \cdot {8^2}} \right) ...”
December 13, 2018
fskilnik@GMATH posted a reply to My current age is two more than thrice the age of one of my in the Problem Solving forum
“$$? = \left| {M - R} \right|\,\,{\mathop{\rm int}} \,\,{\rm{minimum}}$$ $$\left\{ \matrix{ A = 3R + 2 \hfill \cr A + N = 3\left( {M + N} \right) + 2 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\, - N = 3\left( {R - M} \right) - 3N\,\,\,\,\,\, ...”
December 13, 2018
GMATGuruNY posted a reply to Three congruent circles overlap in such a way that each circ in the Problem Solving forum
“Area of an equilateral triangle = (s²/4)√3. √3 ≈ 1.7. https://i.postimg.cc/1gCbnSTK/three-congruent-circles.png Each circle has a radius of 8, yielding the equilateral triangle above. Area of the equilateral triangle = (8²/4)√3 = 16√3 ≈ (16)(1.7) = 27. The three circles form ...”
December 13, 2018
Brent@GMATPrepNow posted a reply to If Mike buys a biclycle and a helmet for a total cost of in the Data Sufficiency forum
“Target question: How much does the helmet cost? Given: bicycle + helmet = $315 Statement 1: The bicycle costs twice as much as the helmet. Let x = cost of helmet So, 2x = cost of bicycle Since the total cost is $315, we can write: x + 2x = 315 Simplify: 3x = 315 Solve: x = 315/3 = ...”
December 13, 2018
Brent@GMATPrepNow posted a reply to In isosceles triangle DEF, what is the measure of angle E? in the Data Sufficiency forum
“Target question: What is the measure of ∠E? Given: Triangle DEF is an ISOSCELES triangle This tells us that there are 2 equal angles Statement 1: ∠D measures 42 degrees Here it''s hard to tell whether there''s a second 42-degree angle or whether the other two angles are different. ...”
December 12, 2018
Brent@GMATPrepNow posted a reply to Ramon wants to cut a rectangular board into identical square in the Problem Solving forum
“If we aren''t wasting any wood, the length and width must be divisible by one side of the square So, this question is a clever way of asking us what the greatest common divisor (GCD) of 18 and 30 The GCD of 18 and 30 is 6, so if we cut squares that are 6 x 6, then we won''t waste any wood. We ...”
December 12, 2018
Brent@GMATPrepNow posted a reply to How many perfect squares lie between 2^4 and 2^8, inclusive? in the Problem Solving forum
“First rewrite 2^4 and 2^8 as SQUARES of integers (aka perfect squares) 2^4 = (2²)² = 4² 2^8 = (2^4)² = 16² So, we want to find the number of perfect squares FROM 4² to 16² inclusive Let''s list them: 4², 5², 6², 7², 8², 9², 10², 11², 12², 13², 14², 15², and 16² There are ...”
December 12, 2018
Brent@GMATPrepNow posted a reply to If 5x + 3y = 17, what is the value of x? in the Data Sufficiency forum
“Target question: What is the value of x? Given: 5x + 3y = 17 Statement 1: x is a positive integer Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = 4 (these values satisfy the given equation, 5x + 3y = 17). In ...”
December 12, 2018
fskilnik@GMATH posted a reply to In isosceles triangle DEF, what is the measure of angle E? in the Data Sufficiency forum
“All measures are in degrees. $$\Delta DEF\,\,{\rm{isosceles}}\,\,\,\,\left( * \right)$$ $${\rm{?}}\,\,{\rm{ = }}\,\,\angle {\rm{E}}$$ $$\left( 1 \right)\,\,\angle {\rm{D}}\,\,{\rm{ = }}\,\,{\rm{42}}\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {\angle {\rm{D}}\,{\rm{;}}\,\angle ...”
December 12, 2018
fskilnik@GMATH posted a reply to If 5x + 3y = 17, what is the value of x? in the Data Sufficiency forum
“$$5x + 3y = 17\,\,\,\left( * \right)$$ $$? = x$$ $$\left( 1 \right)\,\,x \ge 1\,\,{\mathop{\rm int}} \,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,4} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 1\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4, - ...”
December 12, 2018
fskilnik@GMATH posted a reply to If n is a positive integer, is in the Data Sufficiency forum
“$$n \ge 1\,\,{\mathop{\rm int}} \,\,\,\,\left( * \right)$$ $$\sqrt {n + 1} \,\,\mathop = \limits^? \,\,{\text{int}}\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\boxed{\,?\,\,\,\,:\,\,\,\,n + 1\,\,{\text{perfect}}\,\,{\text{square}}\,}$$ $$\left( 1 \right)\,\,n = ...”
December 12, 2018
fskilnik@GMATH posted a reply to How many perfect squares lie between 2^4 and 2^8, inclusive? in the Problem Solving forum
“$${2^4} \le {M^2} \le {2^8}\,\,,\,\,\,M\,\,{\mathop{\rm int}} \,\,\,\mathop \ge \limits^{{\rm{WLOG}}} \,\,\,0\,\,\,\,\,\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 12, 2018
GMATGuruNY posted a reply to A baseball team’s season consists of playing 162 games. At in the Problem Solving forum
“The team has won 58 percent of the games it has played. 58% = 58/100 = 29/50. The fraction in blue implies that the number of wins must be a MULTIPLE OF 29: If 50 games are played, the number of wins = (29/50)(50) = 29. If 100 games are played, the number of wins = (29/50)(100) = 58. If 150 ...”
December 12, 2018
GMATGuruNY posted a reply to Effect of several Tsunamis in the Sentence Correction forum
“A method is a PROCEDURE for accomplishing a particular goal. Since the clause in red does not discuss a procedure, it cannot be summed up as a METHOD.”
December 11, 2018
fskilnik@GMATH posted a reply to The quadrilateral ABCD is a square with sides of length 12. in the Problem Solving forum
“Very nice problem, Max. Congrats! https://i.ibb.co/hZmP0Lc/11-Dec18-5r.gif $$? = {S_{{\rm{shaded}}}} = {S_{\Delta {\rm{ADC}}}} - {S_{\Delta {\rm{AEF}}}}$$ $${S_{\Delta {\rm{ADC}}}} = {{{S_{{\rm{square}}}}} \over 2}\,\, = \,\,{{12 \cdot 12} \over 2}\,\, = \,\,72$$ $${S_{\Delta ...”
December 11, 2018
GMATGuruNY posted a reply to Effect of several Tsunamis in the Sentence Correction forum
“The SC above is modeled -- not altogether successfully -- after SC30 in the OG12: https://www.beatthegmat.com/not-sure-about-the-answer-of-a-question-from-og12-t265701.html Rather than study the SC above, stick to the official SC.”
December 11, 2018
GMATGuruNY posted a reply to The table above shows the number of students in three clubs in the Problem Solving forum
“The values in the chart DOUBLE-COUNT any student who belongs to 2 of the 3 clubs. The totals for chess and drama -- 40 and 30 -- double-count the 10 students who belong to both chess AND drama. The totals for chess and math -- 40 and 25 -- double-count the 5 students who belong to both chess AND ...”
December 11, 2018
Brent@GMATPrepNow posted a reply to How many integers between 324,700 and 458,600 have tens in the Problem Solving forum
“We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...”
December 11, 2018
Brent@GMATPrepNow posted a reply to The quadrilateral ABCD is a square with sides of length 12. in the Problem Solving forum
“This question could take a while to answer (especially if you don''t know where to begin! :-). Fortunately, we can take advantage of an IMPORTANT feature about geometric diagrams on the GMAT: The diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise. We have ...”
December 11, 2018
Brent@GMATPrepNow posted a reply to A palindrome is a number that reads the same forward and in the Problem Solving forum
“Take the task of building palindromes and break it into stages. Stage 1: Select the ten-thousands digit We can choose 1, 2, or 3 So, we can complete stage 1 in 3 ways Stage 2: Select the thousands digit We can choose 1, 2, or 3 So, we can complete stage 2 in 3 ways Stage 3: Select ...”
December 11, 2018
fskilnik@GMATH posted a reply to A palindrome is a number that reads the same forward and in the Problem Solving forum
“$$\matrix{ {\underline {{\rm{A}}\,\,{\rm{free}}} } \cr 3 \cr } \,\,\,\matrix{ {\underline {{\rm{B}}\,\,{\rm{free}}} } \cr 3 \cr } \,\,\,\matrix{ {\underline {{\rm{C}}\,{\rm{free}}} } \cr 3 \cr } \,\,\,\matrix{ {\underline {{\rm{D}}\,{\rm{ = ...”
December 11, 2018
GMATGuruNY posted a reply to This year, a woman has a lucrative one-year position. During in the Problem Solving forum
“Let r=9, with the result that 1+r = 10. Her husband can turn each dollar she gives him into 1+r, which will be deposited in a bank account. Let the wife give the husband $1, implying that the husband turns this $1 into 1+r = $10. Thus, the amount deposited into the account = $10. The ...”
December 11, 2018
Brent@GMATPrepNow posted a reply to This year, a woman has a lucrative one-year position. During in the Problem Solving forum
“Let T = the woman''s total salary for the year During this year, she will give a fraction f of her salary to her husband, a private investor, to invest and they will live this year on the remainder. So, the amount SAVED (and then given to huspand)= fT This means the amount SPENT = T - fT ...”
December 11, 2018
Brent@GMATPrepNow posted a reply to A frog is climbing a greasy pole. The frog can climb 2 in the Problem Solving forum
“Let''s solve this by making table Time elapsed | height 1 hours | 4 cm 2 hours | 8 cm REST (slide) 2.5 hours | 7 cm 3.5 hours | 11 cm 4.5 hours | 15 cm REST (slide) 5 hours | 14 cm 6 hours | 18 cm 7 hours | 22 cm REST (slide) 7.5 hours | 21 cm 8.5 hours | 25 cm 9.5 hours | 29 cm ...”
December 11, 2018
Brent@GMATPrepNow posted a reply to Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to in the Problem Solving forum
“GIVEN: oil: vinegar : water = 3 : 2 : 1 Let''s first try to use ALL 8 cups of oil Take 3 : 2 : 1 and multiply all 3 parts by 8/3 to get the EQUIVALENT ratio 8 : 16/3 : 8/3 Simplify to get: 8 : 5 1/3 : 2 2/3 So, in this case, the dressing is comprised of 8 cups of oil, 5 1/3 cups of vinegar, ...”
December 10, 2018
Brent@GMATPrepNow posted a reply to Line DB divides Rectangle ABCD into two equal triangles. Is in the Data Sufficiency forum
“IF all 4 sides of the rectangle have EQUAL length (i.e,, the shape is a square), then the diagonal will create two 45-45-90 right triangles. However, if the sides are not all the same length, the resulting triangles will NOT be 45-45-90 right triangles. Cheers, Brent”
December 10, 2018
GMATGuruNY posted a reply to Line DB divides Rectangle ABCD into two equal triangles. Is in the Data Sufficiency forum
“Yes, the line will be a diagonal, but the four angles created by this diagonal will each be 45 degrees only if the rectangle is a square.”
December 10, 2018
Brent@GMATPrepNow posted a reply to A father distributed his total wealth to his two sons. How in the Data Sufficiency forum
“ Given: A father distributed his total wealth to his two sons. Target question: How much wealth did the father have? Statement 1: The elder son received 3/5 of the wealth. Without any dollar values, there''s no way to answer the target question with certainty. So, statement 1 is NOT ...”
December 10, 2018
fskilnik@GMATH posted a reply to A father distributed his total wealth to his two sons. How in the Data Sufficiency forum
“All numbers are in thousands of dollars. $$? = W$$ $$\left( {Y\, = \,\,{\text{younger}}\,\,{\text{part}}\,\,{\text{,}}\,\,\,E = {\text{elder}}\,\,{\text{part}}} \right)$$ $$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,45} \right)\,\,\,\,\, ...”
December 10, 2018
Brent@GMATPrepNow posted a reply to At what speed was Erik running when he was at the halfway po in the Data Sufficiency forum
“IMPORTANT: The two statements essentially provide the exact same information. If it took Erik 2 hours to travel 10 miles, we can conclude that his average speed was 5 miles per hour. When the two statements provide the same information in a Data Sufficiency question, the correct answer must be ...”
December 10, 2018
Brent@GMATPrepNow posted a reply to [x] is the greatest integer less than or equal to x. What is in the Data Sufficiency forum
“Here are a few similar questions to practice with: - https://www.beatthegmat.com/if-is-the-greatest-integer-less-than-or-equal-to-x-what-t302459.html - https://www.beatthegmat.com/g-x-is-the-greatest-integer-less-than-or-equal-to-x-t298237.html - ...”
December 10, 2018
fskilnik@GMATH posted a reply to In the figure above, acr QRO is a semicircle. What is the in the Data Sufficiency forum
“$$? = {S_{{\text{big}}\,\, \odot }}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = OP\,}\,$$ https://i.ibb.co/tDn3WCn/10-Dec18-2h.gif $$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{ \,\left( 2 \right)\,\,\, \Rightarrow \,\,\,OQ = 5 \hfill \cr \,\left( 1 \right)\,\,\, \Rightarrow ...”
December 10, 2018
fskilnik@GMATH posted a reply to Tom drives from town A to town B, driving at a constant spee in the Problem Solving forum
“Perfect opportunity for UNITS CONTROL, one of the most powerful tools of our method! $$LCM\left( {36,60} \right) = 180\,\,\,\,\left\{ \matrix{ \,A \to C\,\,\,:\,\,\,180\,\,{\rm{miles}}\,\,\,\left( {{{1\,\,{\rm{hour}}} \over {36\,\,{\rm{miles}}}}} \right)\,\,\,\,\, = \,\,\,5\,\,{\rm{hours}}\, ...”
December 10, 2018
fskilnik@GMATH posted a reply to What is the solution set of (1+|x|)(1+x) > 0? in the Problem Solving forum
“$$?\,\,\,:\,\,\,\left( {1 + \left| x \right|\,} \right)\left( {1 + x} \right) > 0\,\,\,{\rm{solution}}\,\,{\rm{set}}\,$$ $$1 + \left| x \right|\,\,\, \ge \,\,\,1\,\,\,\, \Rightarrow \,\,\,\,1 + \left| x \right| > 0\,\,\,\,\,\left( {{\rm{for}}\,\,{\rm{all}}\,\,x} \right)\,\,\,\,\,\left( * ...”
December 10, 2018
fskilnik@GMATH posted a reply to [x] is the greatest integer less than or equal to x. What is in the Data Sufficiency forum
“$$? = x$$ $$\left( 1 \right)\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 10, 2018
GMATGuruNY posted a reply to What is the solution set of (1+|x|)(1+x) > 0? in the Problem Solving forum
“x=0 satisfies (1+|x|)(1+x) > 0. Since x=0 is not included in B, C, D or E, eliminate B, C, D and E. The correct answer is A.”
December 10, 2018
GMATGuruNY posted a reply to Tom drives from town A to town B, driving at a constant spee in the Problem Solving forum
“Let the distance between A and B = 120 miles. Since the 120-mile distance between A and B is twice the distance between B and C, the distance between B and C = 60 miles, implying that the total distance = 120+60 = 180 miles. Since the average speed for the 120-mile leg between A and B = 60 ...”
December 10, 2018
Brent@GMATPrepNow posted a reply to When 6 is multiplied by x, the result is the same as when x in the Problem Solving forum
“When 6 is multiplied by x, the result is the same as when x is added to 9 In other words: 6x = 9 + x Subtract x from both sides: 5x = 9 Divide both sides by 5 to get: x = 9/5 Answer: E Cheers, Brent”
December 9, 2018
Brent@GMATPrepNow posted a reply to Three photographers, Lisa, Mike and Norm, take photos of a w in the Problem Solving forum
“We can also solve the question using 1 variable Norms photos number 10 more than twice the number of Lisa''s photos Let x = the number of photographs that Lisa took. So, 2x + 10 = the number of photographs that Norm took. The total of Lisa and Mikes photos is 50 less than the sum of ...”
December 9, 2018
Brent@GMATPrepNow posted a reply to At a certain factory, each employee working the second shift in the Problem Solving forum
“Let''s assign a "nice" value to the number of widgets made by ONE employee. We''ll also assign a nice value to the number of employees on each shift. At a certain factory, each employee working the SECOND shift produced 2/3 as many widgets as each employee working the FIRST shift. ...”
December 9, 2018
fskilnik@GMATH posted a reply to Is the perimeter of triangle ABC greater than 12 cm? in the Data Sufficiency forum
“All lengths are measured in centimeters. $$a + b + c\,\,\mathop > \limits^? \,\,12$$ $$\left( 1 \right)\,\,{\rm{WLOG}}\,\left( * \right)\,\,\,a = 6\,\,\,\,\,\mathop \Rightarrow \limits^{\Delta \,\,{\rm{exists!}}} \,\,\,\,6 = a < b + c\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left\langle ...”
December 9, 2018
fskilnik@GMATH posted a reply to In the figure above, polygon N has been partially covered by in the Data Sufficiency forum
“$$? = N\,\,\left( {{\rm{number}}\,\,{\rm{of}}\,\,{\rm{sides}}\,\,{\rm{of}}\,\,{\rm{polygon}}\,\,M} \right)$$ All measures are in degrees. Each statement alone is insufficient, as PROVEN by the Geometric Bifurcations shown below: https://i.ibb.co/sFg5tYN/09-Dec18-4d.gif $$\left( {1 + 2} ...”
December 9, 2018
GMATGuruNY posted a reply to If the average (arithmetic mean) of five consecutive negativ in the Problem Solving forum
“The value of k is irrelevant. For any set of 5 consecutive integers, the difference between the greatest and least will always be 4. The correct answer is A.”
December 9, 2018
fskilnik@GMATH posted a reply to If the average (arithmetic mean) of five consecutive negativ in the Problem Solving forum
“We have a finite arithmetic sequence, hence the average of the 5 integers is their median, that is the third (middle) term. Conclusion: the greatest is (2k-1) + 2 and the least is (2k-1) - 2 , and their difference (our FOCUS) is ”
December 9, 2018
GMATGuruNY posted a reply to Three photographers, Lisa, Mike and Norm, take photos of a w in the Problem Solving forum
“The sum for Lisa and Mike is 50 less than the sum for Norm and Mike. Since Mike is common to both sums, the 50-photo difference must be yielded solely by Lisa and Norm. Implication: Lisa took 50 fewer photos than Norm. We can PLUG IN THE ANSWERS, which represent the number of photos taken ...”
December 9, 2018
fskilnik@GMATH posted a reply to A cow is tethered to the corner of a rectangular shed. in the Problem Solving forum
“Very nice problem! Be sure you understand the figure below: https://i.ibb.co/C8r2Qcc/08-Dec18-7b.gif $$? = {3 \over 4}\pi \cdot {5^2} + {1 \over 4}\pi \cdot {1^2} + {1 \over 4}\pi \cdot {2^2} = {\pi \over 4}\left( {80} \right) = 20\pi $$ This solution follows the notations and ...”
December 9, 2018
fskilnik@GMATH posted a reply to Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to in the Problem Solving forum
“Excellent opportunity for the k technique! $$\left\{ \matrix{ \,{\rm{oil}} = 3k\,\,\,\,\,\, \to \,\,\,\,\,\,3k \le 8\,\,\, \Rightarrow \,\,\,k \le 2{2 \over 3} \hfill \cr \,{\rm{vin}} = 2k\,\,\,\,\,\, \to \,\,\,\,\,\,2k \le 7\,\,\, \Rightarrow \,\,\,k \le 3{1 \over 2} \hfill \cr ...”
December 9, 2018
fskilnik@GMATH posted a reply to A grocer stacked orange in a pile. The bottom layer was in the Problem Solving forum
“$$? = \# \,\,\max \,\,{\rm{oranges}}\,\,{\rm{in}}\,\,{\rm{top}}\,\,{\rm{layer}}$$ https://i.ibb.co/S6gM8CM/08-Dec18-4m.gif $${\rm{? = 3}}\,\,\left( {{\rm{blue}}\,\,{\rm{in}}\,\,{\rm{figure}}\,\,{\rm{above}}} \right)$$ This solution follows the notations and rationale taught in the GMATH ...”
December 9, 2018
fskilnik@GMATH posted a reply to A furniture store sells only two models of desks, model A in the Problem Solving forum
“$$\left\{ \matrix{ {\rm{model}}\,A\,:\,\,\,\,A = {1 \over 4}\left( {2000} \right) = 500\,\,{\rm{units}}\,\,,\,\,\$ 120/{\rm{unit}} \hfill \cr {\rm{model}}\,{\rm{B}}\,{\rm{:}}\,\,\,\,B = 1500\,\,{\rm{units}}\,\,,\,\,{\rm{\$ }}{{120} \over {0.3}} = 400/{\rm{unit}} \hfill \cr} \right.$$ $$? ...”
December 9, 2018
fskilnik@GMATH posted a reply to Andrew sells vintage clothing at a flea market at which he in the Problem Solving forum
“$$\left\{ \matrix{ \,{\rm{constant}} = {{\$ \,\,150} \over {1\,\,{\rm{day}}}} \hfill \cr \,{\rm{variable}} = {{\$ \,\,10} \over {1\,\,{\rm{hour}}}} \hfill \cr} \right.$$ $$?\,\,\,\, = \,\,\,\,{\rm{profit}}\,\,{\rm{per}}\,\,{\rm{day}}\left( {\rm{h}} \right)\,\,\,\, = \,\,\,\,{{\left( ...”
December 9, 2018
GMATGuruNY posted a reply to Andrew sells vintage clothing at a flea market at which he in the Problem Solving forum
“Let h=3. Since an average of $78 is sold per hour, the total revenue for 3 hours = 3*78 = 234. Since the cost for the day is composed of $150 for the table rental and $10 per hour for the assistant, the cost for the day = 150 + 3*10 = 180. P = profit = revenue - cost = 234 - 180 = 54. The ...”
December 9, 2018
GMATGuruNY posted a reply to OG2019 -Logical flow in the Critical Reasoning forum
“It takes for granted that X implies that X is an ASSUMPTION: a statement that must be true for the conclusion to hold. Thus, when X is negated, the conclusion must be invalidated. B: It takes for granted that the volunteers with the highest levels of self-esteem had better social skills than did ...”
December 8, 2018
GMATGuruNY posted a reply to OG2019 -Logical flow in the Critical Reasoning forum
“Premise: Volunteers with the highest levels of self-esteem consistently rated themselves as having much better social skills than did the volunteers with moderate levels. Conclusion: Attaining an exceptionally high level of self-esteem greatly improves one’s social skills. The correct answer ...”
December 8, 2018
Brent@GMATPrepNow posted a reply to If two of the four expressions x+y, x+5y, x-y, and 5x-y are in the Problem Solving forum
“Okay, first recognize that x² - (by)² is a DIFFERENCE OF SQUARES. Here are some examples of differences of squares: x² - 25y² 4x² - 9y² 49m² - 100k² In general, we can factor differences of squares as follows: a² - b² = (a-b)(a+b) So . . . x² - 25y² = (x+5y)(x-5y) 4x² - ...”
December 8, 2018
fskilnik@GMATH posted a reply to Is x > y? in the Data Sufficiency forum
“$$x\,\,\mathop > \limits^? \,\,y$$ $$\left( 1 \right){\kern 1pt} \,\,x + y\,\, > \,\,2\,\,\,\,\,\left\{ \matrix{ \,\,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {0,3} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,\,{\rm{Take}}\,\,\left( ...”
December 7, 2018
Brent@GMATPrepNow posted a new topic called CHALLENGE: What is the value of k? in the Data Sufficiency forum
“What is the value of k? $$(1) k^2-5k-66=0$$ $$(2) \frac{2k}{k^2+5k}=\frac{1}{8}$$ Source: www.gmatprepnow.com Answer: B Estimated difficulty level: 600-650”
December 7, 2018
Brent@GMATPrepNow posted a reply to Circle question help in the Problem Solving forum
“We''ll begin by arbitrarily placing point A somewhere on the circumference. https://i.imgur.com/hRHtq4o.png So, we want to know the probability that a randomly-placed point B will yield a chord AB that is at least 2 cm long. So, let''s first find a location for point B that creates a chord ...”
December 7, 2018
Brent@GMATPrepNow posted a reply to Let C be defined as the sum of all prime numbers between in the Problem Solving forum
“C = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129 So, C/3 = 129/3 = 43 Answer: E Cheers, Brent”
December 7, 2018
Brent@GMATPrepNow posted a reply to 2k years ago Frank was 3k years old. In k years Frank's age, in the Problem Solving forum
“These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the input-output approach. Mitch has solved the question using the input-output approach, so let''s use the algebraic approach. 2k years ago Frank was 3k years old. We''re given Frank''s ...”
December 7, 2018
GMATGuruNY posted a reply to 2k years ago Frank was 3k years old. In k years Frank's age, in the Problem Solving forum
“Let k=10. 2k years ago Frank was 3k years old. Since k=10, 20 years ago Frank was 30 years old, implying that his age now = 30+20 = 50. In k years Frank''s age, in years, will be: Since Frank is now 50 years old, Frank''s age in 10 years = 50+10 = 60. The correct answer must yield a value ...”
December 7, 2018
GMATGuruNY posted a reply to Which of the following equations is satisfied by x=1+√2? in the Problem Solving forum
“Alternate approach: For any quadratic in the form x² + bx + c = 0, where b and c are rational numbers: If one of the roots is m+√n, then the other root is m-√n. Sum of the roots = -b Product of the roots = c Here, since one of the roots is 1+√2, the other root is 1-√2. Thus: -b ...”
December 7, 2018
fskilnik@GMATH posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“Excellent opportunity for the grid (aka double-matrix)! Important: we have chosen the blue expression wisely and the others follow from it. (Justify all of them!) https://i.ibb.co/m5vT1CG/06-Dec18-7k.gif $$? = {\left( {50 - M} \right)_{\min }}$$ $$\left( {50 - M} \right)\,\,{\mathop{\rm ...”
December 7, 2018
Brent@GMATPrepNow posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”
December 6, 2018
Brent@GMATPrepNow posted a reply to If all of the telephone extensions in a certain company must in the Problem Solving forum
“NOTE: Always SCAN the answer choices before performing any calculations. Here, we notice that the answer choices are pretty small, so if we don''t come up a full solution, we should consider LISTING AND COUNTING We get the following extensions: 1236 1326 1362 1632 2136 2316 3126 3162 ...”
December 6, 2018
Brent@GMATPrepNow posted a reply to If all of the telephone extensions in a certain company must in the Problem Solving forum
“Take the task of arranging the 4 digits and break it into stages. We’ll begin with the most restrictive stage. Stage 1: Select the digit in the units position Since the 4-digit extension must be EVEN, the unit digit must be either 2 or 6 So, we can complete stage 1 in 2 ways Stage ...”
December 6, 2018
Brent@GMATPrepNow posted a reply to What was the revenue that a theater received from the sale in the Data Sufficiency forum
“Target question: What was the revenue that a theater received from the sale of 400 tickets Jump straight to . . . Statements 1 and 2 combined The combined statements tell us that 100 tickets sold for the full price of $25 each. The remaining 300 tickets were sold at some reduced price. ...”
December 6, 2018
Brent@GMATPrepNow posted a reply to A certain high school offers two foreign languages, Spanish in the Problem Solving forum
“Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of students, and the two characteristics are: - ...”
December 6, 2018
Brent@GMATPrepNow posted a reply to In year x, it rained on 40% of all Mondays and 20% of all in the Data Sufficiency forum
“In any given year, there will be 52 or 53 Mondays, 52 or 53 Tuesdays, etc. So, it''s impossible to say that it rained on 40% of all Mondays or 20% of all Tuesdays, etc. For example, if there are 52 Mondays, then 40% of 52 = 20.8, which means that it rained on 20.8 days (impossible). Cheers, ...”
December 6, 2018
fskilnik@GMATH posted a reply to The first and second numbers in a sequence of numbers are in the Data Sufficiency forum
“$$\left( {{a_1},{a_2}} \right)\,\,,\,\,\left( {{a_3},{a_4}} \right)\,\,,\,\,\left( {{a_5},{a_6}} \right)\,\,,\,\,\, \ldots \,\,\,\, \to \,\,\,{\text{all}}\,\,{\text{points}}\,\,{\text{belong}}\,\,{\text{to}}\,\,{\text{a}}\,\,{\text{certain}}\,\,{\text{line}}\,\,{\text{L}}$$ ...”
December 6, 2018
fskilnik@GMATH posted a reply to If a and b are integers, is a-b an even number? in the Data Sufficiency forum
“$$a,b\,\,{\rm{ints}}$$ $$a - b\,\,\mathop = \limits^? \,\,{\text{even}}\,\,\,\,\,\,\mathop { \Leftrightarrow \,}\limits^{\left( * \right)} \,\,\,\,\,\boxed{\,?\,\,\,:\,\,\,\left( {a,b} \right) = \left( {{\text{odd}}\,{\text{,}}\,{\text{odd}}} \right)\,\,\,{\text{or}}\,\,\,\,\left( {a,b} \right) = ...”
December 6, 2018
GMATGuruNY posted a reply to Each day at Dan’s new job, he earns $10 more than the day in the Data Sufficiency forum
“Since each payday is $10 more than the preceding payday, the list of 15 paydays constitutes an EVENLY SPACED SET. Statement 1: For any evenly spaced set: Median = Sum/Quantity. Thus: Pay on the 14th day = median of the 3 most recent days = sum/quantity = 690/3 = 330. Since the pay on the ...”
December 6, 2018
GMATGuruNY posted a reply to Tom saved $10,000 at a constant compound interest rate of r in the Problem Solving forum
“Original deposit: 10,000. The balance doubles every 10 years. After 10 years, we get: 2*10,000 = 20,000. After 20 years, we get: 2*20,000 = 40,000. After 30 years, we get: 2*40,000 = 80,000. The correct answer is E.”
December 6, 2018
fskilnik@GMATH posted a reply to x is a positive number. What is the median of x, √x and x^ in the Data Sufficiency forum
“$$x > 0$$ $$? = {\rm{Med}}\left( {x,\sqrt x ,{x^2}} \right)$$ $$\left( 1 \right)\,\,x = {x^2}\,\,\,\,\mathop \Rightarrow \limits^{:\,\,x\,\left( { \ne 0} \right)\,} \,\,1 = x\,\,\,\,\, \Rightarrow \,\,\,? = {\rm{Med}}\left( {1,1,1} \right) = 1\,\,\,\,\, \Rightarrow ...”
December 6, 2018
fskilnik@GMATH posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“$$a,b,c\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$ $$a - b = 6Q + r\,\,,\,\,\,\left\{ \matrix{ \,Q,r\,\,\,{\mathop{\rm int}} {\rm{s}} \hfill \cr \,0 \le r \le 5 \hfill \cr} \right.$$ $$? = r$$ $$\left( 1 \right)\,\,a = {c^3}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( ...”
December 6, 2018
fskilnik@GMATH posted a reply to If a, b, and c are positive integers such that a < b < in the Data Sufficiency forum
“$$1 \le a < b < c\,\,\,{\rm{ints}}\,\,\,\left( * \right)$$ $$\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 6, 2018
fskilnik@GMATH posted a reply to If w, x, and y are consecutive odd positive integers and w & in the Problem Solving forum
“$$\left\{ \matrix{ w = 2M - 1 \hfill \cr x = 2M + 1 \hfill \cr y = 2M + 3 \hfill \cr} \right.\,\,\,\,\,\,\,\left( {M \ge 1\,\,{\mathop{\rm int}} } \right)$$ $$? = y - x - w = - 2M + 3\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{alternatives!}}} \,\,\,\, - 1\,\,\,\,\,\,\,\left( ...”
December 6, 2018
fskilnik@GMATH posted a reply to A triangle is formed by connecting three randomly chosen ver in the Problem Solving forum
“https://i.ibb.co/B45S11j/06-Dec18-4b.gif $$? = 1 - {{\,\,\# \,\,\Delta \,\,\,{\rm{no}}\,\,\,{\rm{sides}}\,\,\,{\rm{in}}\,\,\,{\rm{hexag}}\,\,\,} \over {\# \,\,\Delta \,\,{\rm{total}}}} = 1 - {2 \over {C\left( {6,3} \right)}} = 1 - {2 \over {20}} = {9 \over {10}}$$ This solution follows the ...”
December 6, 2018
fskilnik@GMATH posted a reply to What is the difference between the number of three-member in the Problem Solving forum
“$$? = 3!C\left( {9,3} \right) - C\left( {9,3} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,\,84\left( {3! - 1} \right) = 5 \cdot 84 = 420$$ $$\left( * \right)\,\,\,C\left( {9,3} \right) = {{9 \cdot 8 \cdot 7} \over {3 \cdot 2}} = 3 \cdot 4 \cdot 7 = 84$$ This solution follows the notations ...”
December 6, 2018
fskilnik@GMATH posted a reply to 190 students go to a school bake sale. 95 buy a chocolate in the Problem Solving forum
“Excellent opportunity for the Venn diagram (aka overlapping sets)! https://i.ibb.co/N23M1ph/06-Dec18-2x.gif $$? = {\left( R \right)_{\min }}$$ $$R = 190 - \left( {95 + 75 - {\rm{both}}} \right) = 20 + {\rm{both}}$$ $${\rm{both}} \ge 12\,\,\,\left( {{\rm{given}}} \right)\,\,\,\,\,\,\, ...”
December 6, 2018
fskilnik@GMATH posted a reply to A certain high school offers two foreign languages, Spanish in the Problem Solving forum
“Excellent opportunity for the Venn diagram (aka overlapping sets)! https://i.ibb.co/sbhmDrV/05-Dec18-4r.gif $$? = S = a + 50$$ $$\left\{ \matrix{ a + b = 7T\,\,\,\left( {{\rm{given}}} \right) \hfill \cr a + \underbrace {b + 50}_{5T} = 9T \hfill \cr} \right.\,\,\,\, \Rightarrow ...”
December 6, 2018
GMATGuruNY posted a reply to If a, b, and c are positive integers such that a < b < in the Data Sufficiency forum
“Does (a/100) * (b/100) * c = integer? Test integer values such that a < b < c. Statement 1: b = (a/100)¯¹ Thus, b = 100/a. Test the smallest possible value for a. Case 1: a=1 Here, b =100/1 = 100. In this case, (a/100) * (b/100) * c = 1/100 * 100/100 * c = c/100. If c ...”
December 5, 2018
Brent@GMATPrepNow posted a reply to Three men sit at a table. One dollar is placed in front of in the Problem Solving forum
“Let''s see what happens if a man waits until the last (5th) round to take the money. Round #1: $1 placed in front of the man (but he doesn''t take it) Round #2: Now, $2 placed in front of the man (but he doesn''t take it) Round #3: Now, $4 placed in front of the man (but he doesn''t take it) ...”
December 5, 2018
Brent@GMATPrepNow posted a reply to If a, b, and c are positive integers such that a < b < in the Data Sufficiency forum
“Target question: Is a% of b% of c an integer? This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: a% of b% of c is the same as (a/100)(b/100)(c), which equals abc/10,000 So, we can rephrase the target ...”
December 5, 2018
Brent@GMATPrepNow posted a reply to If w, x, and y are consecutive odd positive integers and w & in the Problem Solving forum
“Here''s a 3rd approach: GIVEN: w, x, and y are consecutive odd positive integers and w < x < y Since consecutive odd integers go up by 2, we can write: x = w + 2, and y = w + 2 + 2 = w + 4 So, y - x - w = (w + 4) - (w + 2) - w = w + 4 - w - 2 - w = 2 - w Since w is an ODD integer, ...”
December 5, 2018
Brent@GMATPrepNow posted a reply to What is the difference between the number of three-member in the Problem Solving forum
“The number of three-member committees that can be formed from a group of nine members Since the order in which we select the 3 people does not matter, we can use combinations. We can choose 3 people from 9 people in 9C3 ways 9C3 = (9)(8)(7)/(3)(2)(1) = 84 three-member committees The total ...”
December 5, 2018
Brent@GMATPrepNow posted a reply to All the 7 books of the fictional character series Horry in the Problem Solving forum
“At $8 per book, the 8 books SHOULD have cost $64 (8 x $8 = $64) However, Harry bought the 8 books for $60 So, the amount Harry saved = $64 - $60 = $4 What is savings percentage for Harry, who bought the whole set together? Percent savings = 100(amount saved)/(original price) = 100(4)/64 = ...”
December 5, 2018
GMATGuruNY posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=3, with the result that a=3³=27 and that b=(3-2)³=1 In this case, a-b = 27-1 = 26. Dividing 26 by 6, we get: 26/6 = 4 R2 Case 2: c=4, with the ...”
December 5, 2018
GMATGuruNY posted a reply to If w, x, and y are consecutive odd positive integers and w & in the Problem Solving forum
“Test easy cases: 5-3-1 = 1 7-5-3 = -1 The case in green indicates that -1 is a possible value of y-x-w. The correct answer is C.”
December 5, 2018
GMATGuruNY posted a reply to x is a positive number. What is the median of x, √x and x^ in the Data Sufficiency forum
“To determine the median of x, √x and x², we need to know the value of x. Statement 1: Since x is positive, we can safely divide both sides by x: x²/x = x/x x = 1 SUFFICIENT. Statement 2: x² + x + 1 = 3x x² - 2x + 1 = 0 (x-1)² = 0 x = 1 SUFFICIENT. The correct answer is D.”
December 5, 2018
GMATGuruNY posted a reply to A triangle is formed by connecting three randomly chosen ver in the Problem Solving forum
“Let the 6 vertices = A, B, C, D, E and F. P(the triangle includes AT LEAST 1 side of the hexagon) = 1 - P(the triangle includes NO sides of the hexagon). From the 6 vertices, the number of ways to choose 3 to form a triangle = 6C3 = (6*5*4)/(3*2*1) = 20. Of these 20 triangles, only 2 include ...”
December 5, 2018
fskilnik@GMATH posted a reply to Working together, Machine A and Machine B can produce a in the Data Sufficiency forum
“$$200\,\,{\rm{widgets}}\,\,\,\left\{ \matrix{ \,A\,\, = \,\,? \hfill \cr \,B\, \hfill \cr \,4\,\,\, \to \,\,\,{\rm{together}} \hfill \cr} \right.\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
December 5, 2018
fskilnik@GMATH posted a reply to n is a positive integer. Is n divisible by 3? in the Data Sufficiency forum
“$$n \ge 1\,\,{\mathop{\rm int}} $$ $${n \over 3}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}} $$ $$\left( 1 \right)\,\,\,\left( {{{36} \over n} = {\mathop{\rm int}} \,\,{\rm{and}}} \right)\,\,\,{{12} \over n} = {{36} \over {3n}} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{ ...”
December 5, 2018
fskilnik@GMATH posted a reply to If s and t are two different numbers on the number line, is in the Data Sufficiency forum
“$$s \ne t\,\,\,\,\left( * \right)$$ $$s + t\,\,\mathop = \limits^? \,\,0$$ $$\left( 1 \right)\,\,\,\left| s \right| = \left| t \right|\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,s = - t\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$ $$\left( 2 ...”
December 5, 2018
fskilnik@GMATH posted a reply to How many positive two-digit integers have a remainder of 1 w in the Problem Solving forum
“$$?\,\,:\,\,\# \,\,N\,\,{\rm{with}}\,\,\left( 1 \right),\left( {2{\rm{a}}} \right),\left( {3{\rm{a}}} \right),\left( {4{\rm{a}}} \right)$$ $$10\,\, \le \,\,N\,\,{\mathop{\rm int}} \,\, \le \,\,99\,\,\left( 1 \right)$$ $$\left\{ \matrix{ \,N = 2M + 1,\,\,M\,\,{\mathop{\rm int}} \,\,\,\,\left( ...”
December 5, 2018
GMATGuruNY posted a reply to Working together, Machine A and Machine B can produce a in the Data Sufficiency forum
“Since A+B take 4 hours to produce 200 widgets, the combined rate for A+B = w/t = 200/4 = 50 widgets per hour. To determine A''s time to produce 200 widgets, we need to know A''s rate. Question stem, rephrased: What is A''s rate? Statement 1: Since B takes 5 hours to produce 50 widgets, B''s ...”
December 4, 2018
Brent@GMATPrepNow posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico Ci in the Problem Solving forum
“Average speed = (total distance traveled)/(total travel time) So, Average speed = 1200/2.5 = 2400/5 = 4800/10 = 480 mph Answer: D Cheers, Brent”
December 4, 2018
Brent@GMATPrepNow posted a reply to In her position as a real estate agent, Sarah receives a bon in the Problem Solving forum
“Last week, Sarah earned a $4,000 bonus, which decreased her average bonus amount to $4800. This represents a decrease of 4%. Let x = OLD average bonus amount We can write: x - 0.04x = $4800 Simplify: 0.96x = $4800 Solve: x = $4800/(0.96) = $5000 How many sales has Sarah made? Let n = the ...”
December 4, 2018
GMATGuruNY posted a reply to How many positive two-digit integers have a remainder of 1 w in the Problem Solving forum
“A quick lesson on remainders: Onto the problem at hand: a remainder of 1 when divided by 2 x = 2a + 1 = 1, 3, 5, 7... In other words, x must be ODD. a remainder of 4 when divided by 5 x = 5b + 4 = 4, 9, 14, 19... Since x must be odd, we get: x = 9, 19, 29.... a remainder of ...”
December 4, 2018
fskilnik@GMATH posted a reply to What is the value of (2^x + 2^x)/2^y ? in the Data Sufficiency forum
“$$? = {{2 \cdot {2^x}} \over {{2^y}}} = {2^{\left( {x + 1} \right) - y}} = {2^{x - y + 1}}$$ $$\left( 1 \right)\,\,x - y = 8\,\,\,\, \Rightarrow \,\,\,\,? = {2^{8 + 1}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$ $$\left( 2 \right)\,\,{x \over y} = - 3\,\,\,\left\{ \matrix{ ...”
December 4, 2018
fskilnik@GMATH posted a reply to If a child is randomly selected from Columbus Elementary in the Data Sufficiency forum
“$$? = {b \over {b + {\rm{g}}}}$$ $$\left( 1 \right)\,\,{{b - 25} \over {\left( {b - 25} \right) + g}} = {3 \over 4}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {28,1} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{28} \over {29}} \hfill \cr \,{\rm{Take}}\,\,\left( {b,g} ...”
December 4, 2018
fskilnik@GMATH posted a reply to Mary is building a pyramid out of stacked rows of soup cans. in the Problem Solving forum
“$$?\,\,\, = \,\,\,\# \,\,{\rm{soup}}\,\,{\rm{cans}}$$ The number of soup cans constitute a finite arithmetic sequence, hence the average number of cans per row is equal to M = (1+N)/2 , where N is the number of cans in the 16th row, that is, 1+15*6 = 91. Hence: $$M = {{1 + 91} \over 2}\,\,\,\, ...”
December 4, 2018
fskilnik@GMATH posted a reply to If there are 4 pairs of twins, and a committee will be in the Problem Solving forum
“$$\left. \matrix{ \# \,\,{\rm{total}}\,\,{\rm{committees}}\,\,{\rm{ = }}\,\,\,{\rm{C}}\left( {8,3} \right) = {{8 \cdot 7 \cdot 6} \over {3!}} = 56 \hfill \cr \# \,\,{\rm{committees}}\,\,{\rm{with}}\,\,{\rm{siblings}}\,\,{\rm{ = }}\,\,\,\underbrace ...”
December 3, 2018
Brent@GMATPrepNow posted a reply to If there are 4 pairs of twins, and a committee will be in the Problem Solving forum
“Here''s another approach. Take the task of selecting the 3 committee members and break it into stages. Stage 1: Select the 3 twins from which we will select 1 spouse each. There are 4 sets of twins, and we must select 3 of them. Since the order in which we select the 3 twins does not ...”
December 3, 2018
GMATGuruNY posted a reply to If there are 4 pairs of twins, and a committee will be in the Problem Solving forum
“Number of options for the 1st person = 8. Number of options for the 2nd person = 6. (Of the 7 people left, we can''t use the twin of the 1st person chosen, leaving 7-1= 6 choices.) Number of options for the 3rd person = 4. (Of the 6 people left, we can''t use the twins of the 2 people already ...”
December 3, 2018
fskilnik@GMATH posted a reply to Is x + 1/x > 2? in the Data Sufficiency forum
“Very nice problem, Max. Congrats! $$x + {1 \over x}\,\,\mathop > \limits^? \,\,2$$ $$\left( 1 \right)\,\,x > 0\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,x = 2\,\,\,\, \Rightarrow ...”
December 3, 2018
fskilnik@GMATH posted a reply to If x^3 < x^2, what is the value of the integer x? in the Data Sufficiency forum
“$$x\,\,{\mathop{\rm int}} \,\,\left( * \right)$$ $${x^3} < {x^2}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{x^2}\left( {x - 1} \right) < 0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x \ne 0\,\,\,{\rm{and}}\,\,x < 1\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,x \le - ...”
December 3, 2018
fskilnik@GMATH posted a reply to If n is a positive integer, which of the following could be in the Problem Solving forum
“$$n \ge 1\,\,{\mathop{\rm int}} \,\,\left( * \right)$$ $$?\,\,:\,\,\,{\left( {n + 1} \right)^3} - {n^3}\,\,\underline {{\rm{could}}} \,\,{\rm{be}}$$ $${\left( {n + 1} \right)^3} - {n^3}\,\,\, = \,\,\, \ldots \,\,\, = \,\,\,3{n^2} + 3n + 1\,\,\, = \,\,\,3\left( {{n^2} + n} \right) + 1\,\,\, = ...”
December 3, 2018
fskilnik@GMATH posted a reply to A certain bookstore, each notepad costs x dollars and each in the Data Sufficiency forum
“Do not forget that there are noninteger dollar values, but all values in cents are integers! $$\left\{ \matrix{ \,{\rm{notepads}}\,,\,\,\$ \,n\,\,{\rm{cents}}\,\,{\rm{each}}\,\,\,\left( {n = 100x} \right) \hfill \cr \,{\rm{markers}}\,,\,\,\$ \,m\,\,{\rm{cents}}\,\,{\rm{each}}\,\,\,\left( ...”
December 2, 2018
GMATGuruNY posted a reply to For each of her sales, a saleswoman receives a commission in the Problem Solving forum
“The first $500 of the $800 sale earns 20% commission, while the remaining $300 earns 30%. Average commission percentage per $800 = (500*20 + 300*30)/800 = (5*20 + 3*30)/8 = 190/8 = 23.75 ≈ 24. The correct answer is B.”
December 1, 2018
Brent@GMATPrepNow posted a reply to For each of her sales, a saleswoman receives a commission in the Problem Solving forum
“Saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 30 percent of the total amount in excess of $500 If she sold $800, then... Commission = (20 percent of $500) + (30 percent of $300) = $100 + $90 = $190 The saleswoman''s commission ...”
December 1, 2018
Brent@GMATPrepNow posted a reply to Portia purchased a laptop for $480, but after checking the in the Problem Solving forum
“Let x = the INTENDED price of the laptop Portia was overcharged by 20% So, x + (20% of x) = the amount Portia paid In other words: x + 0.2x = $480 Simplify: 1.2x = 480 Solve: x = 480/1.2 = 400 So, Portia was SUPPOSED to pay $400, but she actually paid $480 So, Portia was overcharged ...”
December 1, 2018
Brent@GMATPrepNow posted a reply to When a certain tree was first planted, it was 4 feet tall in the Problem Solving forum
“Height of tree on day 0 = 4 Let d = the height increase each year Height of tree at the end of the 1st year = 4+d Height of tree at the end of the 2nd year = 4+d+d = 4 + 2d Height of tree at the end of the 3rd year = 4+d+d+d = 4 + 3d Height of tree at the end of the 4th year = 4+d+d+d+d = 4 + ...”
December 1, 2018
GMATGuruNY posted a reply to When a certain tree was first planted, it was 4 feet tall in the Problem Solving forum
“Let x = the yearly increase. Height after 4 years = 4 + 4x. Height after 6 years = 4 + 6x. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. The phrase in red implies the following: The height in the 6th year was 6/5 of the height in the 4th ...”
December 1, 2018
fskilnik@GMATH posted a reply to Of the employees at a company, 60 percent were men and, of in the Problem Solving forum
“$$? = {{\# \,\,{\rm{women}}\,\,{\rm{still}}\,{\rm{employed}}} \over {\# \,\,{\rm{women}}}}$$ Trivial problem for the grid technique (aka double-matrix): https://i.ibb.co/HPwXL1T/01-Dez18-3x.gif $$? = {{30} \over {100 - 60}} = {3 \over 4} = 75\% $$ This solution follows the notations and ...”
December 1, 2018
fskilnik@GMATH posted a reply to Reggie purchased a car costing $8,700. As a down payment he in the Problem Solving forum
“All numbers presented below are in dollars. $$8700\,\,\,\,\left\{ \matrix{ \,2300 \hfill \cr \,{{15} \over {100}}\left( {8700 - 2300} \right) = 15 \cdot 64 = 960 \hfill \cr \,\$ \,\,?\,\,\,\left( {{\rm{borrowed}}} \right) \hfill \cr} \right.$$ $$? = 8700 - \left( {2300 + 960} \right) ...”
December 1, 2018
fskilnik@GMATH posted a reply to If k is a positive integer and n=(k-1)k(k+1), is n a multipl in the Data Sufficiency forum
“$$k \ge 1\,\,{\mathop{\rm int}} \,\,\,\,\left( * \right)$$ $${{\left( {k - 1} \right)k\left( {k + 1} \right)} \over {{2^3}}}\,\,\mathop = \limits^? \,\,{\rm{int}}$$ $$\left( 1 \right)\,\,k\,\, = 2M + 1\,\,\,\left( {M\mathop \ge \limits^{\left( * \right)} 0\,\,{\mathop{\rm int}} } \right)$$ ...”
December 1, 2018
fskilnik@GMATH posted a reply to If x is a positive integer, is x a prime integer? in the Data Sufficiency forum
“$$x \geqslant 1\,\,\operatorname{int} $$ $$x\,\,\mathop = \limits^? \,\,{\text{prime}}$$ $$\left( 1 \right)\,\,x + 1\,\,{\rm{prime}}\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,x = 2\,\,\,\, ...”
December 1, 2018
fskilnik@GMATH posted a reply to The juice stall at the circus stocked just 2 brands of in the Problem Solving forum
“$${\text{Particular}}\,\,{\text{case}}\,\,:\,\,n = 100\,\,\, \Rightarrow \,\,\,{\text{only}}\,\,A\,\,{\text{sold}}\,\,\,\, \Rightarrow m = 100\,\,\,\left( {{\text{target}}\,\,{\text{value}}} \right)$$ $$\left( A \right)\,\,\frac{{100 \cdot 100}}{{150 - 100}}\,\,\mathop = \limits^? ...”
December 1, 2018
fskilnik@GMATH posted a reply to In a business school case competition, the top three teams in the Problem Solving forum
“$$?\,\,\, = \underbrace {C\left( {4,1} \right) \cdot 3!}_{\,\,\,\,\,\,{\text{A}}\,{\text{yes}}{\text{,}}\,\,{\text{B}}\,\,{\text{too}}} + \,\,\,\,\underbrace {C\left( {5,3} \right) \cdot 3!}_{A\,\,{\text{no}}}\,\,\,\, = \,\,\,\,24 + 60\,\,\,\, = \,\,\,\,84$$ This solution follows the notations ...”
December 1, 2018
fskilnik@GMATH posted a reply to When running a mile during a recent track meet, Nuria was in the Problem Solving forum
“\The above follows the notations and rationale taught in the GMATH method. Regards, Fabio. P.S.: the alternative choices DO help you avoid the precise calculations above, but with proper (and very useful) tools those calculations are easy! ”
December 1, 2018
fskilnik@GMATH posted a reply to If x^2=x+1, then x^4=? in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
December 1, 2018
Brent@GMATPrepNow posted a reply to Last Friday a certain shop sold 3/4 of the sweaters in its in the Data Sufficiency forum
“ Given: Last Friday a certain shop sold 3/4 of the sweaters in its inventory. Each sweater sold for $20. Target question: What was the total revenue last Friday from the sale of this sweaters? Statement 1: When the shop opened last Friday, there were 160 sweaters in its inventory. 3/4 ...”
November 30, 2018
Brent@GMATPrepNow posted a reply to When running a mile during a recent track meet, Nuria was in the Problem Solving forum
“The long approach is to meticulously convert 11/25 of a minute to seconds, and then ADD that unaccounted time to Nuria''s recorded time (of 5 minutes, 44 seconds) However, when we check the answer choices before performing any calculations (ALWAYS check the answer choices before performing any ...”
November 30, 2018
GMATGuruNY posted a reply to If k is a positive integer and n=(k-1)k(k+1), is n a multipl in the Data Sufficiency forum
“Every other even integer is a MULTIPLE OF 4: 2, 4, 6, 8, 10, 12... Thus, the product of two consecutive even integers = product of a multiple of 4 and an even non-multiple of 4 = MULTIPLE OF 8: 2*4 = 8 4*6 = 2*2*2*3 = 8*3 10*12 = 2*5*2*2*3 = 8*15 Statement 1: Since k is odd, k-1 and k+1 ...”
November 30, 2018
GMATGuruNY posted a reply to If x^2=x+1, then x^4=? in the Problem Solving forum
“Squaring both sides, we get: (x²)² + (x+1)² x⁴ = x² + 2x + 1 Substituting x²=x+1 into x⁴ = x² + 2x + 1, we get: x⁴ = (x+1) + 2x + 1 x⁴ = 3x + 2 The correct answer is A.”
November 30, 2018
GMATGuruNY posted a reply to Is the positive integer p a multiple of 50? in the Data Sufficiency forum
“Any integer that is a multiple 10 is also a multiple of 5. Implication: Any integer that satisfies Statement 1 will also satisfy Statement 2. Both statements are satisfied by the following cases: Case 1: p=10, which is a multiple of 10 (and thus is also a multiple of 5) In this case, p is NOT a ...”
November 30, 2018
GMATGuruNY posted a reply to The point A, B, C, and D are on the number line, not in the Data Sufficiency forum
“The drawings below satisfy both statements: http://s4.postimage.org/1yjxdhskk/ABCD_number_line.jpg Since in the first case BD=1 and in the second case BD=17, the two statements combined are insufficient. The correct answer is E.”
November 30, 2018
fskilnik@GMATH posted a reply to if the straight line y = x + c is tangent to the circle (x-1 in the Problem Solving forum
“\Algebraic approach: \This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
November 30, 2018
GMATGuruNY posted a reply to In a business school case competition, the top three teams in the Problem Solving forum
“Case 1: Team A wins a prize, with the result that Team B must win a prize Number of prizes that could be won by A = 3. Number of remaining prizes that could be won by B = 2. Number of teams that could win the third prize = 4. (Any of the 4 remaining teams.) To combine these options, we ...”
November 30, 2018
GMATGuruNY posted a reply to The juice stall at the circus stocked just 2 brands of in the Problem Solving forum
“Let n=50, implying that 50% of the sold juice packs are A, while the other half are B. In other words, the store sells an EQUAL NUMBER of each type of juice pack. Let the store sell 2 OF EACH TYPE of juice pack. Revenue from two $1 packs of A = 2*1 = 2. Revenue from two $1.5 packs of B = ...”
November 29, 2018
fskilnik@GMATH posted a reply to If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime fac in the Problem Solving forum
“There are at least two GMAT-scope ways to find the identity given, therefore it could have been omitted from the question stem! 1st way (the famous trick related to the sum of a finite sequence of terms of a geometric sequence): $$S = 1 + \underline {{2^1} + {2^2} + \ldots + {2^{n - 1}} + ...”
November 29, 2018
Brent@GMATPrepNow posted a reply to GMAT PREP CR... why is A wrong? in the Critical Reasoning forum
“A student asked me to answer this question, so here it goes . . . 1) Read the question stem to determine the question type. Tricky! With fill-in-the-blank questions, it''s often difficult to determine the question type. The last sentence reads Unitron is not going to hire department heads ...”
November 29, 2018
fskilnik@GMATH posted a reply to Inequality in the Data Sufficiency forum
“$$? = \left| {x - 2} \right|$$ $$\left( 1 \right)\,\,\,{\rm{dist}}\left( {x,4} \right) = \left| {x - 4} \right| = 2\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{ \,x = 6\,\,\,\, \Rightarrow \,\,\,\,? = 4 \hfill \cr \,x = 2\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \cr} ...”
November 29, 2018
fskilnik@GMATH posted a reply to If m and n are positive integers, what is the greatest commo in the Data Sufficiency forum
“$$m,n\,\, \geqslant 1\,\,{\text{ints}}$$ $${\text{?}}\,\,{\text{ = }}\,\,{\text{GCD}}\left( {m,n} \right)$$ $$\left( 1 \right)\,\,\,m = n + 1\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\,\,\left( ...”
November 29, 2018
fskilnik@GMATH posted a reply to If m and n are positive integers, what is the greatest commo in the Data Sufficiency forum
“$$m,n\,\, \geqslant 1\,\,{\text{ints}}$$ $${\text{?}}\,\,{\text{ = }}\,\,{\text{GCD}}\left( {m,n} \right)$$ $$\left( 1 \right)\,\,\,m = n + 1\,\,\,\,\, \Rightarrow \,\,\,\,? = 1\,\,\,\,\,\left( ...”
November 29, 2018
fskilnik@GMATH posted a reply to New cars leave a car factory in a repeating pattern of red, in the Problem Solving forum
“$$?\,\,\,:\,\,\,{463^{{\text{rd}}}}\,\,\,{\text{in}}\,\,\,\boxed{\text{R}}{\text{,U,A,G,}}\boxed{\text{R}}{\text{,U,A,G,}}\boxed{\text{R}}, \ldots \,\,\,\,{\text{sequence}}$$ $${\text{R}}\,\,{\text{positions}}\,\,\,{\text{::}}\,\,\,\,{\text{1}}\,\,{\text{,}}\,\,\,{\text{1 + ...”
November 29, 2018
fskilnik@GMATH posted a reply to The equation of a circle in the x-y coordinate plane is x^2 in the Problem Solving forum
“$$?\,\,\,:\,\,\,\,\# \,\,\left( {x,y} \right)\,\,\,{\rm{integer}}\,\,{\rm{coordinates}}\,\,{\rm{solutions}}\,\,{\rm{for}}\,\,\,{x^2} + {y^2} = 25$$ $$\left| x \right| = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {x,y} \right) = \left( {0,5} \right)\,\,\,{\rm{or}}\,\,\,\left( {x,y} \right) = ...”
November 29, 2018
Brent@GMATPrepNow posted a reply to New cars leave a car factory in a repeating pattern of red, in the Problem Solving forum
“Let''s examine the pattern. CAR # | color 1 | red 2 | blue 3 | black 4 | gray 5 | red 6 | blue 7 | black 8 | gray 9 | red . . . The pattern REPEATS EVERY 4 CARS. So, we say the pattern has CYCLE 4 Also, notice that every car # that''s divisible by 4 is gray So, let''s find a ...”
November 29, 2018
GMATGuruNY posted a reply to James started from his home and drove eastwards at a in the Problem Solving forum
“Let James'' rate = 3 mph. James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James ...”
November 29, 2018
GMATGuruNY posted a reply to The equation of a circle in the x-y coordinate plane is x^2 in the Problem Solving forum
“The equation for a circle with its center at the origin and a radius of r is as follows: x² + y² = r². Thus, x² + y² = 25 is a circle with its center at the origin and a radius of 5. A point on this circle will have integer coordinates in three cases: Case 1: The radius is horizontal ...”
November 29, 2018
fskilnik@GMATH posted a reply to A casino pays players with chips that are either turquoise in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 29, 2018
Brent@GMATPrepNow posted a reply to If each of the two digits X and Y is distinct, is the two di in the Data Sufficiency forum
“Target question: Is the two-digit integer xy prime? Given: Each of the two digits x and y is distinct Statement 1: Each of the digits x and y is the sum of 2 distinct single digit prime numbers. Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here ...”
November 29, 2018
Brent@GMATPrepNow posted a reply to Joan spent $10 to buy at least one piece each of apples and in the Data Sufficiency forum
“Target question: How many apples did Joan buy? Given: Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. Since there are only a handful of possible outcomes, we might benefit from quickly listing them: i) Joan ...”
November 29, 2018
fskilnik@GMATH posted a reply to Joan spent $10 to buy at least one piece each of apples and in the Data Sufficiency forum
“\The correct answer is therefore (A). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 29, 2018
fskilnik@GMATH posted a reply to If n is a positive integer, is √17n an integer? in the Data Sufficiency forum
“\The correct answer is therefore (D). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 29, 2018
Brent@GMATPrepNow posted a reply to If 320 people attended the wedding and 200 attendees drank in the Data Sufficiency forum
“This question is somewhat ambiguous, since it''s hard to say whether "nondrinkers" in statement 1 refers to people who drank neither beer nor wine, or did not drink beer. I''m assuming that it means to not drink beer, so I''ve add that to the question below. One approach is to use ...”
November 28, 2018
Brent@GMATPrepNow posted a reply to Difficult Manhatan Problem in the Problem Solving forum
“Target question: What is the hundreds digit of the product AB? Given: The difference between positive two-digit integer A and the smaller two-digit integer B is twice A‘s units digit Let x = the tens digit of A, and let y = the units digit of A So, the VALUE of A = 10x + y From the ...”
November 28, 2018
Brent@GMATPrepNow posted a reply to If a child is randomly selected from Columbus Elementary in the Data Sufficiency forum
“Target question: What is the probability that the child will be a boy? This is a good candidate for rephrasing the target question. Let G = # of girls in the school Let B = # of boys in the school So, G + B = total number of children in the school So, P(selected child is a boy) = B/(G + B) ...”
November 28, 2018
Brent@GMATPrepNow posted a reply to A club has 10 members. One president and two vice-presidents in the Problem Solving forum
“Take the task of selecting the president and two vice-presidents and break it into stages. Stage 1: Select the president There are 10 people to choose from. So, we can complete stage 1 in 10 ways Stage 2: Select two people to be the vice-presidents Since the order in which we select the ...”
November 28, 2018
Brent@GMATPrepNow posted a reply to On a partly cloudy day, Derek decides to walk back from work in the Problem Solving forum
“Let''s PLUG IN a nice value for the total distance traveled. If Derek''s average speed is 2.8 mph, then let''s say that he traveled a total of 28 miles. At an average rate of 2.8 mph, a 28 mile trip will take 10 hours. Since Derek''s average speed is BETWEEN 2 and 3 mph, we can conclude that ...”
November 28, 2018
GMATGuruNY posted a reply to On a partly cloudy day, Derek decides to walk back from work in the Problem Solving forum
“The average speed -- 2.8 miles per hour -- must be BETWEEN the two individual rates (s and s+1). Thus, s = 2 miles per hour and s+1 = 3 miles per hour. We can PLUG IN THE ANSWERS, which represent the fraction traveled at 2 miles per hour. When the correct fraction is plugged in, the average ...”
November 28, 2018
GMATGuruNY posted a reply to Eight consecutive integers are selected from the integers 1 in the Data Sufficiency forum
“When consecutive positive integers are divided by positive integer x, the resulting remainders also are consecutive: If x=4: 16/4 = 4 R0. 17/4 = 4 R1. 18/4 = 4 R2. 19/4 = 4 R3. 20/4 = 5 R0. From here, the cycle of remainders will repeat: 0,1,2,3,0,1,2,3... The smallest remainder is 0. The ...”
November 28, 2018
GMATGuruNY posted a reply to A club has 10 members. One president and two vice-presidents in the Problem Solving forum
“Number of options for president = 10. (Any of the 10 members.) From the remaining 9 members, the number of ways to choose 2 to serve as vice-president = 9C2 = (9*8)/(2*1) = 36. To combine these options, we multiply: 10*36 = 360. The correct answer is E.”
November 28, 2018
fskilnik@GMATH posted a reply to In the x-y plane, line l passes through points (-1,-1) and ( in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
November 28, 2018
fskilnik@GMATH posted a reply to A store sells only two types of shirts, branded and in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 28, 2018
fskilnik@GMATH posted a reply to An urn contains 10 balls, numbered from 1 to 10. If 2 balls in the Problem Solving forum
“There are exactly 4 equiprobable events: E1 = first ball odd , second ball odd E2 = first ball odd, second ball even E3 = first ball even, second ball odd E4 = first ball even, second ball even Exactly two of the 4 events mentioned above are favorable (E1 and E4), hence the correct answer ...”
November 28, 2018
fskilnik@GMATH posted a reply to At an auto detailing company, it takes 15 minutes for an in the Problem Solving forum
“\Excellent opportunity for UNITS CONTROL, one of the most powerful tools of our method! \This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 28, 2018
fskilnik@GMATH posted a reply to How many integers from 0 to 50, inclusive, have a remainder in the Problem Solving forum
“$$0 \le 3M + 1 \le 50\,\,\,\,\left( {M\,\,{\mathop{\rm int}} } \right)\,\,$$ $$?\,\,\,:\,\,\,\,\# \,\,M\,$$ $$ - 1 \le 3M \le 49\,\,\,\,\left( {M\,\,{\mathop{\rm int}} } \right)\,\,\,\, \Leftrightarrow \,\,\,\,0 \le 3M \le 48\,\,\,\,\, \Leftrightarrow \,\,\,\,\,0 \le M \le 16$$ $$? = 16 + 1 = ...”
November 27, 2018
Brent@GMATPrepNow posted a reply to The weights of four packages are 1, 3, 5, and 7 pounds, resp in the Problem Solving forum
“That''s MUCH better than my solution!! Cheers, Brent<i class="em em---1"></i>”
November 27, 2018
Brent@GMATPrepNow posted a reply to The weights of four packages are 1, 3, 5, and 7 pounds, resp in the Problem Solving forum
“For each answer choice, if we CAN create the total given weight, then we can ELIMINATE that answer choice. a) 9 = 1 + 3 + 5 ELIMINATE b) 10 = 3 + 7 ELIMINATE c) 12 = 5 + 7 ELIMINATE d) 13 = 1 + 5 + 7 ELIMINATE By the process of elimination, the correct answer is E Cheers, Brent”
November 27, 2018
Brent@GMATPrepNow posted a reply to If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime fac in the Problem Solving forum
“GIVEN: 1 + 2 + 2^2 + ... + 2^n = 2^{n+1} - 1 So, 1 + 2 + 2^2 + ... + 2^7 = 2^{7+1} - 1 = 2^8 - 1 If we recognize that the above expression is a difference of squares, we can factor it to get.... 2^8 - 1 = (2^4 + 1)(2^4 - 1) = (2^4 + 1)(2^2 + 1)(2^2 - 1) = (16 + 1)(4 + 1)(4 - 1) = ...”
November 27, 2018
Brent@GMATPrepNow posted a reply to How many integers from 0 to 50, inclusive, have a remainder in the Problem Solving forum
“When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), ...”
November 27, 2018
fskilnik@GMATH posted a reply to If x and y are integers and 2 < x < y, does y = 16 ? in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
November 27, 2018
Brent@GMATPrepNow posted a reply to Is b even? in the Data Sufficiency forum
“Target question: Is b even? KEY POINT: We are not told that a and b are INTEGERS. As such, we can jump straight to. . . . Statements 1 and 2 combined There are several values of a and b that satisfy BOTH statements. Here are two: Case a: a = 4 and b = 2. Notice that a/b = 4/2 = 2, ...”
November 27, 2018
Brent@GMATPrepNow posted a reply to In the rectangular coordinate system shown above, does the in the Data Sufficiency forum
“Target question: Does line k intersect quadrant II? Statement 1: The slope of k is -1/6 Here are a few lines with slope -1/6 https://i.imgur.com/1p6USLh.png KEY CONCEPT: As we travel from right to left along a line with slope -1/6, we keep moving up. So, at some point, the line will ...”
November 27, 2018
Brent@GMATPrepNow posted a reply to A certain recipe calls for 2 cups of sugar and 3 1/2 cups of in the Problem Solving forum
“Judging from the OA, I''ve added some key text below A certain recipe calls for 2 cups of sugar and 3 1/2 cups of flour So sugar/flour = 2/3.5 Check answer choices . . . . not there. Looks like we need to create a ratio that''s EQUIVALENT to 2/3.5 Multiply top and bottom by 2 to get ...”
November 27, 2018
fskilnik@GMATH posted a reply to if the straight line y = x + c is tangent to the circle (x-1 in the Problem Solving forum
“\The solution I present below is essentially geometric: https://i.ibb.co/LPqCH5R/26-Nov18-4z.gif \I invite other members of this great community to present other approaches. (I will show an algebraic solution in a couple of days, if nobody offers it before!) Regards, Fabio.”
November 26, 2018
Brent@GMATPrepNow posted a reply to When the positive integer x is divided by 6, the remainder in the Problem Solving forum
“Good catch - thanks Fabio! I''ve edited my response accordingly. Cheers, Brent”
November 26, 2018
fskilnik@GMATH posted a reply to When the positive integer x is divided by 6, the remainder in the Problem Solving forum
“Brent´s second solution is the one I value most. Just a small correction: x = 6k + 3 + 1 = 3 (2k+1) + 1. (Since Q=2k+1 must be an integer, x=3Q+1 is not divisible by 3 and it is done.) Regards, Fabio.”
November 26, 2018
Brent@GMATPrepNow posted a reply to In a certain state, gasoline stations compute the price per in the Problem Solving forum
“In a certain state, gasoline stations compute the price per gallon "p", in dollars, charged at the pump by adding a 4 percent sales tax to the dealer''s price per gallon "d", in dollars . . . We can write: p = d + 4% of d = d + 0.04d = 1.04d So, we have: p = 1.04d . . . ...”
November 26, 2018
Brent@GMATPrepNow posted a reply to When the positive integer x is divided by 6, the remainder in the Problem Solving forum
“APPROACH#2 When the positive integer x is divided by 6, the remainder is 4 In other words, x is 4 greater than some multiple of 6 We can write: x = 6k + 4, where k is an integer If x = 6k + 4, we can also write: x = 6k + 3 + 1 Factor to get: x = 3(2k + 1) + 1 Since 2k+1 must be an integer, ...”
November 26, 2018
Brent@GMATPrepNow posted a reply to When the positive integer x is divided by 6, the remainder in the Problem Solving forum
“----ASIDE------------------- When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, ...”
November 26, 2018
Brent@GMATPrepNow posted a reply to A chili recipe calls for the final mixture to consist of 1/2 in the Problem Solving forum
“A chili recipe calls for the final mixture to consist of 1/2 meat and 1/3 beans, with the remainder an even mixture of sauce and various spices Let''s see what fraction of the final mixture is sauce and various spices 1/2 + 1/3 = 3/6 + 2/6 = 5/6 If 5/6 of the mixture is meat and beans, then the ...”
November 26, 2018
Brent@GMATPrepNow posted a reply to A store sells only two types of shirts, branded and in the Data Sufficiency forum
“ Given: All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. Let B = # of branded shirts sold Let N = # of non-branded shirts sold If a TOTAL of 30 shirts were sold, we can write: N + ...”
November 26, 2018
Brent@GMATPrepNow posted a reply to Of the 4,800 voters who voted for or against Resolution K, in the Data Sufficiency forum
“Target question: What was the total number of female voters who voted for Resolution K? When solving Data Sufficiency questions, it''s important that you don''t perform more calculations than are necessary. So, for this question, we need only determine whether or not we have sufficient ...”
November 26, 2018
fskilnik@GMATH posted a reply to For any integers a, b, c, and d, sechigh(a, b, c, d) is the in the Data Sufficiency forum
“$$? = {\rm{sechigh}}\left( {6,7,11,y} \right)\,\,\,\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 26, 2018
fskilnik@GMATH posted a reply to If x and y are positive integers, is √15xy an integer? in the Data Sufficiency forum
“$$x,y\,\, \ge 1\,\,{\rm{ints}}\,\,\,\left( * \right)$$ $$\sqrt {15xy} \,\,\mathop = \limits^? \,\,\operatorname{int} \,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\boxed{\,xy\,\,\mathop = \limits^? \,\,15 \cdot {M^2}\,\,\,,\,\,\,M \geqslant 1\,\,\operatorname{int} \,}$$ ...”
November 26, 2018
fskilnik@GMATH posted a reply to A six-digit positive integer, ABCDEF, is divisible by all in the Problem Solving forum
“Very nice problem, but absolutely not GMAT-time-like! $${{\left\langle {ABCDEF} \right\rangle } \over {LCM\left( {2,3,4,5,6} \right)}} = {\mathop{\rm int}} $$ $$\left\langle {ABCDEF} \right\rangle \,\,\,\,{\rm{with}}\,\,\,\left\{ \matrix{ \,{\rm{A}} \in \left\{ {1,2, \ldots ,6} \right\} \hfill ...”
November 26, 2018
fskilnik@GMATH posted a reply to Let A=2^50, B=3^30, and C=4^20. Which of the following is tr in the Problem Solving forum
“$$?\,\,\,:\,\,\,A\,,\,\,B\,\,,\,\,C\,\,\,{\rm{increasing}}\,\,{\rm{order}}\,$$ $$\left. \matrix{ A = {2^{50}} = {\left( {{2^5}} \right)^{10}} = {32^{10}} \hfill \cr B = {3^{30}} = {\left( {{3^3}} \right)^{10}} = {27^{10}}\,\,\, \hfill \cr C = {4^{20}} = {\left( {{4^2}} \right)^{10}} = ...”
November 26, 2018
fskilnik@GMATH posted a reply to Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} If a, b in the Problem Solving forum
“Set Q is contained in set P , therefore all the differences between any two elements of Q belong to the set of the differences between any two elements of P. That understood, it is immediate that Range P ≥ Range Q . The fact that Range P and Range Q may be equal (see below), guarantees that ...”
November 25, 2018
fskilnik@GMATH posted a new topic called if the straight line y = x + c is tangent to the circle (x-1 in the Problem Solving forum
“If the straight line y = x + c is tangent to the circle (x-1)^2 + (y+2)^2 = 4, what is the maximum possible value for the constant c ? $$(A) \,\, 1 - \sqrt 2 \,\,\,\,\,\, (B) \,\, 1 + \sqrt 2 \,\,\,\,\,\, (C) \,\, 3 - 2 \sqrt 3 \,\,\,\,\,\, (D) \,\, -3 + 2 \sqrt 2 \,\,\,\,\,\, (E) \,\, ...”
November 25, 2018
Brent@GMATPrepNow posted a reply to If x and y are nonnegative integers, what is the value of y? in the Data Sufficiency forum
“The above solutions are great. I just wanted to add that whenever you''re told that a value is non-negative on the GMAT, you should be sure to consider what happens when that value equals zero Keep in mind that, if the test-makers wanted to restrict a value to POSITIVE values only, then they''d ...”
November 25, 2018
Brent@GMATPrepNow posted a reply to If n is the smallest integer such that 432 times n is the in the Problem Solving forum
“IMPORTANT CONCEPT: The prime factorization of a perfect square (the square of an integer) will have an even number of each prime For example: 400 is a perfect square. 400 = 2x2x2x2x5x5. Here, we have four 2''s and two 5''s This should make sense, because the even numbers allow us to split the ...”
November 25, 2018
Brent@GMATPrepNow posted a reply to Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} If a, b in the Problem Solving forum
“The key here is MUST be true. So, if we can find an example in which a statement is NOT true, then we can ELIMINATE it. We have: Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} I''ll make the extra value red so it''s easier to compare the two sets So, the sets COULD be: Set P {1, 2, ...”
November 25, 2018
Brent@GMATPrepNow posted a reply to Every object in a box is either a sphere or a cube, and ever in the Data Sufficiency forum
“Target question: How many objects are in the box? Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green. We can solve this using the Double Matrix Method. This technique can be used for most questions featuring a population in which ...”
November 25, 2018
fskilnik@GMATH posted a reply to Every object in a box is either a sphere or a cube, and ever in the Data Sufficiency forum
“\Let´s go straight to (1+2): \The correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 25, 2018
fskilnik@GMATH posted a reply to If x and y are nonnegative integers, what is the value of y? in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 25, 2018