# meenanke

Brent@GMATPrepNow posted a reply to A children's theater sels tickets to a show. Tickets for in the Data Sufficiency forum
“ Given: Tickets for children cost $10 and tickets for adults cost$35. Ticket revenues from the last performance were 390 Let A = # of adults in attendance Let C = # of children in attendance So, we can write: 35A + 10C = 390 Since A and C must be POSITIVE INTEGERS, there are not many ...” Today GMATGuruNY posted a reply to A number when divided by 4 and 5 leaves remainders 1 and 4 in the Problem Solving forum “Please fix the prompt, which has been transcribed incorrectly. It should include the word in red:” Today fskilnik@GMATH posted a reply to If p, q and r are prime, with p < q < r, p=? in the Data Sufficiency forum “$$p < q < r\,\,{\rm{primes}}\,\,\,\,\left( * \right)$$ $$? = p$$ $$\left( 1 \right)\,\,{\left( {pq} \right)^3} = 216 = {2^3} \cdot {3^3}\,\,\,\,\, \Rightarrow \,\,\,pq = 2 \cdot 3\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left( {p,q} \right) = \left( {2,3} ...” Today fskilnik@GMATH posted a reply to A number when divided by 4 and 5 leaves remainders 1 and 4 in the Problem Solving forum “ Now let´s avoid street fighting and embrace BJJ, a.k.a real MATH !$$\eqalign{ & N = 4Q + 1 \cr & N = 5K + 4 \cr} ? = R\,\,\,\left( {0 \le R \le 19} \right)\,\,\,,\,\,{\rm{where}}\,\,\,N = 20J + R\,\,\,\left( {J\,\,{\mathop{\rm int}} } \right)\,$$...” Today Brent@GMATPrepNow posted a reply to A number when divided by 4 and 5 leaves remainders 1 and 4 in the Problem Solving forum “When it comes to remainders, we have a nice rule that says: If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), ...” Today fskilnik@GMATH posted a reply to A number when divided by 4 and 5 leaves remainders 1 and 4 in the Problem Solving forum “$$\eqalign{ & N = 4Q + 1 \cr & N = 5K + 4 \cr} ? = R\,\,\,\left( {0 \le R \le 19} \right)\,\,\,,\,\,{\rm{where}}\,\,\,N = 20J + R\,\,\,\left( {J\,\,{\mathop{\rm int}} } \right)\,Q,K,J,R\,\,\,{\rm{ints}}$$All alternative choices are numerical, hence we are allowed to ...” Today fskilnik@GMATH posted a reply to A store sold 72 watches for a2,34b, where a2,34b is a 5-dig in the Problem Solving forum “$$? = a + b\,\,\,\,\,\left( {a \ne 0\,\,,\,\,b\,\,\,{\rm{digits}}} \right)\,\,\,\left( * \right){{\left\langle {a234b} \right\rangle } \over {8 \cdot 9}} = {\mathop{\rm int}} \,\,\,\,\,\mathop \Rightarrow \limits^{GCF\left( {8,9} \right)\,\, = \,\,1} \,\,\,\,\,{{\,\left\langle {a234b} ...” Today GMATGuruNY posted a reply to A woman has seven cookies - four chocolate chip and three in the Problem Solving forum “Alternate approach: Case 1: Deborah and Kim each receive an oatmeal cookie In this case, 4 chocolate chip cookies and 1 oatmeal cookie remain. The remaining oatmeal cookie has 5 options: Nicole, Ronit, Mark, Terrance, or no one. Total ways = 5. Case 2: Deborah and Kim each receive a ...” Today fskilnik@GMATH posted a reply to In the xy-plane, point O is located at the origin, point A in the Data Sufficiency forum “$${S_{\Delta ABO}} = \frac{{r \cdot q}}{2}\,\,\mathop < \limits^? \,\,12\,\,\,\,\,\, \Leftrightarrow \,\,\,\boxed{\,\,r \cdot q\,\,\mathop < \limits^? \,\,24\,\,}$$ https://preview.ibb.co/hapUzf/19-Nov18-4j.gif $$\left( 1 \right)\,\,r = 7\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,q = ...” Yesterday Brent@GMATPrepNow posted a reply to The number line above represents which of the following in the Problem Solving forum “We can also solve the question by testing the answer choices Here''s what I mean: The diagram tells us that x= 0 is a solution to the inequality. When we check the answer choices, we see that answer choice D (1 < 2x < 3) does NOT have x = 0 as a solution. When we let x = 0, the ...” Yesterday fskilnik@GMATH posted a reply to If n is an integer between 30 and 50 inclusive, what is the in the Data Sufficiency forum “$$30\,\,\, \le \,\,\,n\,\,{\mathop{\rm int}} \,\,\, \le \,\,\,50\,\,\,\,\left( * \right)? = n\left( 1 \right)\,\,n = 8Q + 7\,\,,\,\,Q\,\,{\mathop{\rm int}} \,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,Q = 3\,\,\,\, \Rightarrow \,\,\,\,\,? = 31\,\, \hfill \cr \,{\rm{Take}}\,\,Q = ...” Yesterday fskilnik@GMATH posted a reply to A rectangular circuit board is designed to have width w in the Problem Solving forum “$$?\,\,\,:\,\,\,\,p,w,k\,\,\,{\rm{relationship}}$$ $$\left\{ \matrix{ \,{\rm{area}}\,\,k \hfill \cr \,{\rm{width}}\,\,w \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{length}} = \,\,{k \over w}$$ $${\rm{perimeter}}\,\,p\,\,\, = \,\,\,2\left( {w + {k \over w}} \right)\,\,\, = ...” Yesterday fskilnik@GMATH posted a reply to The number line above represents which of the following in the Problem Solving forum “$$?\,\,\,:\,\,\, - 3 < x < 1\,\,\,\, \Leftrightarrow \,\,\,\, - 6 < 2x < 2\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{B}} \right)$$This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” Yesterday fskilnik@GMATH posted a reply to Three circles with radii of 2 cm , 3 cm, and 5 cm, in the Problem Solving forum “The correct answer is (B), indeed. https://preview.ibb.co/dhQD9f/19-Nov18-5z.gif This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” Yesterday Brent@GMATPrepNow posted a reply to If n is an integer between 30 and 50 inclusive, what is the in the Data Sufficiency forum “Target question: What is the value of n? Given: n is an integer between 30 and 50 inclusive Statement 1: When n is divided by 8, the remainder is 7 ------ASIDE-------------------------------------- When it comes to remainders, we have a nice rule that says: If N divided by D leaves ...” Yesterday Brent@GMATPrepNow posted a reply to When sold at a 40% discount, a sweater nets the merchant a in the Problem Solving forum “Let''s work BACKWARDS. Let''s say the WHOLESALE price was 100 the merchant made a net profit of 20% on the wholesale cost (which was 100) So, the merchant sold the sweater for 120 Let M = the markup price on the label (before any discounts). So, 40% less than M = 120 In other ...” Yesterday fskilnik@GMATH posted a reply to The Lewiston Road Race is how many kilometers long? in the Data Sufficiency forum “$$? = D\,\,\,\,\,\leftLet´s use UNITS CONTROL, one of the most powerful tools of our method! $$\left( 1 \right)\,\,\,\left( {\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 18, 2018 fskilnik@GMATH posted a reply to All the terms in Set S are integers. Five terms in S are in the Data Sufficiency forum “$$?\,\,\, = \,\,\,x\,\,\, = \,\,\,5 - \left( {\# \,\,{\rm{multiples}}\,\,{\rm{of}}\,\,6} \right)$$https://preview.ibb.co/nxnx0L/18-Nov18-3w.gif$$\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,S = \left\{ {\,2\,,2 \cdot 3\,,2 \cdot {3^2},\,2 \cdot {3^{3\,}},2 \cdot {3^4}\,} ...” November 18, 2018 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! $$? = C\left( {7,k} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = k\,}$$ $$\left( 1 \right)\,\,\,C\left( {7,k + 1} \right) = ...” November 18, 2018 fskilnik@GMATH posted a reply to In the given diagram, the circle touches the y-axis at the in the Problem Solving forum “$$? = \pi {r^2}$$https://preview.ibb.co/bRQWuf/18-Nov18-2.gif$${{7 \cdot r} \over 2} = 21\,\,\,\,\, \Rightarrow \,\,\,\,\,r = 2 \cdot 3\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 36\pi $$This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 18, 2018 fskilnik@GMATH posted a reply to A positive number x is multiplied by 2, and this product is in the Problem Solving forum “$$? = x\,\,\,\,\left( {x > 0} \right)\sqrt {{{2x} \over 3}} = x\,\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,\,{{2x} \over 3} = {x^2}\,\,\,\,\, \Rightarrow \,\,\,\,\,x\left( {3x - 2} \right) = 0\,\,\,\,\,\mathop \Rightarrow \limits^{x\,\, > \,\,0} \,\,\,\,3x - 2 = ...” November 18, 2018 fskilnik@GMATH posted a reply to In a certain two-digit integer, the ratio of the units in the Data Sufficiency forum “\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 17, 2018 fskilnik@GMATH posted a reply to The rate of a certain chemical reaction is directly in the Problem Solving forum “\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 17, 2018 fskilnik@GMATH posted a reply to If p is the sum of the reciprocals of the consecutive intege in the Problem Solving forum “\Conclusion: 10 is greater than 1/p , but 8 and 9 are not. The correct answer is therefore (C). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 17, 2018 GMATGuruNY posted a reply to The Lewiston Road Race is how many kilometers long? in the Data Sufficiency forum “Statement 1: Rate and time have a RECIPROCAL relationship. A rate ratio of (40kph) : (50kph) = 4:5 implies a time ratio of 5:4 = 10:8. The time ratio in blue implies that -- for the time at 40kph to be 2 hours more than the time at 50kph -- the time at 40kph must be 10 hours, while the time at ...” November 17, 2018 Brent@GMATPrepNow posted a reply to Kevin buys beer in bottles and cans. He pays1.00 for each in the Data Sufficiency forum
“Target question: How many bottles of beer did Kevin buy? Given: Kevin pays $1.00 for each can of beer and$1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can ...”
November 16, 2018
GMATGuruNY posted a reply to Tim and Glenn are running laps around a circular track. in the Data Sufficiency forum
“Statement 1: The TIME RATIO for Tim and Glenn = 48:60 = 4:5. Since time and rate have a RECIPROCAL relationship, the RATE RATIO for Tim and Glenn = 5:4. Implication: For every 5 laps that Tim runs, Glenn runs only 4 laps. Thus, after running 5 laps, Tim will have run 1 more lap than Glenn. ...”
November 16, 2018
Brent@GMATPrepNow posted a reply to What is the least possible product of 4 different integers, in the Problem Solving forum
“We want values with the greatest MAGNITUDE So (10)(9)(8)(-5) = -3600 Answer: -3600 Answer: B”
November 16, 2018
Brent@GMATPrepNow posted a reply to A reatil appliance store priced a video recorder at 20 in the Problem Solving forum
“A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200 20% of$200 = $40 So, the retail price =$200 + $40 =$240 If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the ...”
November 16, 2018
Brent@GMATPrepNow posted a reply to Planning is in progress for a fenced, rectangular playground in the Problem Solving forum
“It''s a good idea to first try to understand what the graph is telling us. For example, the leftmost point on the curve has the coordinates (10, 340) This tells us that, if the length of the playground is 10 meters, then a total of 340 meters of fencing is required. This makes sense, since we ...”
November 16, 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 + ...”
November 16, 2018
Brent@GMATPrepNow posted a reply to In the rhombus ABCD, the length of diagonal BD is 6 and the in the Problem Solving forum
“In a rhombus, the diagonals are perpendicular bisectors. http://i1168.photobucket.com/albums/r500/GMATPrepNow/rhmbs1_zps1nyufj6q.png So, we can add our lengths as follows. http://i1168.photobucket.com/albums/r500/GMATPrepNow/rhmbs2_zpskyv3wwkl.png From here, if we focus on one of the 4 ...”
November 16, 2018
fskilnik@GMATH posted a reply to If f(x)=x^2 when x < 0 and f(x)=x when x ≥ 0, what is t in the Data Sufficiency forum
“$$f\left( x \right) = \left\{ \matrix{ \,{x^{2\,\,}},\,\,x < 0 \hfill \cr \,x\,\,,\,\,x \ge 0 \hfill \cr} \right.$$ $$? = f\left( a \right)$$ $$\left( 1 \right)\,\,\,\,\,\left| a \right| = 1\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,a = 1\,\,\,\,\,\, \Rightarrow ...” November 16, 2018 fskilnik@GMATH posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom in the Problem Solving forum “$$? = x\left. \matrix{ {\rm{1 - bed}}\,\,:\,\,\,\$2M\,\,{\rm{per}}\,\,{\rm{month}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,12 \cdot {\rm{\$ }}2M\,\,\,{\rm{per}}\,\,12\,\,{\rm{months}} \hfill \cr {\rm{2 - bed}}\,\,{\rm{:}}\,\,\,\$3M\,\,{\rm{per}}\,\,{\rm{month}}\,\,\,\,\, \Rightarrow ...” November 16, 2018 GMATGuruNY posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom in the Problem Solving forum “Let the one-bedroom rent =$2 per month, implying that the two-bedroom rent = 2 + (50% of 2) = 2 + 1 = $3 per month. Since the rent for a one-bedroom apartment =$2 per month, the total amount to rent a one-bedroom apartment for 12 months = 2*12 = $24. For$24, the number of months yielded for a ...”
November 16, 2018
fskilnik@GMATH posted a reply to Planning is in progress for a fenced, rectangular playground in the Problem Solving forum
“Reading Comprehension is part of the Quantitative Section of the GMAT: https://preview.ibb.co/hXWwpf/16-Nov18-3w.gif Regards, Fabio.”
November 16, 2018
fskilnik@GMATH posted a reply to If 1/x(x-1)+1/x(x+1)=1/(x+1)(x-1), what is the value of x? in the Problem Solving forum
“$$\frac{1}{{x\left( {x - 1} \right)}} + \frac{1}{{x\left( {x + 1} \right)}} = \frac{1}{{\left( {x + 1} \right)\left( {x - 1} \right)}}\,\,\,\,\,\,\,\,\,\,\,\leftThe correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, ...” November 16, 2018 Brent@GMATPrepNow posted a reply to If xy is not equal to zero, what is the ratio of x to y? in the Data Sufficiency forum “NOTE: We can write the ratio x:y as a fraction x/y Target question: What is the value of x/y ? Statement 1: 3x = 4y Divide both sides by y to get: 3x/y = 4 Divide both sides by 3 to get: x/y = 4/3 So, the answer to the target question is x/y = 4/3 Since we can answer the target question ...” November 16, 2018 Brent@GMATPrepNow posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom in the Problem Solving forum “A fast and easy approach is to assign a "nice" value to the monthly rent of a ONE-bedroom apartment. Let''s say the rent on a ONE-bedroom apartment is 100 per month A two-bedroom apartment costs 50% more to rent than a one-bedroom apartment 50% of 100 = 50 So, the rent on a ...” November 15, 2018 fskilnik@GMATH posted a reply to Is the 5-digit positive integer abc000 divisible by 24? in the Data Sufficiency forum “$$\frac{{\left\langle {abc000} \right\rangle }}{{3 \cdot 8}}\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\frac{{\,1000 \cdot \left\langle {abc} \right\rangle }}{{3 \cdot 8}}\,\,\mathop = \limits^? \,\,\,\operatorname{int} \,\,\,\,\,\,\, ...”
November 15, 2018
fskilnik@GMATH posted a reply to If line k in the xy-coordinate plane has the equation Ax + B in the Data Sufficiency forum
“Important: from the stem we know (implicitly) that line k HAS a slope, i.e., line k is non-vertical, i.e., B is nonzero. $$Ax + By = C\,\,\,\,\,\mathop \Leftrightarrow \limits^{B\,\, \ne \,\,0} \,\,\,y\,\, = - {A \over B}\left( x \right)\,\, + \,\,{C \over A}$$ $$? = - {A \over B}$$ ...”
November 15, 2018
fskilnik@GMATH posted a reply to A certain store will order 25 crates of apples. The apples in the Problem Solving forum
“$$?\,\,\, = \,\,\,\min \left( W \right)$$ $$M + R + W = 25\,\,\left( * \right)$$ $$\left\{ \matrix{ \,W > M \ge 1\,\,\,{\rm{ints}} \hfill \cr \,W > R \ge 1\,\,\,{\rm{ints}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{ \,W = M + ...” November 15, 2018 fskilnik@GMATH posted a reply to If xy ≠ 0 and x^2+4y^2=4xy, (x+y)/(x-y)=? in the Problem Solving forum “$$\left. \matrix{ x,y\,\, \ne 0 \hfill \cr {x^2} + 4{y^2} = 4xy\,\,\,\left( * \right)\,\, \hfill \cr} \right\}\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = {{x + y} \over {x - y}}$$Let´s do brutal street fighting (a.k.a. explore a particular case)!$$x = 4\,\,\,\,\,\,\mathop \Rightarrow ...”
November 15, 2018
fskilnik@GMATH posted a reply to Over a four-game stretch, Dennis's bowling scope average 240 in the Problem Solving forum
“$$?\,\,\,\, = \,\,\,\,\Delta \% \left( {240 \to 300} \right)\,\,\, = \,\,\,{{60} \over {240}}\,\,\, = \,\,\,{1 \over 4}\,\,\, = \,\,\,25\%$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 15, 2018
fskilnik@GMATH posted a reply to If xy : yz : zx = 1:2:3, then what is x : y : z ? in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 15, 2018
Brent@GMATPrepNow posted a reply to If line k in the xy-coordinate plane has the equation Ax + B in the Data Sufficiency forum
“ Given: Line k has the equation Ax + By = C Target question: What is the slope of line k ? This is a good candidate for rephrasing the target question. Let''s take the given equation Ax + By = C and rewrite it in slope y-intercept form, y = mx + b, where m = slope and b = y-intercept ...”
November 15, 2018
Brent@GMATPrepNow posted a reply to What is the ratio of x:y:z? in the Data Sufficiency forum
“Target question: What is the ratio of x:y:z? Statement 1: xy = 14 In information about z Statement 1 is NOT SUFFICIENT Statement 2: yz = 21 In information about x Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined There are several values of x, y and z that satisfy BOTH ...”
November 15, 2018
Brent@GMATPrepNow posted a reply to If xy : yz : zx = 1:2:3, then what is x : y : z ? in the Problem Solving forum
“Let''s focus on pairs of values If xy : yz : zx = 1:2:3, then we know that xy : yz = 1:2 Take xy : yz and divide both sides by y to get the EQUIVALENT ratio x:z This means x:z = 1:2 Check the answer choices... A. 2 : 3 : 6 this answer choice says x:z = 2:6. We need x:z = 1:2 ELIMINATE A ...”
November 15, 2018
Brent@GMATPrepNow posted a reply to Over a four-game stretch, Dennis's bowling scope average 240 in the Problem Solving forum
“In other words, an increase from 240 to 300 represents what kind of percent increase? Percent increase = (100)(new - old)/old = (100)(300 - 240)/240 = (100)(60)/240 = (100)(1/4) = 25% Answer: B Cheers, Brent”
November 15, 2018
GMATGuruNY posted a reply to A certain store will order 25 crates of apples. The apples in the Problem Solving forum
“Let W = Winesap crates, M = McIntosh crates, and R = Roma crates. Since a total of 25 crates are ordered, we get: W + M + R = 25. To MINIMIZE the value of W, we must MAXIMIZE the values of M and R. Since the store is to order more crates of Winesap than crates of McIntosh and more crates of ...”
November 15, 2018
GMATGuruNY posted a reply to A marzipan factory has two machines producing marzipan. in the Data Sufficiency forum
“The prompt states: Every day, the two machines operate constantly from 08:00 to 18:00. As shown in my post above, Statement 2 yields the following rate ratio: (W alone) : (W and D together) = 1:5. The rate ratio indicates that -- of every 5 kg produced when W and D work together from 8:00 to ...”
November 15, 2018
GMATGuruNY posted a reply to Organized in 1966 by the Fish and Wildlife in the Sentence Correction forum
“Generally, for + VERBing is an ADJECTIVE serving to modify a NOUN. A: The Breeding Bird Survey uses annual roadside counts along established routes for monitoring. Here, for monitoring seems to be an ADJECTIVE modifying routes, implying that the ROUTES were designed FOR MONITORING. Not the ...”
November 15, 2018
Brent@GMATPrepNow posted a reply to The table above shows the distribution of tests scores for a in the Problem Solving forum
“Since we have an ODD number of values, the median will be the MIDDLEMOST value. In other words, if we arrange all 73 values in ASCENDING order, the median will be the 37th value (i.e., 36 values are below and 36 values are above). The table says the first 2 scores in the 50-59 range. So, the 1st ...”
November 15, 2018
Brent@GMATPrepNow posted a reply to # X-Axis Intercepts in the Problem Solving forum
“Let''s find some points that lie on each of the curves. So, for each equation, we''ll find a pair of values (an x-value and a y-value) that satisfy each equation. We''ll do so by plugging in some x-values and calculating the corresponding y-values. Let''s start with x = 0 Plug x = 0 into ...”
November 14, 2018
GMATGuruNY posted a reply to A marzipan factory has two machines producing marzipan. in the Data Sufficiency forum
“Statement 1: Let N = 50 kg. Since W and D produce the entire 50 kg over the 10 hours between 8:00 and 18:00, the combined rate for W and D = 50/10 = 5 kg per hour. Since W takes 25 hours to produce N/2 = 25 kg, W''s rate alone = w/t = 25/25 = 1 kg per hour. Of every 5 kg produced each hour ...”
November 14, 2018
GMATGuruNY posted a reply to If x and y are unknown positive integers, is the mean of the in the Data Sufficiency forum
“Known values, in ascending order: 1, 5, 6, 7 Statement 1: x+y = 7 Mean = sum/quantity = (1+5+6+7+x+y)/6 = (1+5+6+7+7)/6 = 26/6 = 13/3 = 4.33. Text EXTREMES. Case 1: x and y are far from each other If x=1 and y=6, we get: 1, 1. 5, 6, 6, 7 Median = (5+6)/2 = 11/2 = 5.5 Case 2: x and y ...”
November 14, 2018
GMATGuruNY posted a reply to How many positive two-digit numbers yield a remainder of 1 in the Problem Solving forum
“Let x = the two-digit number. Since dividing by 4 leaves a remainder of 1, x is equal to one more than a multiple of 4: x = 4k + 1 Since dividing by 14 leaves a remainder of 1, x is equal to one more than a multiple of 14: x = 14m + 1 Since the two expressions in blue must be equal, we ...”
November 14, 2018
fskilnik@GMATH posted a reply to Is |x|/x equal to -1? in the Data Sufficiency forum
“Important: the stem implicitly assumes x is nonzero. (Reason: when x=0, |x|/x is not defined and the question itself would not make sense!) \The correct answer is therefore (A). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 14, 2018
fskilnik@GMATH posted a reply to The range of set X is 9 and the range of set Y is 18. Which in the Problem Solving forum
“\The range of Y guarantees that there are two elements in Y that differ by exactly 18 units. Those elements are also in the union of X and Y, therefore the range of XUY is at least 18. The correct answer is therefore (A). This solution follows the notations and rationale taught in the ...”
November 14, 2018
fskilnik@GMATH posted a reply to How many positive two-digit numbers yield a remainder of 1 in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 14, 2018
Brent@GMATPrepNow posted a reply to How many positive two-digit numbers yield a remainder of 1 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 14, 2018
fskilnik@GMATH posted a reply to GMATPrep in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 13, 2018
fskilnik@GMATH posted a reply to In a school election, Joan and Peter were the only candidate in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 13, 2018
fskilnik@GMATH posted a reply to What is the area of the quadrilateral with vertices A, B, C, in the Data Sufficiency forum
“\Let´s BIFURCATE statements (1) and (2) together, so that we prove the correct answer is (E). \https://preview.ibb.co/faEgfA/12-Nov18-7z.gif Note that a square with edge 4 has an area of 16, while the other rhombus (shown in the right) has an area different from 16. (A careful reader ...”
November 13, 2018
fskilnik@GMATH posted a reply to When m and n are positive integers, is m!*n! an integer squa in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
November 13, 2018
fskilnik@GMATH posted a reply to A chemical supply company has 60 liters of a 40% HNO3 in the Problem Solving forum
“Perfect opportunity for the Alligation and Bruce Lee (when we make numerators equal)! https://preview.ibb.co/mPxqs0/13-Nov18-4w.gif \This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
November 13, 2018
fskilnik@GMATH posted a reply to Jake and Ryan worked together on a job for which they were in the Problem Solving forum
“$$\left. \matrix{ {\rm{Ryan}}\,\,\left\{ \matrix{ \,\,5t\,\,\,{\rm{hours}} \hfill \cr \,\,\ \,\,\left( {a - b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a - b} \over {5t}}\,\,\,{\ \over {{\rm{hour}}}} \hfill \cr {\rm{Jake}}\,\,\,\,\left\{ ...” November 13, 2018 GMATGuruNY posted a reply to On a wedding catering service, An experienced chef can in the Problem Solving forum “Let service = 24 units. Rate for each experienced chef = w/t = 24/8 = 3 units per hour. Rate for each novice chef = w/t = 24/12 = 2 units per hour. Combined rate for 1 experienced chef and 1 novice chef working together = 3+2 = 5 units per hour. To produce 24 units in 1.6 hours, rate = w/t = ...” November 13, 2018 GMATGuruNY posted a reply to Jake and Ryan worked together on a job for which they were in the Problem Solving forum “Let the hourly wage = 1 per hour. Let Ryan''s time = 10 hours, implying that Jake''s time = 10 + (20% of 10) = 10 + 2 = 12 hours. Thus: Total number of work hours = 10+12 = 22 hours. Total pay = (hourly wage)(total number of work hours) = 1*22 = 22. Since the total pay = 10+12 = 22, and ...” November 13, 2018 fskilnik@GMATH posted a reply to If 60! is written out as an integer, with how many in the Problem Solving forum “The reason why "the counting of 5´s recipe" (mentioned and shown in the post above) works is explained here: https://www.beatthegmat.com/if-n-is-the-greatest-positive-integer-for-which-5-n-is-a-fac-t304112.html#819465 Regards, Fabio.” November 13, 2018 Brent@GMATPrepNow posted a reply to When Leo imported a certain item, he paid a 7 percent import in the Problem Solving forum “Here''s a step-by-step algebraic solution. Let T = the TOTAL value of the item. Leo paid a 7% import tax on the portion of the total value of the item in EXCESS of 1000 So, Leo pays tax on the amount that''s GREATER then 1000 So, Leo pays 7% tax on (T - 1000) We can write: import tax = ...” November 13, 2018 Brent@GMATPrepNow posted a reply to If xy ≠ 0 and x^2+4y^2=4xy, (x+y)/(x-y)=? in the Problem Solving forum “GIVEN: x² + 4y² = 4xy Subtract 4xy from both sides to get: x² - 4xy + 4y² = 0 Factor left side to get: (x - 2y)(x - 2y) = 0 So, we can conclude that (x - 2y) = 0, which means x = 2y Now take (x+y)/(x-y) and replace x with 2y to get: (x + y)/(x - y) = (2y + y)/(2y - y) = 3y/y = 3 ...” November 13, 2018 GMATGuruNY posted a reply to A store purchased 20 coats that each cost an equal amount in the Data Sufficiency forum “Statement 1: If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been 2,400 When the selling price per coat is doubled, the resulting profit per coat = (total profit)/(number of coats) = 2400/20 = 120. Case 1: Double the selling price = ...” November 13, 2018 GMATGuruNY posted a reply to If 60! is written out as an integer, with how many in the Problem Solving forum “60! = 60*59*58*....*3*2*1. Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 60! will yield a 0 at the end of the integer representation of 60!. The prime-factorization of 60! is composed of FAR MORE 2''S than 5''s. Thus, the number of 0''s depends on the ...” November 13, 2018 fskilnik@GMATH posted a reply to What is the area of the quadrilateral with vertices A, B, C, in the Data Sufficiency forum “\Let´s BIFURCATE statements (1) and (2) together, so that we prove the correct answer is (E). \https://preview.ibb.co/faEgfA/12-Nov18-7z.gif Note that a square with edge 4 has an area of 16, while the other rhombus (shown in the right) has an area different from 16. (A careful reader ...” November 13, 2018 GMATGuruNY posted a reply to In the figure AB and CD are two diameters of circle. in the Problem Solving forum “An INSCRIBED ANGLE is formed by two chords. A CENTRAL ANGLE is formed by two radii. When an inscribed angle and a central angle intercept the same two points on a circle, the inscribed angle is 1/2 the central angle. https://i.postimg.cc/qgbxWKdW/Angle-CEB-1.png Here, inscribed angle CFB and ...” November 12, 2018 fskilnik@GMATH posted a reply to OG #217 question in the Problem Solving forum “$$\left( J \right)\,\,{\text{Junior}}\,\,:\,\,\,1000\,\,{\text{students}}\,\,,\,\,\,{J_1}\,,\,{J_2},\,\, \ldots \,\,,\,\,{J_{60}}\,\,{\text{among}}\,\,{\text{them}}\,\,\,\left( {{\text{the}}\,\,{\text{ones}}\,\,{\text{with}}\,\,{\text{senior}}\,\,{\text{siblings}}} \right)\left( S ...”
November 12, 2018
Brent@GMATPrepNow posted a reply to OG #217 question in the Problem Solving forum
“P(selecting a sibling pair) = P(select a junior with a sibling AND select the senior who is that junior''s sibling) = P(select a junior with a sibling) x P(select the senior who is that junior''s siblingx 1/800 = 60/800,000 = 3/40,000 = A Note: P(select a junior with a sibling) = 60/1000, ...”
November 12, 2018
fskilnik@GMATH posted a reply to What is the value of f(10)? in the Data Sufficiency forum
“The proposer´s idea (when both statements are considered together) is probably based on the following: $$f\left( {10} \right) = 2 \cdot f\left( 7 \right) = {2^2} \cdot f\left( 4 \right) = {2^3} \cdot f\left( 1 \right) = {2^4}$$ If so, there is a continuity problem related to the (not ...”
November 12, 2018
Brent@GMATPrepNow posted a reply to In the figure AB and CD are two diameters of circle. in the Problem Solving forum
“Let''s use some useful circle properties First let''s add a blue line, to divide ∠CEB into 2 angles https://i.imgur.com/xe05QIU.png CD is the DIAMETER of the circle Since ∠CED is an inscribed angle containing (aka "holding") the diameter, we can conclude that ∠CED = 90° ...”
November 12, 2018
fskilnik@GMATH posted a reply to Is the number of workers required to create w1 widgets at r1 in the Data Sufficiency forum
“Excellent opportunity for UNITS CONTROL, one of the most powerful tools of our method! $$N \ge 1\,\,{\mathop{\rm int}} \,\,{\rm{workers}}\,\,\,\,\,\, \to \,\,\,\,\,{w_1}\,\,{\rm{widgets}}\,\,\,\left( {{{1\,\,{\rm{minute}}} \over {N \cdot {r_1}\,\,{\rm{widgets}}}}} \right)\,\,\,\,\, = ...” November 12, 2018 fskilnik@GMATH posted a reply to A state legislature had a total of 96 members. The members in the Data Sufficiency forum “$$96\,\,\left\{ \matrix{ \,25\,\,:\,\,{\rm{absent}} \hfill \cr \,{\rm{3}}\,\,:\,\,{\rm{abstained}} \hfill \cr \,x\,\,:\,\,{\rm{for }} \hfill \cr \,{\rm{96}} - \left( {28 + x} \right)\,\,:\,\,{\rm{against}}\, \hfill \cr} \right.\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,\,\,? = x\left( 1 ...”
November 12, 2018
fskilnik@GMATH posted a reply to What is the area of a regular octagon with side-length 2? in the Problem Solving forum
“$$? = {S_{{\rm{tot}}}} = 2 \cdot {S_{ABCD}} + {S_{ADEH}}$$ https://preview.ibb.co/iQsMCq/12-Nov18-5r.gif $$\left. \matrix{ {S_{ABCD}}\,\,\, = \,\,\,2\left( {{{x \cdot x} \over 2}} \right) + 2x = {x^2} + 2x\,\,\,\, \hfill \cr {S_{ADEH}} = 2\left( {2x + 2} \right) = 4x + 4 \hfill \cr} ...” November 12, 2018 fskilnik@GMATH posted a reply to In the figure AB and CD are two diameters of circle. in the Problem Solving forum “All angles are measured in degrees.$$? = x = \angle CEB$$https://preview.ibb.co/ejhtQA/12-Nov18-4w.gif 01. Triangle AOC is isosceles with base AC, hence the 66-degrees angle is justified. 02. Angle BAC is inscribed in the circle, hence the 132-degrees red arc (CEB) is justified. 03. ...” November 12, 2018 Brent@GMATPrepNow posted a reply to Is the tallest child in Class A taller than tallest child in in the Data Sufficiency forum “Target question: Is the tallest child in Class A is taller than tallest child in Class B? Jump to . . . Statements 1 and 2 COMBINED There are several scenarios that satisfy BOTH statements. Here are two: Case a: Class A heights = {1, 50} and Class B heights = {2, 40}. In this case, the ...” November 12, 2018 Brent@GMATPrepNow posted a reply to Eight women and two men are available to serve on a in the Problem Solving forum “When it comes to probability questions involving "at least," it''s best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting at least 1 man) = 1 - P(not getting at least 1 man) What does it mean to not get at least 1 man? ...” November 11, 2018 Brent@GMATPrepNow posted a reply to If the positive integer n is greater than 6, what is the in the Data Sufficiency forum “Here''s a somewhat long approach (but it works!): Target question: What is the remainder when n is divided by 6? Given: Positive integer n is greater than 6 Statement 1: When n is divided by 9, the remainder is 2. ------ASIDE---------------- When it comes to remainders, we have a ...” November 11, 2018 Brent@GMATPrepNow posted a reply to If x and y are positive integers, what is the remainder when in the Data Sufficiency forum “Hi Swerve, To avoid ambiguity, you might want to add some spaces or brackets to the original expression. As it stands, 10^x+y could be interpreted as either 10^(x+y) or (10^x) + y Cheers, Brent” November 11, 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}}\,?\,\,\,:\,\,\,\left( {{{10}^x} + y} \right)\,\,{\rm{remainder}}\,\,{\rm{when}}\,\,{\rm{divided}}\,\,{\rm{by}}\,\,y\left( 1 \right)\,\,x = 50\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,y = 2\,\,\,\, \Rightarrow \,\,\,\,\,{10^{50}} + 2\,\,{\rm{even}}\,\,\,\, ...”
November 11, 2018
fskilnik@GMATH posted a reply to If the positive integer n is greater than 6, what is the in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to An appliance store purchases a radio for m dollars. The in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to What is the greatest common factor of positive integers in the Data Sufficiency forum
“\This argument follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to If x and y are positive integers such that x = 8y + 12, what in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to A gardener is going to plant 2 red rosebushes and 2 white in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to The Aam-Aadmi Party in the Problem Solving forum
“https://preview.ibb.co/iJa4fA/11-Nov18-4z.gif \This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to Which of the following is closest to the value of (2^23) in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
fskilnik@GMATH posted a reply to Eight women and two men are available to serve on a in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 11, 2018
GMATGuruNY posted a reply to If x and y are positive integers such that x = 8y + 12, what in the Data Sufficiency forum
“Statement 1: x=12u, where u is an integer and x=8y+12. In other words, x is a multiple of 12. For x to be a multiple of 12, 8y must be a multiple of 12. If y=3, then x = 8*3 + 12 = 36. The GCD of 3 and 36 is 3. If y=6, then x = 8*6 + 12 = 60. The GCD of 6 and 60 is 6. Since the ...”
November 11, 2018
GMATGuruNY posted a reply to Eight women and two men are available to serve on a in the Problem Solving forum
“P(at least 1 man) = 1 - P(no men). P(no men): P(1st person selected is a woman) = 8/10. (Of the 10 people, 8 are women.) P(2nd person selected is a woman) = 7/9. (Of the 9 remaining people, 7 are women.) P(3rd person selected is a woman) = 6/8. (Of the 8 remaining people, 6 are women.) To ...”
November 11, 2018
Brent@GMATPrepNow posted a reply to If x and y are positive integers such that x = 8y + 12, what in the Data Sufficiency forum
“Target question: What is the greatest common divisor of x and y? Given: x = 8y + 12 Statement 1: x = 12u, where u is an integer. There are several pairs of values that satisfy the given conditions. Here are two: Case a: x=36 and y=3, in which case the GCD of x and y is 3 Case b: x=60 ...”
November 11, 2018
Brent@GMATPrepNow posted a reply to Which of the following is closest to the value of (2^23) in the Problem Solving forum
“(2^23)(5^26) = (2^23)(5^23)(5^3) = (2^23)(5^23)(5^3) = (10^23)(5^3) = (10^23)(125) ≈ (10^23)(100) ≈(10^23)(10^2) ≈10^25 Answer: C Cheers, Brent”
November 11, 2018
Brent@GMATPrepNow posted a reply to A gardener is going to plant 2 red rosebushes and 2 white in the Problem Solving forum
“We can also apply probability rules: P(2 middle bushes are red) = P(1st bush is white AND 2nd bush is red AND 3rd bush is red AND 4th bush is white) = P(1st bush is white) x P(2nd bush is red) x P(3rd bush is red) x P(4th bush is white) = 2/4 x 2/3 x 1/2 x 1/1 = 1/6 = B Cheers, Brent”
November 11, 2018
Brent@GMATPrepNow posted a reply to A gardener is going to plant 2 red rosebushes and 2 white in the Problem Solving forum
“As with many probability questions, we can also solve this using counting techniques. P(2 middle are red) = (# of outcomes with 2 red in middle)/(total number of outcomes) Label the 4 bushes as W1, W2, R1, R2 total number of outcomes We have 4 plants, so we can arrange them in 4! ways = ...”
November 11, 2018
GMATGuruNY posted a reply to A gardener is going to plant 2 red rosebushes and 2 white in the Problem Solving forum
“Moving LEFT TO RIGHT along the row: P(1st rosebush is white) = 2/4. (Of the 4 rosebushes, 2 are white.) P(2nd rosebush is red) = 2/3. (Of the 3 remaining rosebushes, 2 are red.) P(3rd rosebush is red) = 1/2. (Of the 2 remaining rosebushes, 1 is red.) P(4th rosebush is white) = 1/1. (The one ...”
November 10, 2018
Brent@GMATPrepNow posted a reply to Of the first three dozen cookies baked at a bake shop on a in the Data Sufficiency forum
“ Given: Of the first three dozen (36) cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. 1/2 of the remaining cookies that were baked that day were chocolate chip cookies, 1/3 of 36 = 12. So, 12 chocolate cookies were baked in the first round of baking. Let x = ...”
November 10, 2018
Brent@GMATPrepNow posted a reply to There were 36,000 hardback copies of a certain novel sold in the Problem Solving forum
“From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold Let x = number of hardback copies sold during this time So 9x = number of paperback copies sold during this time So, x + 9x = total number of ...”
November 10, 2018
Brent@GMATPrepNow posted a reply to A box contains 10 balls numbered from 1 to 10 inclusive. If in the Problem Solving forum
“P(Ann and Jane remove same ball) = P(Ann removes ANY ball AND Jane''s ball matches Ann''s ball) = P(Ann removes ANY ball) x P(Jane''s ball matches Ann''s ball) = 1 x 1/10 = 1/10 Answer: D Aside: Once Jane removes her ball (and then replaces it), we have 10 balls, and 1 of them is the one ...”
November 10, 2018
fskilnik@GMATH posted a reply to Every day at noon, a bus leaves for Townville and travels at in the Problem Solving forum
“Alternate approach: 7/6 of speed implies 6/7 of time (for any given distance). The difference of time (30min) is therefore 1/7 (=1-6/7) of the original time, therefore the original time was 7*(1/2 h) = 7/2 hours. It´s done: x = (280 km) / (7/2 h) = 80 km/h This solution follows ...”
November 9, 2018
fskilnik@GMATH posted a reply to If n is contained in the set A, n+5 is contained in set A. I in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 9, 2018
fskilnik@GMATH posted a reply to Every day at noon, a bus leaves for Townville and travels at in the Problem Solving forum
“\Let´s use 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 9, 2018
fskilnik@GMATH posted a reply to If a cube A’s volume is 216 times of a cube B’s, the cub in the Problem Solving forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 9, 2018
GMATGuruNY posted a reply to Every day at noon, a bus leaves for Townville and travels at in the Problem Solving forum
“Time and rate have a RECIPROCAL RELATIONSHIP: 2 times as fast implies 1/2 the time. 3 times as fast implies 1/3 the time. Let t = the normal time. Since the bus travels today at 7/6 its normal rate, the time today is equal to 6/7 of the normal time: (6/7)t. Since the bus leaves 1/2 hour late ...”
November 9, 2018
fskilnik@GMATH posted a reply to On a wedding catering service, An experienced chef can 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 9, 2018
fskilnik@GMATH posted a reply to A box contains 10 balls numbered from 1 to 10 inclusive. If in the Problem Solving forum
“$$?\,\, = \,\,P\left( {{\rm{same}}\,\,{\rm{ball}}\,\,{\rm{twice}}\,{\rm{,}}\,{\rm{with}}\,\,{\rm{replacement}}} \right)$$ Exactly 1 ball extracted in the second extraction (out of 10 equiprobable possibilities) will be the same as (any given) ball extracted in the first extraction. Therefore ...”
November 9, 2018
Brent@GMATPrepNow posted a reply to If CD = 6, what is the length of BC? in the Data Sufficiency forum
“Is there an image? Cheers, Brent”
November 9, 2018
Brent@GMATPrepNow posted a reply to Andrew has a certain number of coins in his pocket. He has in the Problem Solving forum
“Let x = number of QUARTERS in pocket So, 0.25x = VALUE of quarters in pocket He has three times as many dimes as quarters So, 3x = number of DIMES in pocket So, 0.10(3x) = 0.3x = VALUE of dimes in pocket He has six times as many nickels as dimes. So, (6)(3x) = number of NICKELS in ...”
November 8, 2018
fskilnik@GMATH posted a reply to Pipe A runs 30 liters of water per minute into a pool that in the Problem Solving forum
“$$?\,\,\,:\,\,\,{\rm{time}}\,\,{\rm{together}}\,\,{\rm{for}}\,\,3600\,\,{\rm{liters}}$$ Let´s use UNITS CONTROL, one of the most powerful tools of our method! $$\left. \matrix{ A\,\,:\,\,\,{{30\,\,{\rm{liters}}} \over {\,1\,\,{\rm{minute}}\,}}\,\,\,\, \Rightarrow ...” November 8, 2018 fskilnik@GMATH posted a reply to Which of the following are roots of an equation 10x^{-2}+x^{ in the Problem Solving forum “$$?\,\,\,:\,\,\,\,{{10} \over {{x^2}}} + {1 \over x} - 21 = 0\,\,\,{\rm{roots}}$$We can just substitute x with the values presented in the alternative choices. "Luckily" (A) will already be the correct answer. Another approach, probably even faster (at least when the correct ...” November 8, 2018 fskilnik@GMATH posted a reply to The inflation index for the year 1989 relative to the year in the Data Sufficiency forum “$${{{\rm{pric}}{{\rm{e}}_{\,70}}} \over {{\rm{price}}{\,_{89}}}} = {1 \over {3.56}}\,\,\,\,\,\,\left( * \right)?\,\, = {\rm{pric}}{{\rm{e}}_{\,70}}\left( 1 \right)\,\,\,{\rm{pric}}{{\rm{e}}_{\,89}} - {\rm{pric}}{{\rm{e}}_{\,70}} = 102.40\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * ...”
November 8, 2018
fskilnik@GMATH posted a reply to A solution consists of only water and alcohol such that the in the Data Sufficiency forum
“In the solution below, the unit considered is always milliliters. Let´s use the k technique, one of the best tools of our method when dealing with ratios/proportions! $$\left\{ \matrix{ \,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k \hfill \cr \,{\rm{alcohol}}\,\,\left( a \right) = ...” November 8, 2018 fskilnik@GMATH posted a reply to What is the units digit of a positive integer n? in the Data Sufficiency forum “$$n \ge 1\,\,{\mathop{\rm int}} ?\,\,\,:\,\,n\,\,{\rm{units}}\,\,{\rm{digit}}\left( 1 \right)\,\,n\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,LCM\left( {13,14} \right) = 13 \cdot 14\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,n = 13 \cdot 14\,\,\,\,\, \Rightarrow ...”
November 8, 2018
Brent@GMATPrepNow posted a reply to Challenge: Al, Bob, Cal and Don each own 1 hat. If the 4... in the Problem Solving forum
“I created this question to highlight many students'' tendency to avoid listing and counting as a possible approach. As you''ll see, the approach is probably the fastest approach. P(no one receives his own hat) = (# of outcomes in which no one receives his own hat)/(TOTAL number of outcomes) ...”
November 8, 2018
fskilnik@GMATH posted a reply to Is the three-digit number n less than 550? in the Data Sufficiency forum
“Very nice problem! \This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ”
November 8, 2018
fskilnik@GMATH posted a reply to The participants in a race consisted of 3 teams with 3 in the Data Sufficiency forum
“\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
November 8, 2018
fskilnik@GMATH posted a reply to All votes cast in a recent presidential election were for in the Problem Solving forum
“All numbers presented below are in million votes. ${\text{I}}{\text{.}}\,\,\left( {{\text{before}}} \right)\,\,{\text{:}}\,\,\,\frac{{{\text{challenger}}}}{{{\text{total}}}} = \frac{{5.4}}{{5.4 + 5}} = \frac{{54}}{{104}} = \frac{{27}}{{52}}$ ${\text{II}}{\text{.}}\,\,\left( {{\text{after}}} ...” November 8, 2018 fskilnik@GMATH posted a reply to In a recent street fair students were challenged to hit one in the Problem Solving forum “\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 8, 2018 Brent@GMATPrepNow posted a reply to There are 27 different three-digit integers that can be in the Problem Solving forum “Yes, great work, Mitch! I thought I''d mention that, once we know the correct answer is a multiple of 222 (which is also a multiple of 3), then the correct answer will be a multiple of 3. Useful property: If a number is a multiple of 3, then the sum of its digits is also a multiple of 3. When we ...” November 7, 2018 fskilnik@GMATH posted a reply to There are 27 different three-digit integers that can be in the Problem Solving forum “Outstanding, Mitch. Congrats! Regards, Fabio.” November 7, 2018 Brent@GMATPrepNow posted a new topic called Challenge: Al, Bob, Cal and Don each own 1 hat. If the 4... in the Problem Solving forum “Al, Bob, Cal and Don each own 1 hat. If the 4 hats are randomly distributed so that each man receives exactly 1 hat, what is the probability that no one receives his own hat? A) 1/8 B) 1/4 C) 1/3 D) 3/8 E) 1/2 Answer: D Difficulty level: 650 – 700 Source: www.gmatprepnow.com” November 7, 2018 Brent@GMATPrepNow posted a reply to If x, y and z are non-negative integers such that x < y & in the Problem Solving forum “I created this question to show that there can be times when the best (i.e., fastest) way to solve a counting question is by listing and counting How do we know when it''s not a bad idea to use listing and counting? The answer choices will tell us (ALWAYS scan the answer choices before ...” November 7, 2018 Brent@GMATPrepNow posted a reply to How many men are in a certain company's vanpool program? in the Data Sufficiency forum “Target question: How many men are in a certain company''s vanpool program? Statement 1: The ratio of men to women in the program is 3 to 2. Let''s TEST some values. There are several scenarios that satisfy statement 1. Here are two: Case a: There are 3 men and 2 women in the program. In ...” November 7, 2018 GMATGuruNY posted a reply to There are 27 different three-digit integers that can be in the Problem Solving forum “Given any set that is symmetrical about the median: Sum = (quantity)(median) The set of 3-digit integers that can be formed from the digits 1,2 and 3 is symmetrical about the median (222): ...212, 213, 221, 222, 223, 231, 232... Thus: Sum of the 27 integers = (quantity)(median) = 27*222 = ...” November 7, 2018 fskilnik@GMATH posted a reply to There are 27 different three-digit integers that can be in the Problem Solving forum “\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 7, 2018 fskilnik@GMATH posted a reply to Which data set has the greater standard deviation, data set in the Data Sufficiency forum “\The correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. POST-MORTEM: in this very special situation, a careful reader may correctly mention that K=L={0} is enough to guarantee the correct answer is (E). (We ...” November 7, 2018 fskilnik@GMATH posted a reply to Is z equal to the median of the three positive integers, x, in the Data Sufficiency forum “$$The last equality is true if x is equal to z, and it is also true if x is not equal to z.) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 7, 2018 fskilnik@GMATH posted a reply to A newly-opened retail store made 400 profit on the initial in the Problem Solving forum “\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 7, 2018 fskilnik@GMATH posted a reply to Albert spent 100 in total on four different types of in the Problem Solving forum “All numbers presented below are in dollars. B,C,D,G\,\, \ge 0\,\,\,(\ \,\,{\rm{spent}}\,\,{\rm{in}}\,\,{\rm{each}}\,\,{\rm{type}}) B + C + D + G = 100 B,C,D,G\,\,\, \le \,\,40 ? = \min \left\{ {B,C,D,G} \right\} \left( 1 \right)\,C = 2G\,\,\,\left\{ \matrix{ ...” November 7, 2018 fskilnik@GMATH posted a reply to What is the area of the shaded portion in circle O, in the Problem Solving forum “? = {S_{{\rm{circ}}{\rm{.sector}}}} - {S_{\Delta {\rm{equil}}}} {S_{{\rm{circ}}{\rm{.sector}}}} = {{60} \over {360}}\left( {\pi \cdot {{10}^2}} \right) = {1 \over 6}\left( {100\pi } \right) {S_{\Delta {\rm{equil}}}} = {{10 \cdot {h_{{\rm{equil}}}}} \over 2}\mathop = \limits^{\left( * ...” November 7, 2018 fskilnik@GMATH posted a reply to What is the value of A? in the Data Sufficiency forum “? = A\,\,\,\,\left( {\,A \in \left\{ {1,2,3, \ldots ,9} \right\}\,\,:\,\,{\rm{already}}\,\,{\rm{considering}}\,\,{\rm{each}}\,\,{\rm{statement}}\,\,{\rm{alone}}\,} \right) \left( 1 \right)\,\,\,{{\left\langle {A77A} \right\rangle } \over 4} = {\mathop{\rm int}} \,\,\,\,\, \Leftrightarrow ...” November 6, 2018 Brent@GMATPrepNow posted a reply to Speed Time Distance MGMAT in the Problem Solving forum “GIVEN: When the men start walking, Brian has a 30-mile lead Let B = Brian''s walking speed (in miles per hour) Let A = Ashok''s walking speed (in miles per hour) Since Ashok''s speed is greater than Brian''s speed, the rate at which the gap shrinks = (A - B) miles per hour For example, if A ...” November 6, 2018 Brent@GMATPrepNow posted a reply to 2019 GMAC Official Guide applicable for 60-Day Study Guide? in the The 60-Day GMAT Study Guide forum “If you go here (https://www.gmatprepnow.com/content/improvement-chart) and download the Improvement Chart for the OG2016, you''ll see the question breakdown for each topic. This should help. Cheers, Brent” November 6, 2018 Brent@GMATPrepNow posted a reply to In a certain game, a large bag is filled with blue, green, in the Problem Solving forum “This question begs for some prime factorization. 88,000 = (2)(2)(2)(2)(2)(2)(5)(5)(5)(11) First, we can see that there must be one (11-point) red chip. Now, what role do these 2''s play? Since there are no 2''s hiding among the 5-point chips or the 11-point chips, the 2''s must be associated ...” November 6, 2018 Brent@GMATPrepNow posted a reply to [x] is the greatest integer less than or equal x, what is th in the Problem Solving forum “GIVEN: For example, [3.2] = 3, since 3 is the greatest integer that is less than (or equal) to 3.2 Likewise, [8.7] = 8, since 8 is the greatest integer that is less than (or equal to) 8.7 Now onto the question.... √25 = 5 √36 = 6 √49= 7 √64 = 8 Since √30 is BETWEEN √25 ...” November 6, 2018 Brent@GMATPrepNow posted a reply to If in k+1 years from now John will be m years old, then how in the Problem Solving forum “In k+1 years from now John will be m years old So, m - (k + 1) = John''s PRESENT age How old was John t-1 years ago? So, m - (k + 1) - (t - 1) = John''s age (t-1) YEARS AGO Simplify m - (k + 1) - (t - 1) to get: m - k - t Answer: A Cheers, Brent” November 6, 2018 Brent@GMATPrepNow posted a reply to Pipe A runs 30 liters of water per minute into a pool that in the Problem Solving forum “Let''s determine the COMBINED RATE of the two pipes Given: Pipe A''s RATE = 30 liters per minute This is equivalent to 1800 liters per HOUR Pipe B fills a third of the pool in 6 hours So, Pipe B fills the ENTIRE pool (3600 liters) in 18 hours Rate = Output/time = 3600/18 = 200 liters ...” November 6, 2018 fskilnik@GMATH posted a reply to If the total price for n copies of a book is 31.5, what is in the Data Sufficiency forum “? = c\,\,\left( {{\rm{dollar}}\,\,{\rm{cost}}\,\,{\rm{per}}\,\,{\rm{copy}}} \right) n \cdot c = 31.5\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 6, 2018 fskilnik@GMATH posted a reply to If Nicole worked 20% more this week than she worked last in the Data Sufficiency forum “{\rm{this}}\,\, = \,\,{\rm{\# }}\,\,{\rm{h}}\,\,{\rm{Nicole}}\,\,{\rm{worked}}\,\,{\rm{this}}\,\,{\rm{week}} {\rm{last}}\,\, = \,\,{\rm{\# }}\,\,{\rm{h}}\,\,{\rm{Nicole}}\,\,{\rm{worked}}\,\,{\rm{last}}\,\,{\rm{week}} {\rm{this}}\,\,{\rm{ = }}\,\,{6 \over 5}\left( {{\rm{last}}} ...” November 6, 2018 fskilnik@GMATH posted a reply to Find the units digit of in the Data Sufficiency forum “\left\langle M \right\rangle \,\, = \,\,{\rm{units}}\,\,{\rm{digit}}\,\,{\rm{of}}\,\,M \left\langle {{{556}^n}} \right\rangle = \left\langle {{6^n}} \right\rangle = 6\,\,,\,\,\forall n \ge 1\,\,{\mathop{\rm int}} \left\langle {{{339}^k}} \right\rangle = \left\langle {{9^k}} ...” November 5, 2018 GMATGuruNY posted a reply to Is x^2>xy? in the Data Sufficiency forum “For the purposes of a Y/N DS problem, the rephrase is the equivalent of the original question stem. Original question stem: Is x² > xy? The answer will be YES if y/x is less than 1.. The answer will be NO if y/x is NOT less than 1. Thus, the original question stem can be rephrased as ...” November 5, 2018 fskilnik@GMATH posted a reply to A rectangle has sides x and y and diagonal z. What is the in the Data Sufficiency forum “\This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 5, 2018 fskilnik@GMATH posted a reply to In a certain game, you perform three tasks. You flip a quart in the Problem Solving forum “\left. \matrix{ {\rm{i}}\,\,{\rm{:}}\,\,\,{\rm{get}}\,\,{\rm{H}}\,\,{\rm{in}}\,\,{\rm{quarter}} \hfill \cr {\rm{ii}}:\,\,{\rm{get}}\,\,6\,\,{\rm{in}}\,{\rm{die}} \hfill \cr ...” November 5, 2018 Brent@GMATPrepNow posted a new topic called If x, y and z are non-negative integers such that x < y < z, in the Problem Solving forum “If x, y and z are non-negative integers such that x < y < z, then the equation x + y + z = 11 has how many distinct solutions? A) 5 B) 10 C) 11 D) 22 E) 78 Answer: B Difficulty level: 600-650 Source: www.gmatprepnow.com” November 5, 2018 fskilnik@GMATH posted a reply to Is x^2>xy? in the Data Sufficiency forum “The reasoning that comes pre-statements (shown in red) is not correct. In other words, the original question stem and the question stem rephrased (proposed) are not equivalent. I explain: x CAN be zero (only in the original question stem) and, being so, the question asked is answered in ...” November 5, 2018 Brent@GMATPrepNow posted a reply to Challenge question: Is |1 - 4k| < k? in the Data Sufficiency forum “Target question: Is |1 - 4k| < k? Statement 1: k > 4x³ This pretty much tells is that k can have ANY value. For example, notice that, if x = -100, then 4x³ = -4,000,000 So, for this value of x, k can be any number greater than -4,000,000 Let''s TEST some values. There are ...” November 5, 2018 Brent@GMATPrepNow posted a reply to Which sport utility vehicle has a higher list price, the in the Data Sufficiency forum “Target question: Which sport utility vehicle has a higher list price, the Touristo of the Leisure? Statement 1: The list price of the Leisure is 5/6 the list price of the Touristo. If the Leisure''s price is 5/6 of the Touristo''s price, then the answer to the target question is the Touristo ...” November 5, 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 Range and Standard Deviation https://www.youtube.com/watch?v=FbAlIjw2fwY Cheers, Brent” November 5, 2018 GMATGuruNY posted a reply to Is x^2>xy? in the Data Sufficiency forum “x² > xy is true only if x is NONZERO, in which case we can safely divide by x², since the square of a nonzero value must be positive: x²/x² > (xy)/x² 1 > y/x Question stem, rephrased: Is y/x < 1? Statement 1: x > y If x=2 and y=1, then y/x =1/2. so the answer to the ...” November 5, 2018 fskilnik@GMATH posted a reply to If the average (arithmetic mean) of p, q, and r is 6, what i in the Data Sufficiency forum “p + q + r = 18\,\,\,\,\left( * \right) ? = r Embrace math! The homogeneity nature of the average (*) trivializes this problem! \left( 1 \right)\,\,p + r = 0\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,q = 18\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( ...” November 5, 2018 fskilnik@GMATH posted a reply to OG What is the value of integer n in the Data Sufficiency forum “? = n\,\,\,\,\left( {n\,\,{\mathop{\rm int}} } \right) \left( 1 \right)\,\,\,n\left( {n + 1} \right)\, = 6\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\{ \matrix{ \,n = 2\,\,\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, ...” November 5, 2018 fskilnik@GMATH posted a reply to Is x^2>xy? in the Data Sufficiency forum “{x^2}\,\,\mathop > \limits^? \,\,\,xy\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,x\left( {x - y} \right)\,\,\mathop > \limits^? \,\,\,0 \left( 1 \right)\,\,x > y\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {1,0} \right)\,\,\,\, \Rightarrow ...” November 5, 2018 GMATGuruNY posted a reply to | 1 - | 2 - | 3 - | 4 – π | | | | in the Problem Solving forum “Let π=3 in the original expression and simplify the blue portion below: | 1 - | 2 - | 3 - | 4 – 3 | | | | Simplify the red portion below; | 1 - | 2 - | 3 - 1 | | | Simplify the green portion below: | 1 - | 2 - 2 | | = | 1 - 0 | = 1 The correct answer choice must yield a value of ...” November 5, 2018 fskilnik@GMATH posted a reply to | 1 - | 2 - | 3 - | 4 – π | | | | in the Problem Solving forum “?\,\,\,:\,\,\,{\rm{expression}} \left| {4 - \pi } \right| = 4 - \pi \,\,\,\,\,\,\left( {4 - \pi > 0} \right) \left| {3 - \left( {4 - \pi } \right)} \right| = \left| {\pi - 1} \right| = \pi - 1\,\,\,\,\,\,\left( {\pi - 1 > 0} \right) \left| {2 - \left( {\pi - 1} \right)} ...” November 5, 2018 fskilnik@GMATH posted a reply to At the local grocery store, apples normally cost 40 cents in the Problem Solving forum “Trivial application of UNITS CONTROL, one of the most powerful tools of our method! ?\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 4, 2018 fskilnik@GMATH posted a reply to OG12 #70 - value of n? Why isnt n =0 ?? in the Data Sufficiency forum “{\rm{Total}}\,\, = \,\,500 \cdot n + 500 \cdot n \cdot n\,\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. ” November 4, 2018 fskilnik@GMATH posted a reply to Six numbers are randomly selected and placed within a set. in the Data Sufficiency forum “Very nice problem (in which the "structured candidate" has a considerable advantage)! {a_1} \le {a_2} \le \ldots \le {a_6}\,\,\,\,\,\left\{ \matrix{ \,{a_6} = {a_1} + 16\, \hfill \cr \,{a_3} + {a_4} = 12 \hfill \cr \,\sum\nolimits_6 {\, = } \,\,\,42 \hfill \cr ...” November 4, 2018 fskilnik@GMATH posted a reply to If xy=-18, is x less than y? in the Data Sufficiency forum “xy = - 18\,\,\,\left( * \right) x\,\,\mathop < \limits^? \,\,\,y \left( 1 \right)\,\,x < 0\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,y > 0\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \left( 2 \right)\,\,y < ...” November 4, 2018 fskilnik@GMATH posted a reply to Triplets Adam, Bruce, and Charlie enter a triathlon. If ther in the Problem Solving forum “\left\{ \matrix{ \,A\,,B\,,\,{\kern 1pt} C\,\,\,\,\, \to \,\,\,3\,\,{\rm{competitors}} \hfill \cr \,{\rm{D,}}\,\, \ldots \,\,{\rm{,}}\,I\,\,\, \to \,\,\,{\rm{other}}\,\,6\,\,{\rm{competitors}}\, \hfill \cr} \right. \left( {\rm{i}} ...” November 4, 2018 Brent@GMATPrepNow posted a reply to If xy=-18, is x less than y? in the Data Sufficiency forum “ Given: xy = -18 Target question: is x less than y? Statement 1: x < 0 In other words, x is NEGATIVE So, our given information (xy = -18) becomes: (NEGATIVE)(y) = -18 In other words: (NEGATIVE)(y) = NEGATIVE This tells us that y is POSITIVE If y is POSITIVE, and x is NEGATIVE, the ...” November 4, 2018 GMATGuruNY posted a reply to Working alone, three persons P, Q, and R can do a certain in the Problem Solving forum “Let the job = the LCM of the 3 times = 60 widgets. Maximum time: The maximum time is yielded when the slowest person -- R -- works alone. Since R takes 15 hours to complete the 60-widget job, the maximum time = 15 hours. Minimum time: The minimum time is yielded when all 3 people work ...” November 4, 2018 GMATGuruNY posted a reply to Triplets Adam, Bruce, and Charlie enter a triathlon. If ther in the Problem Solving forum “One approach: P(good outcome) = 1 - P(bad outcome). Bad outcome #1: Exactly 1 triplet wins. P(triplet wins 1st place) = 3/9. (Of the 9 competitors, 3 are triplets) P(non-triplet wins 2nd place) = 6/8. (Of the 8 remaining competitors, 6 are non-triplets) P(non-triplet wins 3rd place) = 5/7. ...” November 4, 2018 Brent@GMATPrepNow posted a reply to Challenge #2: If x and y are different positive integers, wh in the Problem Solving forum “i) When x is divided by y, the remainder is 2x The remainder cannot be greater than the dividend (the number we''re dividing) For example, it CANNOT be the case that 17 divided by 5 leaves a remainder of 34 Statement i can never be true Check the answer choices. . . . ELIMINATE A and D ii) ...” November 3, 2018 Brent@GMATPrepNow posted a new topic called Challenge question: Is |1 - 4k| < k? in the Data Sufficiency forum “Is |1 - 4k| < k? (1) k > 4x³ (2) k < 2x – x² - 2 Answer: B Difficulty level: 700+ Source: www.gmatprepnow.com” November 3, 2018 fskilnik@GMATH posted a reply to Is the length of the diagonal of the rectangle bigger than in the Data Sufficiency forum “a \ge b > 0\,\,\,\,\,\leftThis solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” November 3, 2018 fskilnik@GMATH posted a reply to How many positive five-digit integers contain the digit in the Problem Solving forum “The solution posted above is related to another problem (as mentioned). Let´s solve the one originally proposed, in which there are double-counting´s to be dealt with! ?\,\,:\,\,5{\rm{ - digit}}\,\,{\rm{positive}}\,\,{\rm{integers}}\,\,{\rm{with}}\,\,57{\rm{ - block}}\left( {\rm{s}} ...” November 3, 2018 fskilnik@GMATH posted a reply to If the sum of the three different numbers is 54, what is the in the Data Sufficiency forum “\left\{ \matrix{ a > b > c \hfill \cr a + b + c = 54\,\,\,\,\,\, \hfill \cr} \right.\,\,\,\,;\,\,\,\,\,\,\,\,\,\,?\,\, = \,\,a Let´s start with statement (2) not only because it´s easier, but also because it will help us finding (uniqueness or) a BIFURCATION of the other ...” November 2, 2018 fskilnik@GMATH posted a reply to If 1/3 = 1/m + 1/n, where m and n are different positive int in the Problem Solving forum “Another beautiful problem of yours, Max. Congrats! \left\{ \matrix{ m,n\,\,{\rm{distinct}}\,\,\, \ge \,\,{\rm{1}}\,\,\,{\rm{ints}}\,\,\,\,\left( * \right) \hfill \cr {1 \over 3} = {1 \over m} + {1 \over n}\,\,\,\left( {**} \right) \hfill \cr} \right. ? = m + n 1st way ...” November 2, 2018 GMATGuruNY posted a reply to Ryunosuke Akutagawa in the Sentence Correction forum “Nicely done! Because the comparison in D allows for more than one logical interpretation, eliminate D. In fact, the ambiguity cited above is the most compelling reason to eliminate D.” November 2, 2018 GMATGuruNY posted a reply to Ryunosuke Akutagawa in the Sentence Correction forum “X led to Y implies that X did not directly cause Y but that X was a factor that helped to yield Y. SC755 in the OG17: An inability to adapt led to their extinction. Here, an inability to adapt did not directly cause the extinction but was a factor that helped to yield the extinction. A cause ...” November 2, 2018 Brent@GMATPrepNow posted a reply to If the average (arithmetic mean) of p, q, and r is 6, what i in the Data Sufficiency forum “ Given: The average (arithmetic mean) of p, q, and r is 6 We can write: (p + q + r)/3 = 6 This means: p + q + r = 18 Target question: What is the value of r? Statement 1: p = -r Given: p + q + r = 18 Replace p with -r to get: -r + q + r = 18 Simplify: q = 18 What about the value of ...” November 2, 2018 Brent@GMATPrepNow posted a reply to Cars J and K are making the trip from City A to City B. in the Problem Solving forum “Car K travels at a constant speed that is 80% the constant speed of Car J Let''s assign some nice values to the speeds. Let''s say Car J travels 40 miles per hour So, Car K travels 32 miles per hour Car J departs from City A 15 minutes after Car K does Let''s calculate the distance that Car ...” November 2, 2018 GMATGuruNY posted a reply to Ryunosuke Akutagawa in the Sentence Correction forum “Generally, COMMA + as-clause implies that the clause after as LEADS to the preceding clause, with the result that the two clauses happen concurrently. An OA in GMATPrep: The steel industry has changed radically over the last two decades, as large, integrated companies such as Bethlehem Steel have ...” November 2, 2018 GMATGuruNY posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum “Let B = Barry''s rate and W = the walkway''s rate. The distance can be ANY VALUE. Let the distance = 240 meters. WITH the walkway, the time = 30 seconds: Here, Barry and the walkway WORK TOGETHER, so we ADD their rates: B+W = d/t = 240/30 = 8 meters per second. AGAINST the walkway, the ...” November 2, 2018 Brent@GMATPrepNow posted a reply to At a family summer party, each of the x members of the in the Problem Solving forum “Let''s use the INPUT-OUTPUT approach. It might be useful to choose a number that works well with the fractions given in the question (1/3 and 1/7). So, let''s say there are 21 family members at the party. In other words, we''re saying that x = 21 1/3 chose to have a hamburger, and of ...” November 1, 2018 GMATGuruNY posted a reply to At a family summer party, each of the x members of the in the Problem Solving forum “Let the x family members = the product of the two denominators = 3*7 = 21. Number who chose to have a hamburger = (1/3)(21) = 7. Since 1/7 of the hamburger-eaters also had a hot dog, the number who had both = (1/7)(7) = 1. Thus, the number who did NOT have both = (total members) - (number who had ...” November 1, 2018 GMATGuruNY posted a reply to How many positive five-digit integers contain the digit in the Problem Solving forum “I believe that the prompt above is outdated; regardless, it does not list a correct answer. The prompt below appears in Manhattan''s 5 lb. Book of GRE Practice Problems: Case 1: 57XXX Number of options for the hundreds digit = 10. (Any digit 0-9.) Number of options for the tens digit = 10. ...” November 1, 2018 Brent@GMATPrepNow posted a reply to When a positive integer n is divided by 19, what is the rema in the Data Sufficiency forum “Target question: When n is divided by 19, what is the remainder? Statement 1: n-17 is a multiple of 19 ----ASIDE------------------------------------------- If N is a multiple of d, then we can write N = dk (for some integer k) For example, if N is a multiple of 5, then we can write N = 5k ...” November 1, 2018 Brent@GMATPrepNow posted a reply to In the diagram above, points A, B, C, D, and E represent the in the Problem Solving forum “points A, B, C, D, and E represent the five teams in a certain league in which each team must play each of the other teams exactly once. Let''s first determine the total number of games that will be played. There are 5 teams, so each team will play 4 games (since a team can''t play itself) So, ...” November 1, 2018 fskilnik@GMATH posted a reply to In the diagram above, points A, B, C, D, and E represent the in the Problem Solving forum “?\,\,\,:\,\,\,{\rm{impossible}}\,\,\% \,\,{\rm{tie}}\,\,{\rm{pairs}} {\rm{Total}}\,\,\# \,\,{\rm{games}}\,\,\,{\rm{ = }}\,\,\,{\rm{C}}\left( {5,2} \right)\,\, = \,\,10\,\,\,\left\{ \matrix{ \,5\,\,{\rm{victory - loss}}\,\,{\rm{pairs}} \hfill \cr \,2\,\,{\rm{tie}}\,\,{\rm{pairs}} \hfill ...” November 1, 2018 fskilnik@GMATH posted a reply to If the average (arithmetic mean) of 3, 8, w, x, and y is 14, in the Problem Solving forum “\left. \matrix{ ? = \,\,{{\left( {w + 2} \right) + \left( {x - 3} \right) + \left( {y + 8} \right)} \over 3} = {{\left( {w + x + y} \right) + 7} \over 3}\,\,\, \hfill \cr {{3 + 8 + w + x + y} \over 5} = 14\,\,\,\,\, \Rightarrow \,\,\,\,w + x + y = 70 - 11 \hfill \cr} \right\}\,\,\,\,\,\, ...” November 1, 2018 fskilnik@GMATH posted a reply to The four-digit number 486X, where X is the units digit of 48 in the Problem Solving forum “? = X {{\left\langle {486X} \right\rangle } \over {{2^2} \cdot {3^2}}} = {\mathop{\rm int}} \,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,\,\left\langle {486X} \right\rangle \,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,4\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {6X} ...” November 1, 2018 GMATGuruNY posted a reply to Two teachers, Ms. Ames and Mr. Betancourt, each had N in the Data Sufficiency forum “Since the N cookies can be divided evenly among 24 or 18 students, N must be divisible by both 24 and 18. One way to determine the LCM of two integers is to take multiples of the LARGER integer until we get a multiple of the SMALLER integer. Multiples of 24: 24, 48, 72... We can stop here: the ...” November 1, 2018 fskilnik@GMATH posted a reply to When a positive integer n is divided by 19, what is the rema in the Data Sufficiency forum “1 \le n = 19Q + R\,\,,\,\,0 \le R \le 18\,\,\,\,\,\left( {Q,R\,\,{\rm{ints}}} \right) ? = R \left( 1 \right)\,\,n - 17 = 19M\,\,,\,\,M \ge 0\,\,{\mathop{\rm int}} n = 19M + 17\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ \,Q = M \hfill \cr \,? = R = 17\,\,\,\,\, \Rightarrow ...” November 1, 2018 fskilnik@GMATH posted a reply to A number of eggs dyed various colors were hidden for an egg in the Data Sufficiency forum “{\rm{Total}}\,\,\left\{ \matrix{ \,{\rm{red}}\,\,:\,\,\,R \ge 1\,\,{\mathop{\rm int}} \hfill \cr \,{\rm{not - red}}\,\,:\,\,\,N \ge 1\,\,{\mathop{\rm int}} \hfill \cr} \right. ? = R + N Let´s go straight to (1+2): a BIFURCATION will prove the correct answer is (E). \left( ...” November 1, 2018 fskilnik@GMATH posted a reply to Two teachers, Ms. Ames and Mr. Betancourt, each had N in the Data Sufficiency forum “\left\{ \matrix{ \left( {{\rm{Ames}}} \right)\,\,N = 24 \cdot Q\,\,,\,\,Q \ge 1\,\,{\mathop{\rm int}} \hfill \cr \left( {{\rm{Betan}}} \right)\,\,N = 18 \cdot K\,\,,\,\,K \ge 1\,\,{\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,N = LCM\left( {24,18} \right) \cdot ...” November 1, 2018 fskilnik@GMATH posted a reply to At a certain high school, there are three sports: baseball, in the Data Sufficiency forum “Nice example of the Venn diagrams ("overlapping sets") and the k technique together! 15:12:18 = 5:4:6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Baseball}} = 5k \hfill \cr \,{\rm{Basketball}} = 4k \hfill \cr \,{\rm{Football}} = 6k \hfill \cr} ...” October 31, 2018 fskilnik@GMATH posted a reply to Is triangle ABC an acute angled triangle? 1) [m]c^2 < a^ in the Data Sufficiency forum “ All angles are measured in degrees. {\rm{all}}\,\,\Delta ABC\,\,{\rm{internal}}\,\,{\rm{angles}}\,\,\mathop < \limits^? \,\,\,{90} (We assume c is the length of the side that is opposite to the internal angle ACB, etc.) \left( 1 \right)\,\,\,\,{c^2} < {a^2} + {b^2}\,\,\,\, ...” October 31, 2018 fskilnik@GMATH posted a reply to Did one of the 3 members of a certain team sell at least 2 in the Data Sufficiency forum “A,B,C\,\, \ge 0\,\,{\rm{ints}}\,\,\,\left( * \right) ?\,\,\,:\,\,\,\,A \ge 2\,\,\,{\rm{or}}\,\,\,B \ge 2\,\,\,{\rm{or}}\,\,\,C \ge 2 \left( 1 \right)\,\,A + B + C = 6\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle ...” October 31, 2018 GMATGuruNY posted a reply to Did one of the 3 members of a certain team sell at least 2 in the Data Sufficiency forum “Statement 1: If NONE of the members sells at least 2 tickets, then the 3 members sell a maximum of 1 ticket each, yielding the following total: 1+1+1 = 3. Too small, since the total number of tickets sold = 6. Implication: For a total of 6 tickets to be sold, one of the 3 members must sell at ...” October 31, 2018 GMATGuruNY posted a reply to A football team averaged 35 points per game over the first in the Problem Solving forum “This is a weighted average/mixture problem. Average score for the first N games = 35. Score for the final game = 28. Average score for the MIXTURE of all the games = 34. Step-by-step instruction for the alligation approach: Step 1: Plot the 3 averages on a number line, with the average ...” October 31, 2018 Brent@GMATPrepNow posted a reply to In four years, Andy will be twice as old as Betsy. How old in the Data Sufficiency forum “ Given: In four years, Andy will be twice as old as Betsy. Let A = Andy''s PRESENT age Let B = Betsy''s PRESENT age So, A+4 = Andy''s age IN 4 YEARS And so, B+4 = Betsy''s age IN 4 YEARS If Andy will be twice as old as Betsy IN 4 YEARS, we can write: A+4 = 2(B+4) Expand: A + 4 = 2B + 8 ...” October 31, 2018 Brent@GMATPrepNow posted a reply to If m and n are integers, is m+m^2-n an even number? in the Data Sufficiency forum “ Given: m and n are integers Target question: Is m + m² - n an even number? This is a good candidate for rephrasing the target question Aside: Here’s a video with tips on rephrasing the target question: We can take the expression, m + m² - n and rewrite it as m(1 + m) - n Now notice ...” October 31, 2018 Brent@GMATPrepNow posted a reply to In 1995 a certain store had 1,800 tools in stock that had in the Problem Solving forum “1,000 of these tools were sold in 1995 for 40 each So, the REVENUE = (1000)(40) = 40,000 The 1000 tools were purchased for 30 each. So, the EXPENSE = (1000)(30) = 30,000 PROFIT for 1995 = 40,000 - 30,000 = 10,000 ----------------------------------------------- The remaining 800 ...” October 31, 2018 GMATGuruNY posted a reply to 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 in the Problem Solving forum “The difference between the endpoints of the range = 200-10 = 190. Since neither endpoint is a multiple of 3, we can count the multiples of 3 simply by dividing 3 into 190: 190/3 ≈ 63. The correct answer is D.” October 31, 2018 fskilnik@GMATH posted a reply to The terms of a sequence are defined by an=an-2+3. Is 411 a t in the Data Sufficiency forum “Very nice problem, Max. Congrats! S\,\,{\rm{sequence:}}\,\,\left\{ \matrix{ {{\rm{a}}_{\rm{1}}},{a_2}, \ldots \hfill \cr {a_n} = {a_{n - 2}} + 3\,\,,\,\,{\rm{for}}\,\,{\rm{all}}\,\,n \ge 3 \hfill \cr} \right.\,\,\,\,\,\left( * \right) 411\,\,\mathop \in \limits^? \,\,\,S ...” October 31, 2018 fskilnik@GMATH posted a reply to If m and n are integers, is m+m^2-n an even number? in the Data Sufficiency forum “m,n\,\,\,{\rm{ints}}\,\,\left( * \right) m + {m^2} - n\,\,\mathop = \limits^? \,\,{\text{even}}\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( {**} \right)} \,\,\,\,\boxed{\,\,n\,\,\mathop = \limits^? \,\,{\text{even}}\,\,} \left( ** \right)\,\,m + {m^2} = m\left( {m + 1} ...” October 31, 2018 fskilnik@GMATH posted a reply to 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 in the Problem Solving forum “? = \# \,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,{\rm{between}}\,\,10\,\,{\rm{and}}\,\,200 \left. \matrix{ 12 = 3 \cdot 4 \hfill \cr 15 = 3 \cdot 5 \hfill \cr \ldots \hfill \cr 195\left( { = 180 + 15} \right) = 3 \cdot 65\,\,\, \hfill \cr 198 = 3 \cdot 66 \hfill \cr} ...” October 31, 2018 fskilnik@GMATH posted a reply to S is a set of n consecutive positive integers. Is the mean in the Data Sufficiency forum “S\,\,\,:\,\,\,n\,\,{\rm{consec}}{\rm{.}}\,\,{\rm{posit}}{\rm{.}}\,\,{\rm{ints}}\,\,\,\,\,\,\left( { \Rightarrow \,\,\,{\rm{mean}} > 0} \right) {\rm{mean}}\,\,\mathop = \limits^? \,\,{\rm{int}}\,\,\,\, \Leftrightarrow \,\,\,\,n\,\,\mathop = \limits^? \,\,{\rm{odd}} \left( 1 ...” October 31, 2018 fskilnik@GMATH posted a reply to If p is a positive integer, is 2p + 1 prime? in the Data Sufficiency forum “p \ge 1\,\,{\mathop{\rm int}} 2p + 1\,\,\mathop = \limits^? \,\,{\rm{prime}} Let´s go straight to (1+2): a BIFURCATION will guarantee (E) as the correct answer! \left( {1 + 2} \right)\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{p = 11}}\,\,\,\, \Rightarrow \,\,\,2p + 1 = ...” October 31, 2018 fskilnik@GMATH posted a reply to A football team averaged 35 points per game over the first in the Problem Solving forum “? = n + 1 Let´s do it using alligation: https://preview.ibb.co/c1pp3L/30-Oct18-7c.gif {1 \over {n + 1}} = {{35 - 34} \over {35 - 28}} = {1 \over 7}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = n + 1 = 7 This solution follows the notations and rationale taught in the GMATH method. ...” October 31, 2018 fskilnik@GMATH posted a reply to m and n are two different numbers selected from the integer in the Problem Solving forum “Beautiful problem, Max. Congrats! m,n\,\,{\rm{distinct}}\,\, \in \left\{ {11,12, \ldots ,20} \right\} ? = \max \left( {{{mn} \over {m - n}}} \right) \left( {\rm{I}} \right)\,\,m > n\,\,\,\,\left( {{\rm{otherwise}}\,\,{{mn} \over {m - n}} < 0\,\,,\,\,{\rm{not}}\,\,\max } \right) ...” October 31, 2018 fskilnik@GMATH posted a reply to A game at the state fair has a circular target with a radius in the Problem Solving forum “? = P\left( {2\,\,{\rm{hits}}\,\,{\rm{in}}\,\,{\rm{circular}}\,\,{\rm{region}}\,\,{\rm{in}}\,\,{\rm{two}}\,\,{\rm{throws}}} \right) We may consider the similar figure(!) in which the radius of the circular target is 1cm and the square board has 3cm on a side. P\left( ...” October 31, 2018 fskilnik@GMATH posted a reply to Tom, Bill, Robert, Roger, and Terry are standing in a row in the Problem Solving forum “A,B,C,D,E ?\,\, = \,\,\# \,\,{\rm{orders}}\,\,{\rm{with}}\,\,A,B\,\,{\rm{not}}\,\,{\rm{together}} (Change names and create expressions to help you unblock your brain!) ?\,\, = \,\,{\rm{Total}} - \left( {\# \,\,{\rm{orders}}\,\,{\rm{with}}\,\,A,B\,\,{\rm{together}}} \right) ?\,\, = ...” October 31, 2018 Brent@GMATPrepNow posted a reply to Tom, Bill, Robert, Roger, and Terry are standing in a row in the Problem Solving forum “One approach is to ignore the rule and determine the total number of ways to arrange all 5 people, and then subtract the number of arrangements that BREAK the rule. I''m sure someone will post that kind of solution shortly. Here''s another approach: Take the task of arranging the 5 men and ...” October 30, 2018 Brent@GMATPrepNow posted a new topic called Challenge #2: If x and y are different positive integers, wh in the Problem Solving forum “If x and y are different positive integers, which of the following COULD be true: i) When x is divided by y, the remainder is 2x ii) When x is divided by 2y, the remainder is y iii) When (2x + y) is divided by (x + y), the remainder is y A) i only B) ii only C) iii only D) i & ii ...” October 30, 2018 Brent@GMATPrepNow posted a reply to Challenge: If x and y are different positive integers, which in the Problem Solving forum “i) When x is divided by y, the remainder is x This occurs any time x < y For example, if x = 5 and y = 7, then statement i becomes: When 5 is divided by 7, the remainder is 5 So true! Scan the answer choices....eliminate D ----------------------------------------------------- ii) When 2x ...” October 30, 2018 Brent@GMATPrepNow posted a reply to Carmelo and LeBron participate in a seven-person footrace on in the Problem Solving forum “Here are three similar questions to practice with: - http://www.beatthegmat.com/counting-six-mobsters-t47167.html - http://www.beatthegmat.com/permutation-and-combination-t273916.html - http://www.beatthegmat.com/permutations-with-waiting-line-t274020.html Cheers, Brent” October 30, 2018 fskilnik@GMATH posted a reply to What is the length in meters of a certain rectangular garden in the Data Sufficiency forum “All lengths are measured in meters. \[? = L\,$ $\left( 1 \right)\,\,L = 2W + 6\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,W = 1\,\,\,\, \Rightarrow \,\,\,\,\,? = L\, = 8\,\, \hfill \\ \,{\text{Take}}\,\,W = 2\,\,\,\, \Rightarrow \,\,\,\,\,? = L\, = 10\,\, \hfill \\ \end{gathered} ...” October 30, 2018 GMATGuruNY posted a reply to A group of 20 friends formed an investment club, with each in the Problem Solving forum “Let d=100. After the value of the stock increases by 40% to 140, the share received by each of the 20 friends = 140/20 = 7. The correct answer must yield a value of 7 when d=100. Only E works: (7d)/100 = (7*100)/100 = 7. The correct answer is E.” October 30, 2018 fskilnik@GMATH posted a reply to If T is a set of 35 consecutive integers, of which 17 are in the Problem Solving forum “\[? = \sum\nolimits_{35} {\,{\text{consecutive}}\,\,{\text{integers}}} \,\,\,\,\,\,\left( {17\,\,{\text{are}}\,\,{\text{negative}}} \right)$ $35\,\,{\text{consecutive}}\,\,{\text{integers}}:\,\,\,\,\underbrace { - 17\,, - 16\,,\,\, \ldots \,\,, - ...” October 30, 2018 fskilnik@GMATH posted a reply to At Perry High School, the ratio of students who participate in the Problem Solving forum “Trivial application of the k technique and Venn diagrams ("overlapping sets"): \[\frac{{B \cup C}}{{{\text{none}}}} = \frac{3}{8}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered} \,B \cup C\,\,{\text{ = }}\,\,{\text{3}}k \hfill \\ \,{\text{none}}\,\, = \,\,8k \hfill \\ ...” October 30, 2018 fskilnik@GMATH posted a reply to A salesperson for an automobile dealer earns an annual in the Problem Solving forum “Let´s explore a particular case, say x = 110,000. Our TARGET is 25,000 + 1/10 * (10,000) = 25,000 + 1,000 = 26,000 (dollars). (A) 25,000 + 11,000 --- wrong, OUT (B) 35,000 + (positive) --- wrong, OUT (C) 125,000 + (positive) --- wrong, OUT (D) 25,000 + 0.1 (negative) < 25,000 --- ...” October 30, 2018 Brent@GMATPrepNow posted a reply to A certain basket contains 10 apples, 7 of which are red and in the Problem Solving forum “Jay has demonstrated a solution that involves counting techniques. Here''s one that involves probability rules. Let''s find the probability of selecting a red apple 1st, a red apple 2nd, and a green apple 3rd (aka RRG) P(red apple 1st AND red apple 2nd AND green apple 3rd) = P(red apple 1st) x ...” October 30, 2018 Brent@GMATPrepNow posted a reply to A salesperson for an automobile dealer earns an annual in the Problem Solving forum “Total earnings = (base salary) + (commission) base salary = 25,000 commission = 10% of total sales OVER 100,000 = 10% of (x - 100,000) = 0.1(x - 100,000) So, total earnings = 25,000 + 0.1(x - 100,000) Answer: E Cheers, Brent” October 30, 2018 Brent@GMATPrepNow posted a reply to There are 16 teams in a soccer league, and team plays each in the Problem Solving forum “Another approach: The question is really asking, "In how many different ways can we create 2-team pairings from 16 teams?" Since the order of the selections does not matter (i.e., selecting teams A and B to play, is the same as selecting teams B and A to play), we can use combinations. ...” October 30, 2018 Brent@GMATPrepNow posted a reply to There are 16 teams in a soccer league, and team plays each in the Problem Solving forum “There are 16 teams. If we ask each team, "How many teams did you play?" we''ll find that each team played 15 teams, which gives us a total of 240 games (since 16 x 15 = 240). From here we need to recognize that each game has been COUNTED TWICE. For example, if Team A and Team B play ...” October 30, 2018 GMATGuruNY posted a reply to The average weight of a class is x pounds. When a new in the Problem Solving forum “We can PLUG IN THE ANSWERS and use alligation. To learn about alligation, check my posts here: https://www.beatthegmat.com/statistics-average-question-t288903.html https://www.beatthegmat.com/alligation-method-t293459.html https://www.beatthegmat.com/mean-t266852.html Let O = the original ...” October 30, 2018 GMATGuruNY posted a reply to Machines X and Y can work at their respective constant rates in the Data Sufficiency forum “Statement 1: Time and rate have a RECIPROCAL relationship. Since X and Y together take 2/3 as long as Y alone, X and Y together work 3/2 as fast as Y alone. Thus, if Y''s rate alone = 2 units per hour, then X and Y''s combined rate = (3/2)(2) = 3 units per hour, implying that X''s rate alone = ...” October 30, 2018 fskilnik@GMATH posted a reply to Machines X and Y can work at their respective constant rates in the Data Sufficiency forum “?\,\,:\,\,{T_X}\,,\,\,{T_Y}\,\,{\rm{relationship}}\,\,\,\,\,\,\left( {? = {T_X}\mathop \to \limits^{\Delta \% } {T_Y} = {{{T_Y} - {T_X}} \over {{T_X}}} = {{{T_Y}} \over {{T_X}}} - 1} \right) Important: the ratio of time taken (for any given job) is the inverse of the ratio of the work done ...” October 30, 2018 fskilnik@GMATH posted a reply to A circus clown is entertaining kids by making balloon in the Problem Solving forum “\left\{ \matrix{ \,4\,{\rm{animals}} \hfill \cr \,5\,{\rm{colors}} \hfill \cr} \right.\,\,\,\,\, \to \,\,\,\,{\rm{randomly}}\,\,{\rm{choice}}\,\,{\rm{of}}\,\,{\rm{one}}\,\,{\rm{of}}\,\,{\rm{each}} {\rm{? = P}}\left( ...” October 30, 2018 fskilnik@GMATH posted a reply to The average weight of a class is x pounds. When a new in the Problem Solving forum “(All weights are in pounds.) ? = x Excellent opportunity to use the homogeneity nature of the average: \sum\nolimits_n { = \,\,nx\,\,\,\,\,\left( {n\,\,{\rm{students}}} \right)} \left\{ \matrix{ 80 + \sum\nolimits_n {\, = \sum\nolimits_{n + 1} {\, = \,\,\left( {n + 1} \right)\left( ...” October 30, 2018 fskilnik@GMATH posted a reply to In 1995 a certain store had 1,800 tools in stock that had in the Problem Solving forum “\[\begin{array}{*{20}{c}} {1800\,\,{\text{units}}} \\ {{\text{cost}}\,\,\ 30\,{\text{each}}} \end{array}\,\,\,\,\,\left\{ \begin{gathered} \,\left( {95} \right)\,\,1000\,\,{\text{units}}\,,\,\,\,{\text{sold}}\,\,\ 40\,\,{\text{each}}\,\,\,\,\, \to ...” October 29, 2018 fskilnik@GMATH posted a reply to Set S contains nine distinct points in the coordinate plane. in the Problem Solving forum “\[? = C\left( {9,3} \right) - C\left( {5,3} \right) = \frac{{9 \cdot 8 \cdot 7}}{{3 \cdot 2}} - \frac{{5 \cdot 4}}{2} = 12 \cdot 7 - 10 = 74$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” October 29, 2018 GMATGuruNY posted a reply to Set S contains nine distinct points in the coordinate plane. in the Problem Solving forum “To form a triangle, we must select 3 points such that at most 2 are collinear. Case 1: Select 3 points not on the x-axis From the 4 points not on the x-axis, the number of ways to choose 3 = 4C3 = (4*3*2)/(3*2*1) = 4. Case 2: Select 1 point on the x-axis and two points not on the x-axis From ...” October 29, 2018 fskilnik@GMATH posted a reply to The average age of a group of n people is 15 yrs. One more in the Problem Solving forum “\Perfect opportunity to use the homogeneity nature of the average: $\left. \begin{gathered} \sum\nolimits_n { = 15 \cdot n} \hfill \\ 39 + \sum\nolimits_n { = \sum\nolimits_{n + 1} { = \,\,\,} 17 \cdot \left( {n + 1} \right)\,\,\,} \, \hfill \\ \end{gathered} \right\}\,\,\,\,\,39 + 15n ...” October 29, 2018 fskilnik@GMATH posted a reply to The figure above represents a rectangular garden bordered by in the Data Sufficiency forum “All lengths are considered in feet. \https://preview.ibb.co/cd9mDA/29-Oct18-3w.gif \[\left( 1 \right)\,\,\,2\left( {a + b} \right) = 124\,\,\,\, \Rightarrow \,\,\,\,? = a + b\,\,\,{\text{unique}}$ $\left( 2 \right)\,\,\left( {a - 6} \right)\left( {b - 6} \right) = 600\,\,\,\,\left\{ ...” October 29, 2018 fskilnik@GMATH posted a reply to For integers a, b, c, a/(b - c)=1 what is the value of (b-c) in the Data Sufficiency forum “\Important: to offer a viable BIFURCATION, we must also control the value of c, so that all restrictions are shown to be obeyed. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” October 29, 2018 fskilnik@GMATH posted a reply to Employees at a company will vote for an executive team of in the Problem Solving forum “\[? = \underbrace {C\left( {8,1} \right)}_{{\text{president}}} \cdot \underbrace {C\left( {7,1} \right)}_{{\text{treasurer}}} \cdot \underbrace {C\left( {6,3} \right)}_{{\text{3}}\,\,{\text{officers}}} = 8 \cdot 7 \cdot \frac{{6 \cdot 5 \cdot 4}}{{3 \cdot 2}} = 56 \cdot 20 = 1220$ This solution ...” October 29, 2018 Brent@GMATPrepNow posted a reply to For integers a, b, c, a/(b - c)=1 what is the value of (b-c) in the Data Sufficiency forum “ Given: a/(b - c) = 1 Target question: What is the value of (b-c)/b ? This is a good candidate for rephrasing the target question. Aside: Here’s a video with tips on rephrasing the target question: If a/(b - c) = 1, then we know that a = b - c The target question asks "What is the ...” October 29, 2018 Brent@GMATPrepNow posted a reply to If a and b are integers such that a > b > 1, which of in the Problem Solving forum “Let''s make an important observation. Some positive multiples of 3 are: 3, 6, 9, 12, . . . . Some positive multiples of 5 are: 5, 10, 15, 20, . . . . Some positive multiples of 12 are: 12, 24, 36, 48, . . . . General observation: the positive multiples of k are all greater than or equal to k ...” October 29, 2018 Brent@GMATPrepNow posted a new topic called Challenge: If x and y are different positive integers, which in the Problem Solving forum “If x and y are different positive integers, which of the following COULD be true: i) When x is divided by y, the remainder is x ii) When 2x is divided by y, the remainder is x iii) When x+y is divided by x , the remainder is x-y A) i only B) i & ii only C) i & iii only D) ii & ...” October 29, 2018 Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum “Target question: What is the value of x? Statement 1: (x + 2)(x + 3) = 0 This means that EITHER x = -2 OR x = -3 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x² + 5x + 6 = 0 Factor the left side of the equation to get: (x + 2)(x ...” October 29, 2018 GMATGuruNY posted a reply to Employees at a company will vote for an executive team of in the Problem Solving forum “Number of options for president = 8. (Any of the 8 candidates.) Number of options for treasurer = 7. (Any of the 7 remaining candidates.) From the 6 remaining people, the number of ways to choose 3 to serve as warrant officers = 6C3 = (6*5*4)/(3*2*1) = 20. To combine these options, we multiply: ...” October 29, 2018 fskilnik@GMATH posted a reply to If a and b are integers such that a > b > 1, which of in the Problem Solving forum “a > b \ge 2\,\,\,{\rm{ints}} ?\,\,:\,\,\underline {{\rm{not}}} \,\,{\rm{multiple}}\,\,{\rm{of}}\,\,a,b\, {\rm{Take}}\,\,\left( {a,b} \right) = \left( {3,2} \right)\,\,\,\,\left\{ \matrix{ \,a - 1\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,b\,\,\,\, \Rightarrow ...” October 29, 2018 fskilnik@GMATH posted a reply to A length of rope is cut into three different lengths. What in the Data Sufficiency forum “All lengths are presented in feet. {\rm{rope}}:\,\,s < i < l\,\,\,\,\left\{ \matrix{ \,? = s\,\,\left( {{\rm{shortest}}} \right) \hfill \cr \,i\,\,\left( {{\rm{intermediate}}} \right) \hfill \cr \,l\,\,\left( {{\rm{longest}}} \right) \hfill \cr} \right. Let go straight to ...” October 29, 2018 fskilnik@GMATH posted a reply to (x^2-3x+2)(y^2-5y+6)=? in the Data Sufficiency forum “? = {{{x^2} - 3x + 2} \over {{y^2} - 5y + 6}}\,\,\,\,\,\,\,\,\,\left[ {\,{y^2} - 5y + 6 \ne 0\,\,{\rm{implicitly}}\,} \right] \left( 1 \right)\,\,x = 1\,\,\,\, \Rightarrow \,\,\,\,? = {{1 - 3 + 2} \over {{y^2} - 5y + 6}} = 0\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}. \left( 2 ...” October 29, 2018 fskilnik@GMATH posted a reply to A set of pencils can be evenly shared between 2, 3, 4, 5 and in the Problem Solving forum “? = LCM\left( {2,3,4,5,6} \right) = LCM\left( {6,4,5} \right) = LCM\left( {12,5} \right) = 60 The correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” October 29, 2018 GMATGuruNY posted a reply to A set of pencils can be evenly shared between 2, 3, 4, 5 and in the Problem Solving forum “For the set of pencils to be shared evenly, the total number of pencils must be divisible by the total number of children. Thus, the correct answer must be divisible by 2, 3, 4, 5 and 6. Of the five answer choices, only E is divisible by 2, 3, 4, 5 and 6. The correct answer is E.” October 29, 2018 GMATGuruNY posted a reply to (x^2-3x+2)(y^2-5y+6)=? in the Data Sufficiency forum “Statement 1: Substituting x=1 into (x² - 3x + 2)(y² - 5x + 6), we get: (1 - 3*1 + 2)(y² - 5x + 6) = (0)(y² - 5x + 6) = 0. SUFFICIENT. Statement 2: Substituting y=1 into (x² - 3x + 2)(y² - 5x + 6), we get: (x² - 3x + 2)(1² - 5*1 + 6) = (x² - 3x + 2)(2). Since the value of x is ...” October 29, 2018 Brent@GMATPrepNow posted a reply to A length of rope is cut into three different lengths. What in the Data Sufficiency forum “Target question: What is the length of the shortest rope? Let''s assign some variables. Let x = length of shortest rope Let y = length of middle rope Let z = length of longest rope Statement 1: The combined length of the longest two pieces is 6 feet. In other words, y + z = 6 Since we ...” October 28, 2018 Brent@GMATPrepNow posted a reply to Challenge question: At noon, Joe and a hummingbird leave in the Problem Solving forum “The main idea here is that all 3 travelers travel for the SAME amount of time. So, let''s first determine the time it takes for Joe and Sue to meet. This is a shrinking gap question. To determine the rate at which the gap shrinks, we''ll ADD the travel speeds of Joe and Sue That is, ...” October 28, 2018 fskilnik@GMATH posted a reply to Two pieces of fruit are selected out of a group of 8 pieces in the Data Sufficiency forum “$2\,\,{\text{extractions}}\,\,{\text{from}}\,\,8\,\,\left\{ \begin{gathered} \,{\text{apples}}\,\,\left( A \right) \hfill \\ \,{\text{bananas}}\,\,\left( {B = 8 - A} \right) \hfill \\ \end{gathered} \right.$ $? = P\left( {{\text{both}}\,{\text{extractions}}\,\,{\text{bananas}}} ...” October 28, 2018 fskilnik@GMATH posted a reply to N is a two-digit number, whose tens digit is 9. If the units in the Data Sufficiency forum “\left\langle N \right\rangle = {\rm{units}}\,\,{\rm{digit}}\,\,{\rm{of}}\,\,N\,\,\, \a = 0,1,2,3,5,6,7,8 or 9, when a is put to an odd positive power, we don´t get units digit equal to 4, as needed. This solution follows the notations and rationale taught in the GMATH method. ...” October 28, 2018 fskilnik@GMATH posted a reply to How many integers are there between, but not including, in the Data Sufficiency forum “?\,\, = \,\,s - r - 1\,\,\,\,\left( {{\rm{the\,\, fingers}}\,\,{\rm{counting}}\,\,{\rm{technique}}} \right) \left( 1 \right)\,\,s - r = 10\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 9\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\, \left( 2 \right)\,\,\left( {s + 1} \right) - \left( ...” October 28, 2018 fskilnik@GMATH posted a reply to If x and y are positive, what is the value of y ? in the Data Sufficiency forum “\Let´s go straight to (1+2). Our BIFURCATION will guarantee that the correct answer is (E) immediately! \left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{ \,xy = {M^2}\,,\,\,M\,\,{\mathop{\rm int}} \hfill \cr \,6x = 2y\,\,\, \Rightarrow \,\,\,y = 3x \hfill \cr} \right.\,\,\,\,\,\left( * ...” October 28, 2018 fskilnik@GMATH posted a reply to Jonah drove the first half of a 100-mile trip in x hours and in the Problem Solving forum “\[?\,\,\,\, = \,\,\,\frac{{\,{\text{total}}\,\,{\text{# }}\,\,{\text{miles}}\,}}{{{\text{total}}\,\,{\text{# }}\,\,{\text{hours}}}}\,\,\, = \,\,\,\frac{{100}}{{x + y}}\,\,\,\,\,\,\,\left[ {\,{\text{mph}}\,} \right]$ This solution follows the notations and rationale taught in the GMATH method. ...” October 28, 2018 fskilnik@GMATH posted a reply to What is the height of P from AB in the figure in the Problem Solving forum “\Important: the distance between a given straight line r and a given point P that does not belong to r is equal to the length of the line segment PQ, where Q is the intersection of r and the perpendicular to this line that passes through P (see figure, in this case Q=B). ...” October 28, 2018 fskilnik@GMATH posted a reply to In the figure above, an equilateral triangle is inscribed in in the Problem Solving forum “?\,\,\,:\,\,\,D = 2r\,\,\,\,\underline {{\rm{could}}} \,\,\,{\rm{be}} 4\pi \,\,\, < \,\,\,{\rm{arc}}\,\,{\rm{length}}\,\,{\rm{ = }}\,\,{1 \over 3}\left( {2\pi r} \right)\,\,\, < \,\,\,6\pi \,\,\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi \,\,\,{\rm{and}}\,\,\, \cdot \,\,3} \,\,\,\,\,4 ...” October 28, 2018 fskilnik@GMATH posted a reply to Recently, scientists were able to sequence an individual's h in the Problem Solving forum “Let´s use UNITS CONTROL, one of the most powerful tools of our method! \left. \matrix{ {{1\,\,{\rm{job}}} \over {\,4\,{\rm{weeks}}\,}}\,\,{\rm{each}}\,\,{\rm{of}}\,\,x\,\,{\rm{new}}\,\,{\rm{computers}}\,\, \Rightarrow \,\,\,{{1 \cdot 6 \cdot x\,\,{\rm{jobs}}} \over {\,4 \cdot ...” October 28, 2018 Brent@GMATPrepNow posted a reply to If x and y are positive, what is the value of y ? in the Data Sufficiency forum “Target question: What is the value of y? Given: x and y are positive Statement 1: xy is the square of an integer. There are several values of x and y that satisfy this condition. Here are two: Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this ...” October 28, 2018 GMATGuruNY posted a reply to How many integers are there between, but not including, in the Data Sufficiency forum “Statement 1: Case 1: r=0 and s=10 Integers between r and s: 1, 2, 3, 4, 5, 6, 7, 8, 9 --> 9 integers Case 2: r=1 and s=11 Integers between r and s: 2, 3, 4, 5, 6, 7, 8, 9, 10 --> 9 integers Case 3: r=2 and s=12 Integers between r and s: 3, 4, 5, 6, 7, 8, 9, 10, 11 --> 9 ...” October 28, 2018 GMATGuruNY posted a reply to Both Betty and Wilma earn annual salaries of more than 5000 in the Data Sufficiency forum “Statement 1: Betty''s annual salary is closer to 50000 than Wilma''s is. On a number line: -----50,000---B---W Thus, W > B. SUFFICIENT. Statement 2: Betty''s annual salary is closer to 35000 than it is to Wilma''s annual salary. Case 1: -----35,000-----50,000---B---W Case 2: ...” October 28, 2018 fskilnik@GMATH posted a reply to When the positive integer n is divided by 25, the remainder in the Data Sufficiency forum “\left\{ \matrix{ n \ge 1\,\,{\mathop{\rm int}} \hfill \cr n = 25Q + 13,\,\,Q \ge 0\,\,{\mathop{\rm int}} \hfill \cr} \right. ? = n \left( 1 \right)\,\,n < 100\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{Q = 0}}\,\,\,\, \Rightarrow \,\,\,\,\,n = 13 \hfill \cr ...” October 28, 2018 fskilnik@GMATH posted a reply to In the triangle above what is the measure of angle CDB? in the Data Sufficiency forum “? = \angle CDB = x (All angles are measured in degrees.) (1) Using the exterior angle property (to justify 30+30 in red), triangle BCD is equilateral (hence x=60). Sufficient! (2) The constructions shown below are viable and present two different possible values for x. Insufficient! ...” October 28, 2018 fskilnik@GMATH posted a reply to Both Betty and Wilma earn annual salaries of more than 5000 in the Data Sufficiency forum “All numbers presented below are annual salaries expressed in thousands of dollars. B,W\,\, > \,\,50\,\,\left( * \right) W\,\,\mathop > \limits^? \,\,B \left( 1 \right)\,\,{\rm{and}}\,\,\left( * \right)\,\,\,B - 50 < W - 50\,\,\,\, \Rightarrow \,\,\,\,B < W\,\,\,\,\, ...” October 28, 2018 fskilnik@GMATH posted a reply to If a certain wheel turns at a constant rate of x revolutions in the Problem Solving forum “x\,\,{\rm{revol}}\,\,\, \leftrightarrow \,\,\,1\,\,\min  ?\,\,=\,\,\# \,\,{\rm{revol}}\,\,{\rm{in}}\,\,k\,\,\sec  Trivial application of UNITS CONTROL, one of the most powerful tools of our method! ? = k\,\,\sec \,\,\left( {{{1\,\,\min } \over {60\,\,\sec }}} \right)\,\,\left( ...” October 28, 2018 Brent@GMATPrepNow posted a new topic called Challenge question: At noon, Joe and a hummingbird leave in the Problem Solving forum “At noon, Joe and a hummingbird leave point A and travel towards point B, which is 12 miles away. At the same time Sue leaves point B and travels toward point A. Joe, Sue and the hummingbird travel at constant speeds of 3 miles per hour, 4 miles per hour, and 84 miles per hour respectively. When the ...” October 27, 2018 Brent@GMATPrepNow posted a reply to There are n students in a class. Of them, k boys and k girls in the Data Sufficiency forum “Target question: What is the probability that Harvey will be paired with Jessica? Given: There are n students in a class. Of them, k boys and k girls (including Harvey and Jessica) are selected for a dance performance in which students will dance in pairs of one boy and one girl. ...” October 27, 2018 Brent@GMATPrepNow posted a reply to When the positive integer n is divided by 25, the remainder in the Data Sufficiency forum “Target question: What is the value of n? Given: When the positive integer n is divided by 25, the remainder is 13. -------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, ...” October 27, 2018 Brent@GMATPrepNow posted a reply to A circus clown is entertaining kids by making balloon in the Problem Solving forum “As with many probability questions, we can solve this by using counting techniques or rules of probability. Let''s use rules of probability P(balloon animal is an elephant) = 1/4 P(balloon animal is purple) = 1/5 P(clown makes a purple elephant balloon animal) = P(balloon animal is ...” October 27, 2018 Brent@GMATPrepNow posted a reply to In a right triangle, the longer leg is two more than three in the Problem Solving forum “In a right triangle, the longest side is called the hypotenuse, and the two sides that meet to create a 90-degree angle are called the legs. So, one leg will be the triangle''s base, and the other leg will be the triangle''s height. Let x = length of the triangle''s base (which, for this ...” October 27, 2018 GMATGuruNY posted a reply to In a right triangle, the longer leg is two more than three in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the length of the shorter leg. When the correct answer is plugged in, the area = 400. B: 20 Longer leg = two more than three times the shorter leg = 2 + 3*20 = 62. Area = (1/2)(20)(62) = 620. Since the area is too great, a smaller answer choice is ...” October 27, 2018 GMATGuruNY posted a reply to A framed picture is shown above. The frame, shown shaded, is in the Data Sufficiency forum “Statement 1: Test one case that also satisfies Statement 2. Case 1: The frame is 8 inches tall, with the result that the total area of the frame and picture combined = 6*8 = 48 Area of the picture = (total area) - (shaded region) = 48-24 = 24. Implication: The width of the frame is 1 inch, ...” October 27, 2018 fskilnik@GMATH posted a reply to Six congruent circles are packed into an equilateral in the Data Sufficiency forum “?\,\,\, = \,\,\,{S_\Delta } - 6 \cdot {S_ \circ } The GMATH widget (a.k.a "GW") is defined in the figure below. It is formed combining an equilateral triangle (side length 4r) and three "legs" (length r each), where r is any positive number. ...” October 26, 2018 fskilnik@GMATH posted a reply to Set S contains consecutive natural numbers from 1 to 100, in in the Problem Solving forum “{{{S_{\,{\rm{even}}}}} \over {{S_{\,{\rm{odd}}}}}} = {{16} \over {85}}\,\,\,\,\,;\,\,\,\,\,\,? = n It´s easy to find a PATTERN! n = 2\,\,\,\, \to \,\,\,{{2 + 4} \over {97 + 99}} = {{2 \cdot 3} \over {2 \cdot 98}} = {3 \over {98}}\,\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{numerator}} = n + 1 ...” October 26, 2018 fskilnik@GMATH posted a reply to When Q is divided by W, the quotient is R and the remainder in the Problem Solving forum “Brent´s nice explanation is (part of) the so-called Division Algorithm. I would like to add that the remainder is always a non-negative integer less than the divisor. (In GMAT´s scope, the divisor is always a positive integer.) (In our case, 0 <= E < W.) Let´s explore a particular ...” October 26, 2018 Brent@GMATPrepNow posted a reply to If a and b are two positive numbers, what is the product of in the Data Sufficiency forum “Target question: What is the value of ab? Statement 1: The LCM of a and b is 16 Let''s TEST some values. There are several values of a and b that satisfy statement 1. Here are two: Case a: a = 1 and b = 16 (the LCM of 1 and 16 is 16). In this case, the answer to the target question is ab = ...” October 26, 2018 Brent@GMATPrepNow posted a reply to In the mid-1960's a newly installed radar warning system in the Sentence Correction forum “The idiom here is "Mistake x FOR y" So, we can eliminate A, C and E We''re left with B and D D conveys an ambiguous message, because it suggests that the moon was rising for an attack. ELIMINATE D Answer: B Cheers, Brent” October 26, 2018 GMATGuruNY posted a reply to What is the largest prime factor of the expression 3^8 − 2 in the Problem Solving forum “A general rule: Given x^(even power) - y^(even power), where x and y are distinct positive integers, we can always simplify by applying the difference of two squares. Each time we apply the difference of two squares to the expression in blue, the exponents are reduced by 1/2. For example: x⁸ - ...” October 26, 2018 Brent@GMATPrepNow posted a reply to What is the largest prime factor of the expression 3^8 − 2 in the Problem Solving forum “There''s a difference of squares "hiding" in the expression 3^8 − 2^12 That is 3^8 − 2^12 = (3^4)² − (2^6)² We know that: x² - y² = (x + y)(x - y) So, we get: (3^4)² − (2^6)² = (3^4 + 2^6)(3^4 - 2^6) = (81 + 64)(81 - 64) = (145)(17) = (5)(29)(17) The greatest ...” October 26, 2018 GMATGuruNY posted a reply to Jazz and blues recordings accounted for 6 percent of the in the Data Sufficiency forum “Let J = jazz and blues revenue in 1998. Statement 1: Case 1: Total revenue in 1998 = 100 In this case, J = 5% of 100 = 5. Case 2: Total revenue in 1998 = 1000 In this case, J = 5% of 1000 = 50. Since J can be different values, INSUFFICIENT. Statement 2: In other words: (jazz and blues ...” October 26, 2018 Brent@GMATPrepNow posted a reply to When Q is divided by W, the quotient is R and the remainder in the Problem Solving forum “-----ASIDE----------------------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, ...” October 26, 2018 GMATGuruNY posted a reply to x and y are non-negative integers. If xy+2x+3y=0, then y=? in the Problem Solving forum “NONNEGATIVE implies that we should test ZERO. Let x=0. Substituting x=0 into xy + 2x + 3y = 0, we get: 0*y + 2*0 + 3y = 0 3y = 0 y = 0 The correct answer is A.” October 26, 2018 GMATGuruNY posted a reply to Set S contains consecutive natural numbers from 1 to 100, in in the Problem Solving forum “For any evenly spaced set: sum = (count)(median) Sum of the first n even numbers = n * median of the first n even numbers Sum of the last n odd numbers = n * median of the last n odd numbers Since the ratio of the two sums = 16/85, we get: (n * median of the first n even numbers) / (n * ...” October 26, 2018 fskilnik@GMATH posted a reply to n is an integer. Is n(n+2) a multiple of 8? in the Data Sufficiency forum “{{n\left( {n + 2} \right)} \over 8}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}} \,\,\,\,\,\,\,\left( {n\,\,\,{\mathop{\rm int}} } \right) \left( 1 \right)\,\,n\,\,{\rm{even}}\,\,\, \Rightarrow \,\,\,{\rm{n = 2M}}{\rm{,}}\,\,\,{\rm{M}}\,\,{\mathop{\rm int}}  {{n\left( {n + 2} \right)} ...” October 26, 2018 fskilnik@GMATH posted a reply to x and y are non-negative integers. If xy+2x+3y=0, then y=? in the Problem Solving forum “\left\{ \matrix{ x,y \ge 0\,\,{\rm{ints}}\,\,\,\left( * \right) \hfill \cr xy + 2x + 3y = 0\,\,\left( {**} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,? = y You should realize the pair (x,y)=(0,0) satisfies all above, hence y=0 must be the right answer. On the other ...” October 26, 2018 Brent@GMATPrepNow posted a reply to Tricky: If AB || DE, and AB = 10, what is the length of DE? in the Data Sufficiency forum “Let''s first add the given information (and their implications) to the diagram If AB || DE, we know that ∠BAC = ∠CED and ∠ABC = ∠DCE Also, since vertically opposite angles are equal, we know that ∠ACB = ∠DCE https://i.imgur.com/fgDp7Yh.png Now that we''ve identified 3 pairs of ...” October 26, 2018 fskilnik@GMATH posted a reply to When 900 is divided by positive integer d, the remainder is in the Data Sufficiency forum “Very nice conceptual problem! d,D\,\,\, \ge 1\,\,\,;\,\,\,\,N\,\,\, \ge \,\,5001\,\,\,\,\,\,\left( {\,{\rm{ints}}\,} \right) \left\{ \matrix{ 900 = {Q_1} \cdot d + r\,\,\,\,\,\,\left[ {\,0 \le r < d\,\,,\,\,\,\,r\,\,{\mathop{\rm int}} \,} \right]\,\,\,\,\,\,\,\left( * \right) \hfill ...” October 25, 2018 Brent@GMATPrepNow posted a new topic called Tricky: If AB || DE, and AB = 10, what is the length of DE? in the Data Sufficiency forum “https://i.imgur.com/jyTAK6n.png If AB || DE, and AB = 10, what is the length of DE? (1) BC = 6 and CE = 4 (2) DC = 3 and CB = 6 Answer: B Difficulty level: 650 – 700 Source: www.gmatprepnow.com” October 25, 2018 fskilnik@GMATH posted a reply to Tom drives from town A to town B, driving at a constant in the Problem Solving forum “?\,\, = \,\,\,{V_{B \to C}}\,\,\,\,\,\,\leftUNITS CONTROL, one of the most powerful tools of our method! {\rm{Let}}\,\,B \to C = 180\,\,{\rm{miles}}\,\,\,\,\,\left[ {\,180 = LCM\left( {60,36} \right)\,} \right] \left. \matrix{ \left. {\matrix{ {A \to B} \cr {2 \cdot ...” October 25, 2018 fskilnik@GMATH posted a reply to Quentin's income is 60% less than Rex's income, and Sam's in the Problem Solving forum “? = {Q \over S} \left. \matrix{ Q = {2 \over 5}R\,\,\,\,\left( {40\% R} \right)\,\,\,\,\,\,\,\,\,\,\, + \,\,\,\,\,\,{2 \over 5}R\,\,\,\,\left( {40\% R} \right)\,\,\,\,\, = \,\,\,{4 \over 5}R \hfill \cr S = {3 \over 4}Q\,\,\,\left( {75\% Q} \right) = \,\,{3 \over 4}\left( {{2 \over 5}R} ...” October 25, 2018 fskilnik@GMATH posted a reply to If |x-6|=2x, then x=? in the Problem Solving forum “?\,\,\,:\,\,\,\,x\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,\,\left| {x - 6} \right| = 2x\,\,\,\,\,\left( {{\rm{Note}}\,\,{\rm{that}}\,\,\,2x \ge 0\,\,,\,\,{\rm{hence}}\,\,x \ge 0} \right) \left| {x - 6} \right| = 2x\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,\,\,\,\,{\left( ...” October 25, 2018 Brent@GMATPrepNow posted a reply to If |x-6|=2x, then x=? in the Problem Solving forum “There are 3 steps to solving equations involving ABSOLUTE VALUE: 1. Apply the rule that says: If |x| = k, then x = k or x = -k 2. Solve the resulting equations 3. Plug solutions into original equation to check for extraneous roots Step 1: x - 6 = 2x or x - 6 = -2x case a: x - 6 = 2x Step ...” October 25, 2018 GMATGuruNY posted a reply to Quentin's income is 60% less than Rex's income, and Sam's in the Problem Solving forum “Let Rex''s income = 100. Since Quentin''s income is 60% less than Rex''s, Quentin''s income = 100 - (60% of 100) = 100-60 = 40. Since Sam''s income is 25% less than Quentin''s, Sam''s income = 40 - (25% of 40) = 40-10 = 30. After Rex gives 60% of his income to Sam, Sam''s new income = 30 + (60% ...” October 25, 2018 GMATGuruNY posted a reply to If |x-6|=2x, then x=? in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the value of x. Since an absolute value cannot be equal to a negative value, the correct answer cannot be A or B. D: x=2 If we plug x=2 into |x-6|=2x, we get: |2-6| = 2*2 |-4| = 4 4 = 4. Success! The correct answer is D.” October 25, 2018 GMATGuruNY posted a reply to Tom drives from town A to town B, driving at a constant 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 mph, ...” October 25, 2018 fskilnik@GMATH posted a reply to In the coordinate geometry plane, region P is defined by all in the Data Sufficiency forum “3y + 12 > 2x\,\,\,\,\, \Leftrightarrow \,\,\,\,\,2x - 3y < 12 \left( {a,b} \right)\,\,\,\mathop \in \limits^? \:\,{\text{region}}\,P\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\boxed{\,\,\,2a - 3b\,\,\,\mathop < \limits^? \,\,\,\,12\:\,} Let´s BIFURCATE (1+2), that is, present two ...” October 24, 2018 fskilnik@GMATH posted a reply to For integers m and n, the operation △ is defined by m△n in the Data Sufficiency forum “m\ \triangle\ n\ =\ \left(m-1\right)^2+\left(n+1\right)^2 \,\,\,\,\,\left[ {m,n\,\,{\rm{ints}}} \right] ? = x\,\,\,\,\,\,\left[ {\,x\,\,{\mathop{\rm int}} \,} \right] \left( 1 \right)\,\,\,4 = x\,\vartriangle \:1\,\, = \,\,{\left( {x - 1} \right)^2} + {\left( {1 + 1} ...” October 24, 2018 fskilnik@GMATH posted a reply to The discount offer "Buy 2 and get 3" is equivalent in the Problem Solving forum “?\,\, = \,\,\Delta \% \,\,\,\,\,\,\,\left( {\Delta \% < 0} \right) Three items with price of (say) 10 each would cost 30 (all 3 of them) but they are offered by 20 (all 3 of them). Hence: ?\,\,\,\, = \,\,\,\,\Delta \% \,\,\left( {30 \to 20} \right)\,\,\,\, = \,\,\,\,{{20 - 30} \over ...” October 24, 2018 fskilnik@GMATH posted a reply to All attendees at a university gathering are faculty or in the Data Sufficiency forum “In the Venn diagram shown below I present a (1+2) BIFURCATION, that is, two possible viable scenarios for (1+2). https://preview.ibb.co/kvmTDA/23-Oct18-7h.gif The correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, ...” October 24, 2018 GMATGuruNY posted a reply to gmat prep 2 in the Critical Reasoning forum “The negation test is not recommended for Evaluate CRs. It can be applied to Assumption CRs and Inference CRs.” October 24, 2018 GMATGuruNY posted a reply to Computer-based activities in the Critical Reasoning forum “The answer choices are already phrased as statements. The OA is a statement that weakens the conclusion. OA: Computer owners in the United States predominately belong to a demographic group that have long been known to spend less time watching television. This statement indicates that a lack of ...” October 24, 2018 GMATGuruNY posted a reply to Noelle walks from point A to point B at an average speed of in the Problem Solving forum “Let the distance between A and B = the LCM of the two speeds = 5*6 = 30 kilometers, implying that the distance for the entire round trip = 60 kilometers. At a rate of 5 kph, the time to travel the 30 kilometers from A to B = d/r = 30/5 = 6 hours. At a rate of 6 kph, the time to travel the entire ...” October 24, 2018 Brent@GMATPrepNow posted a reply to CHALLENGE: 10 teams (A, B, C, D, E, F, G, H, I and J) partic in the Problem Solving forum “First determine the TOTAL number of games played. We can select 2 teams from 10 teams in 10C2 ways (= 45 ways) So, there will be 45 games in TOTAL IMPORTANT: Each team plays 9 games For each game, 2 points are awarded. So, the TOTAL number of POINTS awarded = (2)(45) = 90 Teams A, B, C, ...” October 24, 2018 Brent@GMATPrepNow posted a reply to Noelle walks from point A to point B at an average speed of in the Problem Solving forum “For these kinds of questions, I typically follow the approach that Fabio used (assign a nice value to the distance). But we can also solve the question algebraically: Let d = the distance between Points A and B. Let x = the Noelle''s speed from Point B to Point A. We want the average ...” October 24, 2018 GMATGuruNY posted a reply to What is the median number of employees assigned per project in the Data Sufficiency forum “In ascending order of EMPLOYEES PER PROJECT, let the projects be numbered 1 through 100: 1, 2, 3.....49, 50, 51, ....98, 99, 100. Projects 50 and 51 determine the MEDIAN number of employees: Question rephrased: How many employees are assigned to PROJECTS 50 and 51? Looking at the two ...” October 24, 2018 Brent@GMATPrepNow posted a reply to What is the median number of employees assigned per project in the Data Sufficiency forum “Target question: What is the median number of employees assigned per project? Statement 1: 25 percent of the projects at Company Z have 4 or more employees assigned to each project. Let''s pretend that there are 4 projects altogether. There are several sets of values that meet this condition. ...” October 24, 2018 GMATGuruNY posted a reply to Three photographers , Lisa, Mike and Norm, take photos of a 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 by ...” October 24, 2018 fskilnik@GMATH posted a reply to Noelle walks from point A to point B at an average speed of in the Problem Solving forum “\left. \matrix{ {V_{A \to B}} =\,\, 5\,\,{{{\rm{km}}} \over {\rm{h}}} \hfill \cr {V_{B \to A}} =\,\, ?\,\,{{{\rm{km}}} \over {\rm{h}}}\,\, \hfill \cr} \right\}\,\,\,{\rm{for}}\,\,{V_{{\rm{average}}}} = 6\,\,{{{\rm{km}}} \over {\rm{h}}} {\rm{Take}}\,\,{\rm{dist}}\left( {A,B} \right) ...” October 24, 2018 GMATGuruNY posted a reply to Circle ABCD in the diagram above is defined by the equation in the Problem Solving forum “Circle ABCD: The equation for a circle with a center at the origin and a radius of r is x² + y² = r². The equation for circle ABCD is x² + y² = 5². Thus, circle ABCD has a radius of 5. Line EF: 3y = 4x + 25 y = (4/3)x + 25/3 Slope = 4/3. A radius drawn to a point of tangency forms ...” October 24, 2018 fskilnik@GMATH posted a reply to Circle ABCD in the diagram above is defined by the equation in the Problem Solving forum “Obs.: when a given line is tangent to a given circle, the point of tangency is (by definition) unique. Therefore the part in red in the question stem could (and should) be omitted! \left( * \right)\,\,\left\{ \matrix{ \,\left( {\rm{I}} \right)\,\,\,{x_p}^2 + {y_p}^2 = 25 \hfill \cr ...” October 24, 2018 fskilnik@GMATH posted a reply to Suppose f(x)=ax^4+bx^2+1, where a and b are constants. If f( in the Problem Solving forum “f\left( x \right) = a \cdot {x^4} + b \cdot {x^2} + 1\,\,\,\,\,\,\left( {a,b\,\,{\rm{conts}}} \right) ? = f\left( { - 3} \right) = a \cdot {\left( { - 3} \right)^4} + b \cdot {\left( { - 3} \right)^2} + 1 = a \cdot {3^4} + b \cdot {3^2} + 1 9 = f\left( 3 \right) = a \cdot {3^4} + b \cdot ...” October 24, 2018 fskilnik@GMATH posted a reply to In a certain company, the ratio of the number of manager to in the Problem Solving forum “Excellent opportunity for the k technique: \left\{ \matrix{ \,{\rm{managers}} = 5k \hfill \cr \,{\rm{workers}}\, = \,\,72k \hfill \cr} \right.\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,? = 5k {{5k} \over {72k + 8}} = {5 \over {74}}\,\,\,\,\,\,\,\,\mathop ...” October 23, 2018 Brent@GMATPrepNow posted a reply to In a certain company, the ratio of the number of manager to in the Problem Solving forum “One option is to use TWO VARIABLES Let M = CURRENT # of managers Let W = CURRENT # of production-line workers The ratio of the number of managers to the number of production-line workers is 5 to 72. So, we can write: M/W = 5/72 Cross multiply to get: 5W = 72M If 8 additional ...” October 23, 2018 Brent@GMATPrepNow posted a reply to When 100 is divided by positive integer x, the remainder is in the Problem Solving forum “A fast approach is to find a value of x that meets the given condition: When 100 is divided by positive integer x, the remainder is 2 Well, x = 98 satisfies that condition, since 100 divided by 98 = 1 with remainder 2 What is the remainder when 198 is divided by x? Well, 198 divided by 98 ...” October 23, 2018 fskilnik@GMATH posted a reply to At a constant speed of 72 kilometers per hour, a vehicle in the Problem Solving forum “Love that, Ceilidh! :) I created the expression because "values follow units", in other words, the units themselves "take control"... Kind Regards, Fabio.” October 23, 2018 fskilnik@GMATH posted a reply to A factory has three types of machines, each of which works in the Problem Solving forum “First of all, I owe you my apologies, Mitch. (I simply did not see the time stamps. My fault.) Very elegant observations, Ceilidh! I have already shown my respect to Mitch´s competence in the near past, by the way: https://www.beatthegmat.com/agatha-christiea-acute-s-escalator-t303990.html ...” October 23, 2018 GMATGuruNY posted a reply to A factory has three types of machines, each of which works in the Problem Solving forum “In many cases, similar or identical solutions are posted when two experts respond at virtually the same time, with the result that the second poster is not aware of the first. The time stamps for the two solutions here indicate that both solutions were posted at 11:45am.” October 23, 2018 fskilnik@GMATH posted a reply to If Machine B and Machine C work together at their constant in the Data Sufficiency forum “\BIFURCATION for (1+2), that is, two EXPLICIT VIABLE scenarios, each one giving a different answer to our FOCUS! One possible scenario is the following: A does x/2 widgets in 9 hours (hence x/6 in 3 hours and 2x/3 in 12 hours) , B does x/2 widgets in 9 hours and C does x/3 widgets in 12 hours. ...” October 23, 2018 fskilnik@GMATH posted a reply to All attendees at a university gathering are faculty or in the Data Sufficiency forum “In the Venn diagram shown below I present a (1+2) BIFURCATION, that is, two possible viable scenarios for (1+2). https://preview.ibb.co/kvmTDA/23-Oct18-7h.gif The correct answer is therefore (E). This solution follows the notations and rationale taught in the GMATH method. Regards, ...” October 23, 2018 fskilnik@GMATH posted a reply to A factory has three types of machines, each of which works in the Problem Solving forum “Hi there! I would like to suggest that we all avoid posting solutions that are IDENTICAL to solutions that were posted in the very same topic. This is not only in respect for our colleagues but also for the benefit of the whole BTG community. On this matter, if I violate this ...” October 23, 2018 fskilnik@GMATH posted a reply to At a constant speed of 72 kilometers per hour, a vehicle in the Problem Solving forum “Hi, Ceilidh! I am glad to know the Manhattan also considers UNITS CONTROL as one of its prep tools. (You call it UNITS CONVERSIONS but we are talking about the very same thing!) As you have already realized in this forum, this is one of the most powerful (and used) tools we offer in the ...” October 23, 2018 fskilnik@GMATH posted a reply to Which of the following values, when inserted into the set of in the Problem Solving forum “L = \left\{ {5,10,12,13,17,22,22} \right\}\,\, \cup \left\{ x \right\}\,\,\,\, \to \,\,\,\,\,{\rm{Me}}{{\rm{d}}_{\,{\rm{L}}}} = 15 ?\,\,\,\, = \,\,\,x The list L has 8 numbers, hence its median (15) must be the average of the fourth and fifth (when values are considered in increasing ...” October 23, 2018 GMATGuruNY posted a reply to A factory has three types of machines, each of which works in the Problem Solving forum “Rates can be ADDED TOGETHER. 7 Machine As and 11 Machine Bs can produce 250 widgets per hour. 7A + 11B = 250 8 Machine As and 22 Machine Cs can produce 600 widgets per hour. 8A + 22C = 600 4A + 11C = 300 Adding together 7A + 11B = 250 and 4A + 11C = 300, we get: 11A + 11B + 11C = 550 A ...” October 23, 2018 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Range and Standard Deviation Video: https://www.youtube.com/watch?v=FbAlIjw2fwY Cheers, Brent” October 23, 2018 Brent@GMATPrepNow posted a reply to Which of the following values, when inserted into the set of in the Problem Solving forum “Let''s test each answer choice.... A. 2 The new set becomes {2, 5, 10, 12, 13, 17, 22, 22} Since we have an EVEN number of values in the set, the median equals the average of the two middlemost numbers. So, median = (12 + 13)/2 = 25/2 = 12.5 No good - we want the median to be 15 B. ...” October 23, 2018 Brent@GMATPrepNow posted a reply to What are the coordinates of point B in the figure above ? in the Data Sufficiency forum “IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video below. Target question: What ...” October 23, 2018 Brent@GMATPrepNow posted a reply to The range of set A is 24 and the range of set B is 20. What in the Problem Solving forum “If the range of set A is 24, and we add more values (from set B) to set A, then the range of the resulting set must be greater than or equal to 24 (that is, the range of a set cannot get smaller upon adding MORE numbers to that set). For this reason, we can ELIMINATE answer choice A. From ...” October 23, 2018 fskilnik@GMATH posted a reply to In the xy-plane, does the graph of y=ax^2+c intersect the x- in the Data Sufficiency forum “\left\{ {\,\left( {x,y} \right)\,\,:\,\,\,y\,\, = a{x^2} + c\,\,\,,\,\,\,a \ne 0\,} \right\}\,\,\,\, \cap \,\,\,\left\{ {\,\left( {x,y} \right)\,\,:\,\,y = 0} \right\}\,\,\,\,\,\mathop \ne \limits^? \,\,\,\,\,\emptyset \, https://preview.ibb.co/gOaLRV/23-Oct18-3z.gif (1) a> 0 :: ...” October 23, 2018 Brent@GMATPrepNow posted a reply to If x and y are positive integers, what is the remainder when in the Data Sufficiency forum “ Given: x and y are positive integers Target question: What is the remainder when x^y is divided by 10? This is a good candidate for rephrasing the target question. Notice that 43 divided by 10 leaves remainder 3, and 127 divided by 10 leaves remainder 7, and 618 divided by 10 leaves ...” October 23, 2018 fskilnik@GMATH posted a reply to A Hydrogenator water gun has a cylindrical water tank, which in the Problem Solving forum “H = 30\,{\rm{cm}}\,\,\,\,\,\,\,{\rm{;}}\,\,\,\,\,\,\,{{\pi \,\,{\rm{c}}{{\rm{m}}^3}} \over {\,1\,\,{\rm{second}}\,}}\,\,\,{\rm{filling}}\,\,{\rm{rate}} {\rm{?}}\,\,{\rm{ = }}\,\,D\,\,\,\leftUNITS CONTROL, one of the most powerful tools of our method: {\rm{8}}\,{\rm{minutes}}\,\, \cdot ...” October 23, 2018 fskilnik@GMATH posted a reply to The range of set A is 24 and the range of set B is 20. What in the Problem Solving forum “? = \left( {{\rm{Rang}}{{\rm{e}}_{A \cup B}}} \right)\,\,\min  $\left. \begin{gathered} {\text{Rang}}{{\text{e}}_A} = 24{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \mathop \Rightarrow \limits^{{\text{WLOG}}{\mkern 1mu} \left( * \right)} \,\,\,\left\{ \begin{gathered} ...” October 23, 2018 GMATGuruNY posted a reply to 25 integers are written on a board. Are there at least two in the Data Sufficiency forum “The wording in Statement 1 does not convey a clear meaning: For every value in the list, if the value is increased by 1, the number of distinct values in the list does not change. Here, the term in red could convey to some test-takers that EVERY VALUE in the list is to be increased by 1. Not the ...” October 23, 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}}\,\,\left( * \right) ?\,\, = \,\,\left\langle {\,{x^{\,y}}} \right\rangle \,\,{\rm{ = }}\,\,{\rm{units}}\,\,{\rm{digit}}\,\,{\rm{of}}\,\,\,{x^{\,y}} \left( 1 \right)\,\,x = 26\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,? = ...” October 22, 2018 Brent@GMATPrepNow posted a new topic called CHALLENGE: 10 teams (A, B, C, D, E, F, G, H, I and J) partic in the Problem Solving forum “10 teams (A, B, C, D, E, F, G, H, I and J) participate in a soccer tournament in which each team plays every other team once. For each game played, points are awarded to the teams as follows: 0 points for losing the game 1 point each for tying the game 2 points for winning the game After ...” October 22, 2018 Brent@GMATPrepNow posted a reply to Clarissa will create her summer reading list by randomly in the Problem Solving forum “Take the task of creating the reading list and break it into stages. Stage 1: Select a book to read 1st There are 10 books to choose from. So, we can complete stage 1 in 10 ways Stage 2: Select a book to read 2nd There are 9 books remaining to choose from (since we already chose a book ...” October 22, 2018 fskilnik@GMATH posted a reply to Is x^3-y^3 > x^2+xy+y^2? in the Data Sufficiency forum “High-level question. Congrats, Max! {x^2} + xy + {y^2} = \underbrace {{x^2} + 2 \cdot x \cdot {y \over 2} + {{{y^2}} \over 4}}_{{{\left( {x + {y \over 2}} \right)}^{\,2}}} + {{3{y^2}} \over 4} \ge 0\,\,\,\,\,\,\,\leftcompleting the squares" technique (above) is carefully explained in our ...” October 22, 2018 Brent@GMATPrepNow posted a reply to A jar contains only green pencils and red pencils. If the in the Data Sufficiency forum “Target question: What percentage of the pencils are green? Given: The jar contains only green pencils and red pencils. Statement 1: The jar contains 75 red pencils. If 75 of the 225 pencils are red, then the remaining 150 pencils are GREEN. 150/225 = 2/3 = 66 2/3%, so the answer to ...” October 22, 2018 fskilnik@GMATH posted a reply to What is the number of roots of the equation (x^3-1)/(x^2+x+1 in the Problem Solving forum “?\,\,\,:\,\,\,\# \,\,{\rm{roots}}\,\,{\rm{of}}\,\,\,\,{{{x^{\rm{3}}} - 1} \over {{x^2} + x + 1}} = x\,\,\,\,\left( * \right) {x^3} - 1 = \left( {x - 1} \right)\left( {{x^2} + x + 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{{{x^3} - 1} \over {{x^2} + x + 1}} = x - 1\,\,\,\,\,\,\,\,\,\left[ ...” October 22, 2018 Brent@GMATPrepNow posted a reply to Challenge Question: In the x-y coordinate plane, does line k in the Data Sufficiency forum “Target question: Does line k have a positive x-intercept? Statement 1: (slope of line k)(y-intercept of line k) > 0 There are two possible cases that that satisfy statement 1: - the slope and y-intercept are both positive - the slope and y-intercept are both negative Let''s examine ...” October 21, 2018 fskilnik@GMATH posted a reply to At a certain picnic, each of the guests was served either a in the Data Sufficiency forum “5\,G\,\,{\rm{guests}}\,\,\,\left\{ \matrix{ \,x\,\,{\rm{guests}}\,\,\,::\,\,{\rm{one}}\,\,{\rm{2 - balls}}\,\,{\rm{ice - cream}}\,\,{\rm{each}} \hfill \cr \,\left( {5G - x} \right)\,\,{\rm{guests}}\,\,\,::\,\,{\rm{one}}\,\,1{\rm{ - ball}}\,\,{\rm{ice - cream}}\,\,{\rm{each}} \hfill \cr} ...” October 21, 2018 fskilnik@GMATH posted a reply to From a group of 21 astronauts that includes 12 people with in the Problem Solving forum “21\,\,{\rm{astron}}\,\,\,\left\{ \matrix{ \,12\,\,{\rm{experts}} \hfill \cr \,21 - 12 = 9\,\,{\rm{non}}\,{\rm{experts}} \hfill \cr} \right. ?\,\,\, = \,\,\,\,\# \,\,3\,{\text{people - group}}\,\,,\,\,{\text{exactly}}\,\,1\,\,{\text{expert}} ?\,\,\, = \,\,\,12 \cdot C\left( {9,2} ...” October 21, 2018 fskilnik@GMATH posted a reply to TRICKY Q, Difficulty level: 700, Source: 800 Score in the Problem Solving forum “Beautiful problem! (Be careful to avoid coming to wrong conclusions!) \[100\,\,{\text{balls}}\,\,\,\left\{ \begin{gathered} \,b\,\,{\text{blue}}\,\,\,\,\,,\,\,\,\,\,\,1 \leqslant b \leqslant 49\,\,\,\left( * \right) \hfill \\ \,100 - b\,\,{\text{yellow}} \hfill \\ \end{gathered} ...” October 21, 2018 fskilnik@GMATH posted a reply to Problem solving: Difficulty level: 700, Source: Economist in the Problem Solving forum “\UNITS CONTROL, one of the most powerful tools of our method! \inversely proportional to the filling VOLUME ratio (for any given time), hence: \[{\text{Relative}}\,\,{\text{volume}}\,\,\left( {{\text{filling}}} \right)\,\,{\text{rate}}\,\,\,:\,\,\,\,\frac{1}{4} = \frac{{\frac{{\left( {x - y} ...” October 21, 2018 Brent@GMATPrepNow posted a reply to What is the area of the triangle formed by the intersection in the Problem Solving forum “Here''s a similar question to practice with: https://www.beatthegmat.com/area-of-triangle-formed-by-intersections-of-3-lines-t276079.html Cheers, Brent” October 21, 2018 GMATGuruNY posted a reply to The annual rent collected by a corporation from a certain in the Data Sufficiency forum “Let the 1997 rent = 100. Increase in 1998 = (x/100)(100) = x. Thus, rent in 1998 = 100+x. Decrease in 1999 = (y/100)(100+x) = y + xy/100 For the rent to be greater in 1999 than in 1997, the increase in 1998 (x) must be greater than the decrease in 1999 (y + xy/100). Question stem, ...” October 21, 2018 fskilnik@GMATH posted a reply to Problem solving: Difficulty level: 700 in the Problem Solving forum “\[? = {\left( {{V_{\,{\text{each}}\,\,{\text{cylinder}}}}} \right)_{\,\max }}\,$ There are three possible ways of considering the rectangular shipping box: Base: 3x12 and Height 4 -- we may put each upright cylinder in a base 3x3 (or 3/4 x 12, what is focus-worse) and height 4 , so that ...” October 21, 2018 fskilnik@GMATH posted a reply to What is the area of the triangle formed by the intersection in the Problem Solving forum “\https://preview.ibb.co/nHhwvf/21-Oct18-5r.gif ${\text{point}}\,\,C\,\,\,\left\{ \begin{gathered} \,y = 2x - 2\,\,\,\, \hfill \\ \,y = - \frac{x}{2} + 8\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,4} \,\,\,\,\,4y = - 2x + 32 \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\mathop ...” October 21, 2018 fskilnik@GMATH posted a reply to If there are more than two numbers in a certain list, is in the Data Sufficiency forum “I was asked if there is another formal proof of the sufficiency of the statement (2) but in a more "down-to-earth" arguments. Certainly! Let´s imagine (at first) that there is a negative number among the elements in the given list, say A. In this case, there is another number in ...” October 21, 2018 fskilnik@GMATH posted a reply to In the sequence S, each term after the first is twice the in the Problem Solving forum “\PATTERN is clear: \[{a_{\,\boxed2}} = {2^{\,\boxed1}} \cdot {a_{\,1}}\,\,\,\,\,\,;\,\,\,\,\,\,{a_{\,\boxed3}} = 2 \cdot {a_{\,2}} = {2^{\,\boxed2}} \cdot {a_{\,1}}\,\,\,\,\,\,;\,\,\,\,\,\,{a_{\,\boxed4}} = 2 \cdot {a_{\,3}} = {2^{\,\boxed3}} \cdot {a_{\,1}}\,\,\,\,\,\,;\,\,\,\,\,\, \ldots$ ...” October 21, 2018 GMATGuruNY posted a reply to During a 3 year period, the profits of company X changed by in the Data Sufficiency forum “Statement 1: If profits increase by X from the first year to the second year, then they must increase by 0 from the second year to the third year, with the result that the increase in profits from the first year to the third year (X+0 = X) is the same as the increase in profits from the first ...” October 21, 2018 GMATGuruNY posted a reply to OG The estimated number of homeschooled students in the Problem Solving forum “Percent greater or percent increase: (bigger value - smaller value)/(smaller value) * 100 Percent less or percent decrease: (bigger value - smaller value)/(bigger value) * 100” October 21, 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: 25Q + 10D = 170 5Q + 2D = 34 To minimize the number of coins, we must maximize the value of Q. If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34. In this case, the total number of coins = 6+2 = 8. If the value of Q decreases, then the total number of coins will ...” October 20, 2018 GMATGuruNY posted a reply to doubt 3 in the Sentence Correction forum “having + VERBed is a viable construction. An introductory HAVING + VERBed modifier implies PRIOR ACTION: an action completed before the main verb. HAVING FINISHED his dessert, John LEFT the table. Here, HAVING FINISHED implies PRIOR ACTION -- an action completed before John LEFT the table. ...” October 20, 2018 GMATGuruNY posted a reply to All attendees at a university gathering are faculty or in the Data Sufficiency forum “Neither statement offers any information about the number of attendees who are alumni. Thus, the two statements combined are INSUFFICIENT. The correct answer is E.” October 20, 2018 GMATGuruNY posted a reply to If n is an integer, which of the following must be divisible in the Problem Solving forum “Test n=0. A --> n³ - 4n = 0³ - (4*0) = 0 B --> n³ + 4n = 0³ + (4*0) = 0 C --> n² + 1 = 0² + 1 = 1 D --> n² - 1 = 0² - 1 = -1 E --> n² - 4 = 0² - 4 = -4 Only the options in green yield a multiple of 3. Eliminate C, D and E. Test n=1 in the remaining answer ...” October 20, 2018 GMATGuruNY posted a reply to At a certain industrial manufacturer, an open tank contains in the Problem Solving forum “Since 6% of the 1000-gallon tank is fluorine, the amount of fluorine = (6/100)(1000) = 60 gallons. Since the total volume decreases at a rate of 10 gallons per day for 25 days, the decrease in the total volume = 10*25 = 250 gallons. Remaining total volume = 1000-250 = 750 gallons. Since 60 of the ...” October 20, 2018 GMATGuruNY posted a reply to Is 1+x+x^2+x^3+x^4+x^5+x^6 < 1/(1-x)? in the Data Sufficiency forum “CRITICAL POINTS in an equality occur when the two sides are EQUAL or the inequality is undefined. Here, the two statements provide the critical points for the inequality in the prompt: When x=0, the two sides are equal. When x=1, the inequality is undefined. To determine the range(s) where the ...” October 20, 2018 fskilnik@GMATH posted a reply to Is 1+x+x^2+x^3+x^4+x^5+x^6 < 1/(1-x)? in the Data Sufficiency forum “Alternate way: ("Algebraic only" solution) $1 - {x^7} = \left( {1 - x} \right)\left( {1 + x + {x^2} + {x^3} + {x^4} + {x^5} + {x^6}} \right)$ $1 + x + {x^2} + {x^3} + {x^4} + {x^5} + {x^6}\,\,\mathop < \limits^? \,\,\,\frac{1}{{1 - x}}\,\,\,\,\,\mathop \Leftrightarrow \limits^{ ...” October 19, 2018 fskilnik@GMATH posted a reply to Is 1+x+x^2+x^3+x^4+x^5+x^6 < 1/(1-x)? in the Data Sufficiency forum “\https://preview.ibb.co/gYYhy0/19-Oct18-4b.gif \[\left( 2 \right)\,\,x < 1\,\,\,\left\{ \begin{gathered} \,\left( {\operatorname{Re} } \right){\text{Take}}\,\,x = \frac{1}{2}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,x = - ...” October 19, 2018 fskilnik@GMATH posted a reply to If there are more than two numbers in a certain list, is in the Data Sufficiency forum “\EMBRACE MATHEMATICS and develop your quantitative maturity to EXCEL IN YOUR EXAM (and in the MBA that goes right after it)! \[\left( 2 \right)\,\,\left\{ \begin{gathered} \,{x_j} + {x_k} = 0 \hfill \\ {x_k} + {x_m} = 0 \hfill \\ \end{gathered} \right.\,\,\,\,\,\mathop \Rightarrow ...” October 19, 2018 Brent@GMATPrepNow posted a new topic called Challenge Question: In the x-y coordinate plane, does line k in the Data Sufficiency forum “In the x-y coordinate plane, does line k have a positive x-intercept? (1) (slope of line k)(y-intercept of line k) > 0 (2) (slope of line k) - (y-intercept of line k) < 0 Answer: A Difficulty level: 650 – 700 Source: www.gmatprepnow.com” October 19, 2018 fskilnik@GMATH posted a reply to The latest model of space shuttle can achieve a maximum in the Problem Solving forum “\ UNITS CONTROL, one of the most powerful tools of our method! \[?\,\, = \,\,\,\frac{{25\,\,{\text{miles}}}}{{1\,\,{\text{second}}}}\,\,\,\left( {\frac{{60\,\,{\text{seconds}}}}{{1\,\,{\text{minute}}}}} \right)\,\,\,\,\left( {\frac{{60\,\,{\text{minutes}}}}{{1\,\,{\text{h}}}}} ...” October 19, 2018 fskilnik@GMATH posted a reply to 90th percentile Q in the Problem Solving forum “Mitch´s ("GMATGuruNY") solution shows a relationship between remainders and (what he calls) "decimals" through examples. Scott´s ("Scott@TargetTestPrep") solution also deals with this relationship through mixed fractions. Mathematically speaking, those arguments ...” October 19, 2018 fskilnik@GMATH posted a reply to John tossed a fair coin 3 times. What is the probability in the Problem Solving forum “? = P\left( {\,{\rm{exact}}\,{\rm{2}}\,\,{\rm{tails}}\,{\rm{in}}\,{\rm{3}}\,{\rm{tosses}}\,} \right) = {{C\left( {3,2} \right)} \over {2 \cdot 2 \cdot 2}} = {3 \over 8} This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.” October 19, 2018 fskilnik@GMATH posted a reply to When positive integer N is divided by positive integer J, in the Problem Solving forum “\Division Algorithm say! N = QJ + 14\,\,,\,\,\,\left\{ \matrix{ \,Q\,\,{\mathop{\rm int}} \hfill \cr \,J \ge 15\,\,\,\,\,,\,\,\,\,\,\,? = J\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\left( * \right) 134.08 = {N \over J} = Q + {{14} \over J}\,\,\,\,\,\,\,\,\mathop \Rightarrow ...” October 19, 2018 Brent@GMATPrepNow posted a reply to When positive integer N is divided by positive integer J, in the Problem Solving forum “ASIDE: 7/2 = 3 1/2 = 3 + 0.5 = 3.5 Notice that 1 is the remainder when we divide 7 by 2. 23/5 = 4 3/5 = 4 + 0.6 = 4.6 Notice that 3 is the remainder when we divide 23 by 5. 31/4 = 7 3/4 = 7 + 0.75 = 7.75 Notice that 3 is the remainder when we divide 31 by 4. GIVEN: N/J = 134.08 This means ...” October 19, 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 ...” October 19, 2018 Brent@GMATPrepNow posted a reply to If there are more than two numbers in a certain list, is in the Data Sufficiency forum “[quote="Jay@ManhattanReview"] Hey Jay, I thought I should point out that case 2 doesn''t satisfy the statement. If we choose 1 and 2 from the set, then the product isn''t 0. That said, {0, 0, 0, 0, 1} meets the given condition, as does {0, 0, 0, 0, 0, 0, 0, 3} etc Cheers, ...” October 19, 2018 Brent@GMATPrepNow posted a reply to If -1<x<0, Which of the following is listed in ascendi in the Problem Solving forum “Let''s test a value of x. If -1 < x < 0, then x COULD equal -1/2 So, x^(-1) = (-1/2)^(-1) = 1/(-1/2) = -2 And, x^(-2) = (-1/2)^(-2) = 1/(-1/2)^2 = 1/(1/4) = 4 And, x^2 = (-1/2)^2 = 1/4 Listed in ascending order, we get: -2, 1/4, 4 In other words, x^(-1), x^2, x^(-2) Answer: A ...” October 19, 2018 GMATGuruNY posted a reply to If a rectangle’s length is a+b and its area is (1/a)+(1/b) in the Problem Solving forum “Let a=b=0.5, implying that the rectangle''s length = a+b = 0.5+0.5 = 1 and that its area = (1/0.5) + (1/0.5) = (10/5) + (10/5) = 2+2 = 4. Since the rectangle has an area of 4 and a length of 1, its width = 4. The correct answer must yield a value of 4 when a=b=0.5. Only E works: 1/ab = 1/(0.5 * ...” October 19, 2018 GMATGuruNY posted a reply to When positive integer N is divided by positive integer J, in the Problem Solving forum “N/J = 134.08 = 13408/100 = 3352/25. The resulting ratio indicates that N must be multiple of 3352 and that J must be a multiple of 25. Of the five answer choices, only E is a multiple of 25. The correct answer is E.” October 19, 2018 GMATGuruNY posted a reply to A container contains 4 red marbles and 8 blue marbles. in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the number of blue marbles in the second container. When the correct answer is plugged in, the probability of selecting 2 red marbles OR 2 blue marbles = 1/2. B: 4 blue marbles, implying a total of 10 marbles in the second container Case1: 2 red ...” October 19, 2018 GMATGuruNY posted a reply to Two printing presses begin printing currency at the same in the Problem Solving forum “Since F produces 1000 5-dollar bills each minute, the dollar amount produced by F each minute = 1000*5 = 5000. Since T produces 200 20-dollar bills each minute, the dollar amount produced by T each minute = 200*20 = 4000. Thus, every minute F surpasses T by 1000. Since F surpasses T by 1000 ...” October 18, 2018 fskilnik@GMATH posted a reply to Overlapping sets question in the Problem Solving forum “\[?\,\,\,:\,\,\,\# \,\,\,\,{\text{not}}\,\,\,\left[ {\,\,\left( {{\text{applied}}\,\,{\text{sciences}}\,\,{\text{degree}}} \right)\,\,{\text{AND}}\,\,\left( {{\text{in}}\,\,{\text{one}}\,\,{\text{of}}...} \right)\,\,} \right]\,\,\,\,\, = \,\,\,\,\# \,\,\,\left[ {\,\,\left( ...” October 18, 2018 fskilnik@GMATH posted a reply to If a, b, and c are consecutive positive integers and a<b& in the Problem Solving forum “\left( {a,b,c} \right) = \left( {a,a + 1,a + 2} \right)\,\,\,\,,\,\,\,a \ge 1\,\,{\mathop{\rm int}} \,\,\,\,\,\left( * \right) ?\,\,\,\,:\,\,\,{\left( {{3^{\,2bc\, - \,2ab}}} \right)_{\,\min }} ?\,\,\,:\,\,\,{3^{2b\,\left( {c - a} \right)\,}}\,\,\,\mathop = \limits^{\left( * \right)} ...” October 18, 2018 fskilnik@GMATH posted a reply to A jar contains 6 red marbles and 9 blue marbles. If Evelyn in the Problem Solving forum “6R\,\,,\,\,9B ? = 1 - P\left( {\,{\rm{get}}\,1\,{\rm{red}},\,1\,{\rm{blue}}\,{\rm{in}}\,{\rm{2}}\,\,{\rm{simult}}{\rm{.}}\,{\rm{extractions}}\,} \right) P\left( {\,{\rm{get}}\,1\,{\rm{red}},\,1\,{\rm{blue}}\,{\rm{in}}\,{\rm{2}}\,\,{\rm{simult}}{\rm{.}}\,{\rm{extractions}}\,} \right) = ...” October 18, 2018 Brent@GMATPrepNow posted a reply to The latest model of space shuttle can achieve a maximum in the Problem Solving forum “GIVEN: The shuttle can travel 25 miles in 1 second So, the shuttle can travel 1500 miles in 60 seconds In other words, the shuttle can travel 1500 miles in 1 MINUTE So, the shuttle can travel 90,000 miles in 60 MINUTES In other words, the shuttle can travel 90,000 miles in 1 HOUR In other ...” October 18, 2018 Brent@GMATPrepNow posted a reply to A jar contains 6 red marbles and 9 blue marbles. If Evelyn in the Problem Solving forum “P(both are same color) = P(1st marble is red AND 2nd marble is red OR 1st marble is blue AND 2nd marble is blue) = x P(2nd marble is red)] + x P(2nd marble is blue)] = x 5/14] + x 8/14] = x 5/14] + x 8/14] = 10/70 + 24/70 = 34/70 = 17/35 Answer: D Cheers, Brent” October 18, 2018 fskilnik@GMATH posted a reply to A professional gambler has won 40% of his 25 poker games for in the Problem Solving forum “If you want the "let-me-be-prepared-for-the-general-case" style, you may follow Jay´s nice suggestion (above) or... use the alligation technique: https://preview.ibb.co/jzKYmL/18-Oct18-5r.gif ? = x {{25} \over {25 + x}} = {{80 - 60} \over {80 - 40}} = {1 \over 2}\,\,\,\,\, ...” October 18, 2018 fskilnik@GMATH posted a reply to A professional gambler has won 40% of his 25 poker games for in the Problem Solving forum “The "aggressive-because-the-occasion-permits" style: 60% is the average of 40% and 80% , therefore 25 games with 40% winning percentage and another 25 games with 80% winning percentage does the trick! The solution is in red. Regards, Fabio.” October 18, 2018 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Time management strategy for test day Video: https://www.youtube.com/watch?v=bWrUiBT83PQ Cheers, Brent” October 18, 2018 Brent@GMATPrepNow posted a reply to In the x-y coordinate plane, line k passes through in the Problem Solving forum “Notice that, if the line passes through the origin, then the line has slope -4/5 (aka a slope of -0.8), but the line will not have a negative x-intercept Notice that, if the line passes through the (0,4), then the line will have slope 0, BUT the line will not have a negative x-intercept. See ...” October 18, 2018 fskilnik@GMATH posted a reply to In the figure above - Angle ABC = Angle ADC = \(90^o$$. Is in the Data Sufficiency forum “AD\,\,\mathop > \limits^? \,\,BC https://preview.ibb.co/fJPbO0/18-Oct18-3z.gif \left( 2 \right)\,\,\underline {{\rm{IF}}} \,\,AD > BC > 0\,\,\,\,,\,\,\,\,A{D^{\,2}} > B{C^{\,2}}\,\,\,\,\, \Rightarrow \,\,\,\,\, - A{D^{\,2}} < - B{C^{\,2}}\,\,\,\,\left( * \right) ...” October 18, 2018 GMATGuruNY posted a reply to Brian purchased a bouquet of 40 flowers for his mother for in the Problem Solving forum “= We can PLUG IN THE ANSWERS, which represent the number of tulips. When the correct answer is plugged in, the total cost = 48. D: 24 tulips, implying 16 roses, for a total of 40 flowers Since each of the 24 tulips costs 1, and each of the 16 roses costs 1.50, we get: Total cost = (24*1) ...” October 18, 2018 Brent@GMATPrepNow posted a reply to f[f{f(x)}]=??? in the GMAT Math forum “Useful property: 1/(a/b) = b/a We want: ff(5)}] = f1/6}] f{1/6} = 1/(1 + 1/6) = 1/(7/6) = 6/7 So, ff{1/6}] = f6/7] Finally, f[6/7] = 1/(1 + 6/7) = 1/(13/7) = 7/13 Answer: B (since 21/39 reduces to the equivalent fraction 7/13) Cheers, Brent” October 18, 2018 Brent@GMATPrepNow posted a reply to In the month of August, Pentheus Corporation made 200,000 in the Problem Solving forum “In the month of August, Pentheus Corporation made 200,000 in profit. Pentheus made 6% of that profit on the second Wednesday of August. 1% of 200,000 = 2,000, so 6% of 200,000 = (6)(2,000) = 12,000 So, the profit on that day = 12,000 If the profits that day were approximately 14.5% of ...” October 18, 2018 fskilnik@GMATH posted a reply to If a and b are positive integers such that when a is divided in the Data Sufficiency forum “Nice conceptual problem, Max. Congrats! a,b\,\, \ge 1\,\,\,{\rm{ints}} a = Qb + 10\,\,\,\,\,\left\{ \matrix{ \,Q\,\,\,{\mathop{\rm int}} \hfill \cr \,{\rm{remainder}}\,\,10\,\,\, \Rightarrow \,\,\,\,b \ge 11\,\, \hfill \cr} \right. ? = b \left( 1 ...” October 18, 2018 fskilnik@GMATH posted a reply to Brian purchased a bouquet of 40 flowers for his mother for in the Problem Solving forum “40\,\,\left\{ \matrix{ \,\,T\,\, = \,\,? \hfill \cr \,R = 40 - T \hfill \cr} \right. \left[ \ \right]\,\,\,\,\left( {40 - T} \right) \cdot \frac{3}{2} + T \cdot 1 = 48\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,60 - \frac{1}{2}T = 48\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\frac{1}{2}T = ...” October 18, 2018 fskilnik@GMATH posted a reply to In the month of August, Pentheus Corporation made 200,000 in the Problem Solving forum “All numbers presented below are in dollars. ? = {\rm{rev}}\,\,\left( {{\rm{certain}}\,\,{\rm{day}}} \right) {\rm{Aug}}\,{\rm{profit}}\,\,:\,\,\,2 \cdot {10^5} {\text{certain}}\,{\text{ day}}\,{\text{profit}}\,\,:\,\,\,\frac{6}{{100}}\left( {\,2 \cdot {{10}^5}} \right) = 12 \cdot ...” October 18, 2018 Brent@GMATPrepNow posted a reply to Brian purchased a bouquet of 40 flowers for his mother for in the Problem Solving forum “We can solve this question using either 1 variable or 2 variables. Here''s an approach that involves 1 variable: Let t = # of tulips in bouquet So. 40 - t = # of roses in bouquet So, (1.00)(t) = the total COST of all t tulips And (1.50)(40 - t) = the total COST of all 40-t roses ...” October 18, 2018 fskilnik@GMATH posted a reply to The rear wheels of a car crossed a certain line 0.5 second in the Problem Solving forum “1\,\,{\rm{mile}}\,\,\, \leftrightarrow \,\,\,5280\,\,{\rm{feet}} V\left( {{\rm{speed}}} \right) = {{\,20\,\,{\rm{feet }}} \over {0.5\,\,{\rm{s}}}}\,\, = \,\,\,?\,\,{\rm{mph}} Perfect opportunity to use UNITS CONTROL, one of the most powerful tools of our course! ?\,\,\, = ...” October 18, 2018 fskilnik@GMATH posted a reply to Units digit in the Problem Solving forum “Hi, Pri187! Thank you for the nice compliment! I am glad I could be helpful. (Try to answer in Anurag´s place is never easy.) Regards, Fabio.” October 18, 2018 fskilnik@GMATH posted a reply to Finance Majors/Non-Finance Majors - Overlapping Set Question in the Problem Solving forum “https://preview.ibb.co/c1Zo1L/17-Oct18-6h.gif VERY beautiful problem, in which the Venn diagram ("overlapping sets") solves the problem nicely. ? = {\rm{None}}\,\,\,\,\left( {\,{\rm{in}}\,\,100\,} \right) The wording in red is clearly presented below and also in the diagram! ...” October 17, 2018 fskilnik@GMATH posted a reply to Vaccinated Against Rubella in the Problem Solving forum “Excellent opportunity to blend two techniques: Venn diagrams ("overlapping sets") and the k technique ! (Hint: understand the values presented in increasing order of letter sizes!) https://preview.ibb.co/kESBo0/17-Oct18-6h.gif ? = 4k 2k = 5,000\,\,\,\, \Rightarrow \,\,\,\,? = ...” October 17, 2018 fskilnik@GMATH posted a reply to cost of package in the Problem Solving forum “My opinion: Brent´s solution (above) is BJJ (Brazilian Jiu-Jitsu) at its best. I mean, it´s THE way to study for the exam so that you develop your mathematical maturity AND, as a sub-product, develop your skills to do some STREET FIGHTING when you feel your opponent is "chicken". ...” October 17, 2018 fskilnik@GMATH posted a reply to If |X| is the number of elements in set X, and “∪” is in the Data Sufficiency forum “?\,\,\,:\,\,\,\# \,\,\,{\rm{common}}\,\,{\rm{elements}} Let´s go straight to (1+2) to show a BIFURCATION: \left\{ \matrix{ \,\,{\rm{Take}}\,\,B = \left\{ {1,2,3, \ldots ,38,39,40} \right\}\, \hfill \cr \,\,{\rm{Take}}\,\,A = \left\{ {41,42,43, \ldots ,49,50} \right\} \hfill \cr} ...” October 17, 2018 Brent@GMATPrepNow posted a reply to In a town of 8,000 residents, 65 percent of all residents 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 residents, and the two characteristics are: ...” October 17, 2018 fskilnik@GMATH posted a reply to If a rectangle’s length is a+b and its area is (1/a)+(1/b) in the Problem Solving forum “Just a glance at the alternative choices makes us realize that all of them get different values when a=b=3, hence... Let´s explore this PARTICULAR CASE! {\rm{rectangle}}\,\,\left\{ \matrix{ \,{\rm{length}} = \,\,6 \hfill \cr \,{\rm{area}} = \,\,{2 \over 3} \hfill \cr} ...” October 17, 2018 fskilnik@GMATH posted a reply to In a town of 8,000 residents, 65 percent of all residents in the Problem Solving forum “https://preview.ibb.co/e3ZYY0/17-Oct18-5r.gif ?\,\, = \,x = 65\% \left( {{\rm{Tot}}} \right) - {\rm{both}} 75\% \left( {{\rm{Tot}}} \right) = 65\% \left( {{\rm{Tot}}} \right) + 55\% \left( {{\rm{Tot}}} \right) - {\rm{both}}\,\,\,\,\,\,\left[ {\,{\rm{simplifier}}\,} ...” October 17, 2018 fskilnik@GMATH posted a reply to If x and y are numbers such that x < - 10 and y > 6, w in the Problem Solving forum “?\,\,\,:\,\,\,\,{\rm{I,II,III}}\,\,\,{\rm{true}} x < - 10\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ \,x + 4 < - 10 + 4 = - 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left| {x + 4} \right| > 6 \hfill \cr \,x - 4 < - 10 - 4 = - 14\,\,\,\,\, \Rightarrow \,\,\,\,\,\left| {x - 4} ...” October 17, 2018 Brent@GMATPrepNow posted a reply to What is the remainder if 7^10 is divided by 100? in the Problem Solving forum “Sweeeeeeeeeeeeet solution, Scott!! Cheers, Brent” October 17, 2018 fskilnik@GMATH posted a reply to The heignt of an equilateral triangle is the side of a in the Problem Solving forum “EXACTLY! The ONLY reason to look at other experts as "competitors" is (in my opinion) stupid. I explain: if someone loves YOUR way of presenting things, this person will NOT be MY "customer", for sure. In other words, we are just presenting our "dishes", but our ...” October 16, 2018 fskilnik@GMATH posted a reply to The heignt of an equilateral triangle is the side of a in the Problem Solving forum “I would like to make this PUBLIC compliment to ceilidh. I explain: in approximately 2 months of mine here (after inactive in this forum since approximately 2012) I realized something as simple as "you are right" is very hard to obtain. More than that: in one or two occasions, after ...” October 16, 2018 fskilnik@GMATH posted a reply to The heignt of an equilateral triangle is the side of a in the Problem Solving forum “Very nice, ceilidh.erickson! To validate your argument, it is important to justify the 90-degrees angle. The figure presented in my post (above) does that. Regards, Fabio.” October 16, 2018 fskilnik@GMATH posted a reply to How many factors does the number X have? in the Data Sufficiency forum “\[?\,\,:\,\,\,\,\# \,\,{\text{of}}\,\,{\text{factors}}\,\,{\text{of}}\,\,{\text{X}}$ $\left( 1 \right)\,\,\,\,\,\frac{X}{{47}} = \operatorname{int} \,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,X = 0\,\,\,\, \Rightarrow \,\,\,{\text{?}}\,\,{\text{ = ...” October 16, 2018 fskilnik@GMATH posted a reply to Is the sum of 7 different positive integers greater than or in the Data Sufficiency forum “(At least to my students) If you don´t know how to begin, do not forget: STRUCTURE rules! \[1 \leqslant {a_{\,1}} < {a_{\,2}} < \,\, \ldots < {a_{\,7}}\,\,\,{\text{ints}}$ $\sum\nolimits_{{\text{them}}\,{\text{7}}} {\,\,\mathop \geqslant \limits^? \,\,\,48}$ $\left( 1 ...” October 16, 2018 fskilnik@GMATH posted a reply to (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? in the Problem Solving forum “\PATTERN: \[1 - \frac{1}{{\boxed{10}}} = \frac{9}{{\boxed{10}}}\,\,$ $\left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{\boxed{11}}}} \right) = \frac{9}{{10}} \cdot \frac{{10}}{{11}} = \frac{9}{{\boxed{11}}}$ $\left( {1 - \frac{1}{{10}}} \right)\left( {1 - \frac{1}{{11}}} \right)\left( ...” October 16, 2018 Brent@GMATPrepNow posted a reply to If x, y, and z are all nonzero numbers, and x = y + z, which in the Problem Solving forum “NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: ...” October 16, 2018 fskilnik@GMATH posted a reply to If x, y, and z are all nonzero numbers, and x = y + z, which in the Problem Solving forum “Perfect opportunity to give emphasis to the connection of the first leg (FOCUS) and the third leg (ALTERNATIVE CHOICES) of our WINNING TRIAD! An additional glance at the relationship between x, y and z (DATA, the second leg) shows us we must... Consider the difference among two of the three ...” October 16, 2018 fskilnik@GMATH posted a reply to In the x-y coordinate plane, line k passes through in the Problem Solving forum “Reminder (to my students) / Suggestion (to the general reader): 1. One property at a time, till the end. Then the other. ("Don´t let your brain dance!") 2. Start with the easier checking property (or the one you feel more comfortable). Indifferent? Start with the first. ...” October 16, 2018 fskilnik@GMATH posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico in the Problem Solving forum “\[?\,\, = \,\,\frac{{\# \,\,{\text{total}}\,\,{\text{miles}}}}{{\# \,\,{\text{total}}\,\,{\text{hours}}}}\,\, = \,\,\,\underleftrightarrow {\frac{{120 \cdot 10}}{{\frac{5}{2}}} = \frac{{120 \cdot 10 \cdot 2}}{5}} = 4 \cdot 120\,\,\,\left[ {{\text{mph}}} \right]$ This solution follows the notations ...”
October 16, 2018
fskilnik@GMATH posted a reply to A certain NYC taxi driver has decided to start charging a in the Problem Solving forum
“Let´s avoid exploring particular cases (undoubtedly very useful) to embrace UNITS CONTROL, one of the most powerful tools of our method! $\frac{{r\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\,\,\mathop \to \limits^{{\text{discount}}} ...” October 16, 2018 fskilnik@GMATH posted a reply to A Martian bat flies at 60 yards per second from its nest to in the Problem Solving forum “Let´s solve this problem without taking into account the "examiner´s generosity" (in terms of inviable alternative choices) nor exploring a particular case. (Both approaches are important. We just want to avoid repetitions and present the UNITS CONTROL, one of the most powerful tools ...” October 16, 2018 Brent@GMATPrepNow posted a reply to Set X consists of different positive numbers arranged in in the Data Sufficiency forum “Target question: What is the arithmetic mean of set X? Given: Set X consists of different positive numbers arranged in ascending order: K, L, M, 5, 7. K, L and M are consecutive integers This means that EITHER K, L, M = 1, 2, 3 respectively, OR K, L, M = 2, 3, 4 respectively Head straight ...” October 16, 2018 Brent@GMATPrepNow posted a reply to A Martian bat flies at 60 yards per second from its nest to in the Problem Solving forum “Rich''s approach is definitely the best (i.e., fastest) way to solve this question. However, if the answer choices weren''t so sweet, here''s an algebraic solution Average speed = (total distance traveled)/(total travel time) Let''s assign nice values to the distances. These values should ...” October 16, 2018 GMATGuruNY posted a reply to A certain NYC taxi driver has decided to start charging a in the Problem Solving forum “Let r=100 cents. For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars. Let x = 2 miles. Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars. With a 50% discount, the cost in dollars = 3. This is the target. Plug x=2 and r=100 into the answers to see which yields the ...” October 16, 2018 Brent@GMATPrepNow posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico 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” October 16, 2018 Brent@GMATPrepNow posted a reply to A certain NYC taxi driver has decided to start charging a in the Problem Solving forum “Here''s an algebraic approach: A certain taxi driver charges a rate of r CENTS per person per mile r CENTS = r/100 DOLLARS Since there are 3 people, the rate is (3)(r/100) DOLLARS per mile In other words, the rate is 3r/100 dollars per mile. With a 50% discount, the new rate = ...” October 16, 2018 Brent@GMATPrepNow posted a new topic called In the x-y coordinate plane, line k passes through in the Problem Solving forum “In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k? i) y = -0.4x - 2 ii) y = 2 - 1.2x iii) y = -0.7x - 1.5 A) i only B) ii only C) iii only D) i & ii only E) i & iii only ...” October 16, 2018 GMATGuruNY posted a reply to (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? in the Problem Solving forum “(1-1/10)(1-1/11)(1-1/12)…(1-1/99)(1-1/100) = (9/10)(10/11)(11/12)....(98/99)(99/100). The values in blue all cancel out, leaving only the values in red: 9/100. The correct answer is C.” October 16, 2018 GMATGuruNY posted a reply to A rectangular garden is to be twice as long as it is wide. in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the length. When the correct answer is plugged in, perimeter = 360. B: 140 Since the length is twice the width, W = 70, with the result that the perimeter = 140+140+70+70 = 420. Since the perimeter is too great, a SMALLER answer choice is needed. ...” October 16, 2018 GMATGuruNY posted a reply to Is the sum of 7 different positive integers greater than or in the Data Sufficiency forum “Statement 1: Least possible case: 1+2+3+9+10+11+12 = 48. Since the least possible case is greater than or equal to 48, the answer to the question stem is YES. SUFFICIENT. Statement 2: Least possible case: 1+2+3+4+5+6+12 = 33. Greatest possible case: 6+7+8+9+10+11+12 = 63. Since the answer ...” October 16, 2018 GMATGuruNY posted a reply to If x, y, and z are all nonzero numbers, and x = y + z, which in the Problem Solving forum “x = y + z is valid if x=2, y=1 and z=1. The correct answer must yield a value of 1 when x=2, y=1 and z=1. Only E works: (x-z)/y = (2-1)/1 = 1. The correct answer is E.” October 16, 2018 GMATGuruNY posted a reply to If |x+1|=2|x-1|, x=? in the Data Sufficiency forum “Case 1: Signs unchanged x+1 = 2(x-1) x+1 = 2x-2 3 = x Case 2: Signs changed on ONE SIDE -x-1 = 2(x-1) -x-1 = 2x-2 1 = 3x 1/3 = x Resulting solutions: x=3 or x=1/3 Statement 1: Since x < 1, only x=1/3 is a viable solution. SUFFICIENT. Statement 2: Since x>0, both x=1/3 ...” October 15, 2018 fskilnik@GMATH posted a reply to A rectangular garden is to be twice as long as it is wide. in the Problem Solving forum “width = x yards length = 2x yards FOCUS: ? = 2x [yards] perimeter = 6x = 360 [yards] ? = 2x = 6x/3 = 120 Regards, Fabio.” October 15, 2018 fskilnik@GMATH posted a reply to The number of years of service of the eight employees in a in the Problem Solving forum “?\,\, = \,\,{\rm{Range}}\,\,{\rm{ = }}\,\,{{\rm{V}}_{{\rm{max}}}} - {V_{\min }} = 17 - 4 = 13 Regards, Fabio.” October 15, 2018 fskilnik@GMATH posted a reply to If |x+1|=2|x-1|, x=? in the Data Sufficiency forum “(I gave some time to other people present an alternate solution... it didn´t happen.) Let´s offer an alternate approach: ? = x \left. \matrix{ {\left| {x + 1} \right|^{\,2}} = {\left( {x + 1} \right)^{\,2}} \hfill \cr {\left| {x - 1} \right|^{\,2}} = {\left( {x - 1} ...” October 15, 2018 fskilnik@GMATH posted a reply to The heignt of an equilateral triangle is the side of a in the Problem Solving forum “(The formula below we suggest you memorize. It will be used here twice.) {h_{eq}} = {{L\sqrt 3 } \over 2}\,\,\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\left( {{\rm{height}}\,\,{\rm{of}}\,\,{\rm{an}}\,\,{\rm{equilateral}}\,\,{\rm{triangle}}\,\,{\rm{with}}\,\,{\rm{side}}\,\,L} \right) ...” October 15, 2018 fskilnik@GMATH posted a reply to In the rectangular coordinate system above, if the in the Data Sufficiency forum “I respectfully disagree: We are told we are in the rectangular coordinate system, we are told about coordinates of points in this rectangular system. In short: we may implicitly assume the dotted lines are parallel to the x-axis and the y-axis. Regards, Fabio.” October 15, 2018 Brent@GMATPrepNow posted a reply to Lindsay can paint 1/x of a certain room in one hour. If in the Problem Solving forum “This appears to be a slightly different version of this official question: https://www.beatthegmat.com/work-rate-problem-5-t292679.html HOWEVER, unless I''m missing something, the correct answer is missing. Cheers, Brent” October 15, 2018 GMATGuruNY posted a reply to Lindsay can paint 1/x of a certain room in one hour. If in the Problem Solving forum “Let the room = 20 units. Let x = 4. Since Lindsay paints 1/x of the room in 1 hour, Lindsay''s rate = (1/4) * 20 = 5 units per hour. Since Lindsay and Joseph paint the entire room in 1 hour, their combined rate = 20 units per hour. Thus, Joseph''s rate = (combined rate) - (Lindsay''s rate) ...” October 15, 2018 Brent@GMATPrepNow posted a reply to How many factors does the number X have? in the Data Sufficiency forum “Target question: How many factors does the number X have? Statement 1: X is divisible by 47 Let''s TEST some values. There are several values of X that satisfy statement 1. Here are two: Case a: X = 47. The factors of 47 are {1, 47}. So, the answer to the target question is X has 2 ...” October 15, 2018 GMATGuruNY posted a reply to The principal feature of the redesigned checks is a series o in the Sentence Correction forum “Generally, a COMMA + VERBing modifier serves to modify the nearest preceding action and the agent of this action. C: instructions that...will help merchants confirm a check''s authenticity, by including reminders to watch the endorsement. .Here, COMMA + by including seems to modify merchants ...” October 15, 2018 Brent@GMATPrepNow posted a reply to A rectangular solid S, has dimensions 4 by 9 by k. What is in the Data Sufficiency forum “Target question: What is the value of k? Given: A rectangular solid S, has dimensions 4 by 9 by k Statement 1: 4 < k < 9 Since k can have ANY value between 4 and 9, statement 1 is NOT SUFFICIENT Statement 2: A cube of side 6 has the same volume as rectangular solid S. So ...” October 15, 2018 fskilnik@GMATH posted a reply to If |x+1|=2|x-1|, x=? in the Data Sufficiency forum “Let´s use the geometric interpretation of the absolute value, so that NO calculations will be needed! \left. \matrix{ \left| {x - 1} \right|\,\, = {\rm{dist}}\left( {x,1} \right) \hfill \cr \left| {x + 1} \right| = \left| {x - \left( { - 1} \right)} \right|\,\,{\rm{ = ...” October 15, 2018 Brent@GMATPrepNow posted a reply to In the rectangular coordinate system above, if the in the Data Sufficiency forum “I think that, if this were an official GMAT question, the correct answer would be E (not B), because we aren''t specifically told that the dotted lines are parallel to the x-axis and the y-axis. If those dotted lines aren''t parallel to those axes, the we can''t determine the value of y. ...” October 15, 2018 fskilnik@GMATH posted a reply to Two positive integers a and b are divisible by 5, in the Data Sufficiency forum “We believe that´s the question stem the proposer had in mind. (This will be the one solved below, anyway.) \left. \matrix{ a,b\,\, \ge 1\,\,{\rm{ints}} \hfill \cr {\rm{GCD}}\left( {a,b} \right) = 5\,\, \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,a = ...” October 15, 2018 fskilnik@GMATH posted a reply to If A={x| x^3 > 8}, B={x| 1 < x^3 < 64}, C={x| x^3 & in the Problem Solving forum “A = \left\{ {\,\left. {x\,\,} \right|\,\,\,{x^3} > {2^3}\,} \right\} B = \left\{ {\,\left. {x\,\,} \right|\,\,\,1 < {x^3} < {4^3}\,} \right\} C = \left\{ {\,\left. {x\,\,} \right|\,\,\,{x^3} < {3^3}\,} \right\} ? = A \cap B \cap C = \left\{ {\,\left. {x\,\,} ...” October 15, 2018 Brent@GMATPrepNow posted a reply to In the figure above, triangle ABC is equilateral, and point in the Problem Solving forum “It may help to add some lines to the diagram. First add lines from the center to the 3 vertices. https://s8.postimg.cc/e412m8uq9/clk1.jpg Aside, we know that each angle is 120º since all three (equivalent) angles must add to 360.º Then draw a circle so that the triangles vertices are on ...” October 15, 2018 fskilnik@GMATH posted a reply to Units digit in the Problem Solving forum “Hi, pri187. I will take the liberty to answer your question, simply because I don´t have any clue whether Anurag is still active (at least in this forum). (*) Let < N > denote the unit´s digit of N, for instance: <2> = 2 and <2^4> = 6 (because 2^4 = 16). With this notation ...” October 14, 2018 GMATGuruNY posted a reply to What is the remainder if 7^10 is divided by 100? in the Problem Solving forum “When a positive integer is divided by 100, the remainder is yielded by the last two digits: 123/100 = 1 R23 548/100 = 5 R48 692/100 = 6 R92 Thus: The remainder when 7¹⁰ is divided by 100 is equal to the last two digits of 7¹⁰. Calculate the last two digits for consecutive powers of 7 ...” October 14, 2018 fskilnik@GMATH posted a reply to A law school admissions office sent letters to each of its in the Problem Solving forum “Another very nice problem in which "blending" the k technique and the grid (double-matrix) "shields" the problem fast and clear! (At least to my students) Study this problem asking yourself why start putting in the grid the 10k "value" was a smart move. ...” October 14, 2018 fskilnik@GMATH posted a reply to In the rectangular coordinate system above, if the in the Data Sufficiency forum “Exactly the same question was posted twice (one right after the other). See here: https://www.beatthegmat.com/in-the-rectangular-coordinate-system-above-if-the-t304691.html Regards, Fabio.” October 14, 2018 fskilnik@GMATH posted a reply to In the rectangular coordinate system above, if the in the Data Sufficiency forum “Trivial problem, but nice to present the GEOMETRIC BIFURCATION (of statement (1)): ? = y \left( 1 \right)\,\,M\,\,{\rm{and}}\,\,P\,\,{\rm{same}}\,\,{\rm{abscissa}}\,\,\left( { = 5} \right) https://preview.ibb.co/koR3dp/14-Oct18-6k.gif \left( 2 \right)\,\,\,N = \left( {0, - 4} ...” October 14, 2018 fskilnik@GMATH posted a reply to The mass of 1 cubic meter of a substance is 800 kg under in the Problem Solving forum “1\,{{\rm{m}}^3}\,\, \leftrightarrow \,\,800\,{\rm{kg}}\,\,\,\,\,\,\,\left( {1\,{\rm{kg}}\,\, = \,\,{{10}^3}\,{\rm{g}}\,\,\,\,\,{\rm{;}}\,\,\,\,1\,{{\rm{m}}^3}\,\, = \,\,{{10}^6}\,{\rm{c}}{{\rm{m}}^3}} \right) {\rm{1}}\,\,{\rm{g}}\,\,\, \leftrightarrow \,\,{\rm{?}}\,\,{\rm{c}}{{\rm{m}}^3} ...” October 14, 2018 fskilnik@GMATH posted a reply to What is the remainder if 7^10 is divided by 100? in the Problem Solving forum “First note that: > 1 is the remainder of 101 (=1*100+1) divided by 100 > 32 is the remainder of 532 (=5*100+32) divided by 100 > 47 is the remainder of 7847 (=78*100+47) divided by 100 {7^{10}} = K \cdot 100 + R{\mkern 1mu} {\mkern 1mu} \,\,{\mkern 1mu} {\mkern 1mu} \left( ...” October 14, 2018 Brent@GMATPrepNow posted a reply to The mass of 1 cubic meter of a substance is 800 kg under in the Problem Solving forum “GIVEN: 1 cubic METER of the substance weighs 800 KILOGRAMS 1 kg =1,000 grams, so we can write: 1 cubic METER of the substance weighs 800,000 GRAMS 1 cubic meter = 1,000,000, so we can write: 1,000,000 cubic CENTIMETERS of the substance weighs 800,000 GRAMS What is the volume in cubic ...” October 14, 2018 fskilnik@GMATH posted a reply to Alice, Barbara, and Cynia work on identical tasks at differe in the Data Sufficiency forum “Obs.: the term approximately invalidates the question because we know NOTHING about the approximation precision. (What should be considered "near" 86%, for instance?) We will consider equality in both cases, with the following (not problematic) aside: the numbers b and c (below) may be ...” October 13, 2018 fskilnik@GMATH posted a reply to The "length" of a positive integer greater than 1 in the Problem Solving forum “?\,\,\, = \,\,\,\# \,\,{\rm{prime}}\,\,{\rm{factors}}\,\,\,\left( {{\rm{not}}\,\,{\rm{necessarily}}\,\,{\rm{distincts}}} \right) 5,950 = 10 \cdot 595\,\,\mathop = \limits^{\left( * \right)} \,\,10 \cdot 5 \cdot \underline {119} \,\,\mathop = \limits^{\left( {**} \right)} \,\,2 \cdot {5^2} ...” October 13, 2018 fskilnik@GMATH posted a reply to A certain family has 3 sons: Richard is 6 years older than D in the Problem Solving forum “? = D - 4 R = D + 6\,\,\,\,\mathop \Rightarrow \limits^{ + \,8} \,\,\,\,\,R + 8 = D + 14\,\,\,\left( 1 \right) D = S + 8\,\,\,\left( 2 \right) R + 8 = 2\left( {S + 8} \right)\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right),\left( 2 \right)} \,\,\,D + 14 = 2D\,\,\,\, ...” October 13, 2018 fskilnik@GMATH posted a reply to A number when divided successively by 4 and 5 leaves in the Problem Solving forum “N = {\rm{original}}\,\,{\rm{number}} ?\,\,\,:\,\,{\rm{remainder}}\,\,{\rm{of}}\,\,N\,\,{\rm{divided}}\,\,{\rm{by}}\,\,20 Explaining the question stem: when the "original number" (N) is divided by 4, the remainder is 1. When the quotient of this division (say Q) is divided by 5, ...” October 13, 2018 Brent@GMATPrepNow posted a reply to At a family summer party, each of the x members of the 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. The Ash Mo solved the question algebraically, so let''s use the INPUT-OUTPUT approach. It might be useful to choose a number that works well with the fractions ...” October 13, 2018 Brent@GMATPrepNow posted a reply to When A and B are positive integers, is AB a multiple of 4? in the Data Sufficiency forum “Target question: Is AB a multiple of 4? Useful property: If N is divisible by d, we can say that N = dk for some integer k For example, if N is divisible by 5, we can say that N = 5k for some integer k Statement 1: The greatest common divisor of A and B is 6 This means that A is divisible ...” October 13, 2018 Brent@GMATPrepNow posted a reply to How much time did it take a certain car to travel 400 in the Data Sufficiency forum “Target question: How long did it take to travel 400km To find the travel time, we need to know the average speed traveled. Let x = the average speed traveled. REPHRASED target question: What is the value of x? Statement 1: The car traveled the first 200 km in 2.5 hrs No info about the ...” October 13, 2018 Brent@GMATPrepNow posted a reply to Challenge question: What is the sum of all in the Problem Solving forum “Approach #1 If we recognize that x^(2/3) = u-substitution. Let u = x^(1/3) Now take original equation and replace x^(1/3) with u to get: u² - u - 2 = 4 Subtract 4 from both sides to get: to get: u² - u - 6 = 0 Factor: (u - 3)(u + 2) = 0 So, the two solutions here are u = 3 and u = -2 ...” October 13, 2018 GMATGuruNY posted a reply to Alice, Barbara, and Cynia work on identical tasks at differe in the Data Sufficiency forum “TIME and RATE have a reciprocal relationship. Statement 1: The time ratio for Barbara and Alice = (14 hours)/(21 hours). The rate ratio for Barbara and Alice is equal to the reciprocal of the time ratio: (B''s rate)/(A''s rate) = 21/14 = 3/2. Let B = 3 units per hour and A = 2 units per ...” October 13, 2018 Brent@GMATPrepNow posted a reply to A certain club has 10 members, including Harry. One of the 1 in the Problem Solving forum “As with many probability questions, we can solve this using counting techniques or probability rules. So, before you embark on one approach, try to determine which one is faster. Here''s the probability approach: P(Harry selected Secretary or Treasurer) = 1 - P(Harry selected president OR ...” October 13, 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 ...” October 13, 2018 GMATGuruNY posted a reply to A certain club has 10 members, including Harry. One of the 1 in the Problem Solving forum “Each of the 10 members has an EQUAL chance of being elected secretary. P(Harry is elected secretary) = 1/10. Each of the 10 members has an EQUAL chance of being elected treasurer. P(Harry is elected treasurer) = 1/10. Since EITHER outcome is favorable, we ADD the fractions: 1/10 + 1/10 = 2/10 = ...” October 13, 2018 fskilnik@GMATH posted a reply to How much time did it take a certain car to travel 400 in the Data Sufficiency forum “400\,{\rm{km}}\,\,\,\,\,\left\{ \matrix{ \,\,\left( {{\rm{real}}\,\,{\rm{speed}}\,,\,\,{\rm{real}}\,\,{\rm{time}}} \right)\,\,\,{\rm{ = }}\,\,\,\left( {{V_R}\,\,,\,\,{T_R}} \right) \hfill \cr \,\,\left( {{\rm{hypothetical}}\,\,{\rm{speed}}\,,\,\,{\rm{hypothetical}}\,\,{\rm{time}}} ...” October 12, 2018 fskilnik@GMATH posted a reply to When A and B are positive integers, is AB a multiple of 4? in the Data Sufficiency forum “Another beautiful problem, Max. Congrats! A,B\,\,\, \geqslant 1\,\,\,{\text{ints}} \frac{{A \cdot B}}{4}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int}  \left( 1 \right)\,\,\,GCD\left( {A,B} \right) = 6\,\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ \,A = 6M\,,\,\,\,M \ge ...” October 12, 2018 Brent@GMATPrepNow posted a reply to The average age of a group of n people is 15 yrs. One more in the Problem Solving forum “The average age of a group of n people is 15 yrs. So, (sum of all n ages)/n = 15 Multiply both sides by n to get: (sum of all n ages) = 15n One more person aged 39 joins the group and the new average is 17 yrs. IMPORTANT: Once this 39-year-old is added to the group, the (NEW sum of ages) = ...” October 12, 2018 fskilnik@GMATH posted a reply to The probability of winning game A is X and the probability in the Problem Solving forum “? = P\left( {{\text{win}}\,\,{\text{just}}\,\,{\text{A}}\,\,{\text{or}}\,\,{\text{win}}\,\,{\text{just}}\,\,{\text{B}}} \right)\,\,\,\, = \,\,\,\,P\left( {{\text{win}}\,\,{\text{A}}\,{\text{or}}\,\,{\text{B}}} \right) - P\left( {{\text{win}}\,\,{\text{both}}} \right) P\left( ...” October 12, 2018 fskilnik@GMATH posted a reply to A snack mix that is 20% raisins is blended with a second mix in the Problem Solving forum “? = x https://preview.ibb.co/j3WKW9/12-Oct18-4w.gif Excellent opportunity for the Alligation (and Bruce Lee): \frac{{10}}{{10 + \left( {5 + x} \right)}} = \frac{{22 - 20}}{{30 - 20}} = \frac{{2 \cdot \boxed5}}{{10 \cdot \boxed5}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,15 + x = ...” October 12, 2018 fskilnik@GMATH posted a reply to If x+(1/x)=4, what is the value of x^2+(1/x^2)? in the Problem Solving forum “FOCUS: ? = {x^2} + {1 \over {{x^2}}} DATA: x + {1 \over x} = 4\,\,\,\,\left( * \right) FOCUS-DATA CONNECTION: ?\,\, = \,\,{x^2} + \underline 2 + {1 \over {{x^2}}} - \underline 2 \,\, = \,\,{\left( {x + {1 \over x}} \right)^2} - 2\,\,\,\mathop = \limits^{\left( * \right)} ...” October 12, 2018 fskilnik@GMATH posted a reply to Challenge question: What is the sum of all in the Problem Solving forum “?\,\,\,:\,\,\,\,\,{\text{sum}}\,\,{\text{of}}\,\,{\text{roots}}\,\,{\text{of}}\,\,\,\,\root 3 \of {{x^2}} - \root 3 \of x - 6 = 0 y = \root 3 \of x \,\,\,\,\,\,\,\,\,\left[ {\,\root 3 \of {{x^2}} = {{\left( {\root 3 \of x } \right)}^2} = {y^2}\,} \right]\, {y^2} - y - 6 = ...” October 12, 2018 GMATGuruNY posted a reply to Challenge question: What is the sum of all in the Problem Solving forum “x^(2/3) - x^(1/3) - 2 = 4 x^(2/3) - x^(1/3) - 6 = 0 D.” October 12, 2018 Brent@GMATPrepNow posted a new topic called Challenge question: What is the sum of all in the Problem Solving forum “What is the sum of all solutions to the equation x^(2/3) - x^(1/3) - 2 = 4? A) -35 B) -19 C) 7 D) 19 E) 35 Answer: D Source: www.gmatprepnow.com Difficulty level: 600 - 650” October 12, 2018 October 12, 2018 Brent@GMATPrepNow posted a reply to Challenge question: j and k are positive integers in the Data Sufficiency forum “ Given: n = 10^j + k Target question: Is n divisible by 15? Key concepts: - If n is divisible by 15, then n must be divisible by 3 AND by 5 - If n is divisible by 3, then the sum of n''s digits must be divisible by 3 (for example, we know that 747 is divisible by 3, because 7+4+7 = 18, ...” October 12, 2018 fskilnik@GMATH posted a reply to Challenge question: j and k are positive integers in the Data Sufficiency forum “n = {\rm{1}}{{\rm{0}}^{\rm{j}}} + k\,\,\,\,;\,\,\,\,\,j,k\,\,\, \ge 1\,\,\,\,{\rm{ints}}\,\,\,\left( * \right) {n \over {3 \cdot 5}}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}}  \left( 1 \right)\,\, \cap \,\,\,\left( * \right)\,\,\, \Rightarrow \,\,\,\left\{ \matrix{ j = ...” October 12, 2018 GMATGuruNY posted a reply to Hard Assumption - Manhattan in the Critical Reasoning forum “The conclusion is constrained to the case at hand: Of the 10 babies recently placed with parents, 8 were given to friends of the staff. The assumption is that the premise (the parents given babies -- including the 8 friends --all far surpassed the agency''s criteria) is sufficient to prove the ...” October 11, 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 "if" versus "whether" https://www.youtube.com/watch?v=F2ZHtB088us Cheers, Brent” October 11, 2018 Brent@GMATPrepNow posted a new topic called Challenge question: j and k are positive integers in the Data Sufficiency forum “j and k are positive integers, and n = 10^j + k. Is n divisible by 15? (1) j and k are each divisible by 3 (2) j and k are each divisible by 5 Answer: A Difficulty level: 700+ Source: www.gmatprepnow.com” October 11, 2018 fskilnik@GMATH posted a reply to In a certain math department, students are required to in the Problem Solving forum “? = {{{\rm{Trig}}\,\, \cap \,\,{\rm{Adv}}} \over {{\rm{Total}}}} Good mix of the k technique with the grid (=double matrix, table, you-name-it)! https://preview.ibb.co/mr5Cip/11-Oct18-8v.gif ?\,\,\, = \,\,\,\frac{k}{{25k}}\,\,\, = \,\,\,\frac{{1 \cdot \boxed4}}{{25 \cdot \boxed4}}\,\,\, ...” October 11, 2018 fskilnik@GMATH posted a reply to If x and y are positive integers, is xy a multiple of 8? in the Data Sufficiency forum “x,y\,\,\, \ge \,\,1\,\,\,{\rm{ints}} {{xy} \over 8}\,\,\,\mathop = \limits^? \,\,\,{\mathop{\rm int}}  \left( 1 \right)\,\,GCD\left( {x,y} \right) = 10\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {10,10} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle ...” October 11, 2018 fskilnik@GMATH posted a reply to If x=0.abcabc........(a repeating infinite decimal), what is in the Data Sufficiency forum “x = 0.\overline {abc} \,\,\,\,\left( {{\rm{common}}\,\,{\rm{russian}}\,\,{\rm{notation}}} \right) ? = a + b + c \left( 1 \right)\,\,\,1 - x = 0.\overline {123} = {{123} \over {999}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x = {{876} \over {999}} = 0.\overline {876} ...” October 11, 2018 fskilnik@GMATH posted a reply to If x=0.abcabc........(a repeating infinite decimal), what is in the Data Sufficiency forum “x = 0.\overline {abc} \,\,\,\,\left( {{\rm{common}}\,\,{\rm{russian}}\,\,{\rm{notation}}} \right) ? = a + b + c \left( 1 \right)\,\,\,1 - x = 0.\overline {123} = {{123} \over {999}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x = {{876} \over {999}} = 0.\overline {876} ...” October 11, 2018 GMATGuruNY posted a reply to If every boy in a kindergarten class buys a soda and every in the Problem Solving forum “Let: b = the number of boys g = the number of girls s = the number of cents for each soda j = the number of cents for each juice box Note: All of the values above must be POSITIVE INTEGERS. Case One: If every boy in a kindergarten class buys a soda and every girl in the same class buys a ...” October 11, 2018 fskilnik@GMATH posted a reply to If every boy in a kindergarten class buys a soda and every in the Problem Solving forum “Although some "common-sense" can avoid math... why avoid math (it will be fast using it, by the way) ?! \left. \matrix{ g\,\,\, = \,\,\# \,\,{\rm{of}}\,\,{\rm{girls}} \hfill \cr b\,\,\, = \,\,\# \,\,{\rm{of}}\,\,{\rm{boys}}\,\,{\rm{ = }}\,\,\,g + k\,\, \hfill \cr} ...” October 11, 2018 fskilnik@GMATH posted a reply to What is the solution of the equation (x-1)/(1-x) = 0? in the Problem Solving forum “Important conceptual question. Congrats, Max! BEFORE any manipulation/calculation is done, the "mathematical entity" (in this case, the fraction) must EXIST. Hence we must impose the denominator different from zero, i.e., x different from 1. We know that any fraction given (if it ...” October 11, 2018 fskilnik@GMATH posted a reply to The above figure shows a sector of a circle. What is the are in the Data Sufficiency forum “(We assume - as part of the definition of a sector a circle - that the "origin" of the angle x shown in the figure is the center of the circle.) The variable R will denote the radius of the circle. All angles are measured in degrees. \https://preview.ibb.co/iPntM9/11_Oct18_2q.gif ...” October 11, 2018 Brent@GMATPrepNow posted a reply to Julie opened a lemonade stand and sold lemonade in two in the Data Sufficiency forum “This question illustrates a common trap on the GMAT. For statement 2, we''re able to write the equation 52x + 58y = 492 , 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 variables to ...” October 11, 2018 fskilnik@GMATH posted a reply to If x and y are positive integers in the Data Sufficiency forum “I finished my solution (posted above) with the following statement: \[x = {\text{prime}}{{\text{s}}^{\,{\text{positive}}\,\,{\text{integers}}}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\# \,\,{\text{posit}}\,\,{\text{div}}\,\,{\text{of}}\,\,{x^3}\,\,\, = \,\,\,\,\left[ ...” October 11, 2018 GMATGuruNY posted a reply to Julie opened a lemonade stand and sold lemonade in two in the Data Sufficiency forum “Let X = the number of 52¢ lemonades and Y = the number of 58¢ lemonades. Since the question stem asks for the number of 52¢ lemonades, we get: What is the value of X? Statement 1: X+Y = 9 Since X can be any value between 0 and 9, inclusive, INSUFFICIENT. Statement 2: 52X + 58Y = 492 ...” October 11, 2018 GMATGuruNY posted a reply to For the students in a Physical Fitness Class Section #1, the in the Data Sufficiency forum “Range = highest - lowest. Thus: Lowest = highest - range. In Section 1, lowest = highest - range = X-R. In Section 2, lowest = highest - range = Y-S. If the lowest weight in Section 1 is greater than the lowest weight in Section 2, we get: X-R > Y-S X+S > Y+R. Question ...” October 11, 2018 fskilnik@GMATH posted a reply to If x and y are positive integers in the Data Sufficiency forum “\[x,y\,\, \geqslant 1\,\,\,{\text{ints}}$ $\frac{{\,\# \,\,{\text{posit}}\,\,{\text{div}}\,\,{\text{of}}\,\,{x^3}\,}}{{\# \,\,{\text{posit}}\,\,{\text{div}}\,\,{\text{of}}\,\,{y^2}}}\,\,\,\mathop = \limits^? \,\,\,\operatorname{int}$ $\left( 1 \right)\,\,\,x = {2^2}\,\,\,\,\, \Rightarrow ...” October 10, 2018 fskilnik@GMATH posted a reply to Angela’s grade was in the 90th percentile out of 80 grades in the Problem Solving forum “\[?\,\, = \,\,\frac{{\# \,\,{\text{below}}\,\,{\text{Angela}}}}{{\# \,\,{\text{total}}}}\, \cdot \,\,100\,\,\,\left( \% \right)$ Alternate approach: Angela was in the "10th best grades" (but not better) in her class (80 students), hence (she is "number 8" and) there are 7 ...”
October 10, 2018
fskilnik@GMATH posted a reply to Angela’s grade was in the 90th percentile out of 80 grades in the Problem Solving forum
“The solution previously presented here was very similar to Mitch´s (above), therefore I have decided to change it. The approximation presented is validated a posteriori, because there are no alternative choices "near" the correct one! (If you prefer an exact solution, choose ...”
October 10, 2018
GMATGuruNY posted a reply to Angela’s grade was in the 90th percentile out of 80 grades in the Problem Solving forum
“Percentile means the percentage below: (total below)/(total grades) * 100. Angela''s 80-student class: Since Angela''s grade was in the 90th percentile, 90% of the grades were below Angela''s: (90/100)(80) = 72. 100-student class: Since 19 grades were higher than Angela''s, the remaining ...”
October 10, 2018
GMATGuruNY posted a reply to There are 5 cars to be displayed in 5 parking spaces with in the Problem Solving forum
“Alternate approach: The 3 red cars must occupy a combination of 3 spaces. From 5 spaces, the number of ways to choose a combination of 3 for the red cars = 5C3 = (5*4*3)/(3*2*1) = 10. Number of options for the blue car = 2. (Either of the 2 remaining spaces.) Number of options for the yellow ...”
October 10, 2018
Brent@GMATPrepNow posted a reply to There are 5 cars to be displayed in 5 parking spaces with in the Problem Solving forum
“Let R, R, R, B, Y represent the cars (by their colors) Notice that the three R''s are identical. So, the question becomes In how many different ways can we arrange the letters R, R, R, B and Y? ----------------ASIDE------------------------------ When we want to arrange a group of items in ...”
October 10, 2018
Brent@GMATPrepNow posted a reply to Is x/11 an integer? in the Data Sufficiency forum
“Target question: Is x/11 an integer? Statement 1: 5x/11 is an integer Let''s TEST some values There are several values of x that satisfy statement 1. Here are two: Case a: x = 11. Notice that 5x/11 = 5(11)/11 = 5, which is an integer. In this case, x/11 = 11/11 = 1. So, the answer to the ...”
October 10, 2018
Brent@GMATPrepNow posted a reply to Dick and Jane each saved $3000 in 1989. In 1990 Dick save 8 in the Problem Solving forum “Here''s the original wording: In 1990, Dick saved 8 percent more than in 1989 So, Dick''s savings in 1990 = 1.08($3000) = $3240 In 1990, Dick and Jane saved a total of$5,000. So, Jane''s savings = $5,000 -$3240 = \$1760 Approximately what percent less did Jane save in 1990 than in ...”
October 10, 2018
Brent@GMATPrepNow posted a reply to Pam and Sue drove in the same car to a business meeting that in the Problem Solving forum
“Travel time = distance/speed Pam''s travel time = 120 miles/60 mph =2 hours Sue''s travel time = 120 miles/50 mph =2.4 hours Time difference = 2.4 hours - 2 hours = 0.4 hours To convert 0.4 hours to minutes, recognize that 1 hour = 60 minutes So, 0.4 hours = (0.4)(60) minutes = 24 minutes ...”
October 10, 2018
fskilnik@GMATH posted a reply to Is x/11 an integer? in the Data Sufficiency forum
“$\frac{x}{{11}}\,\,\mathop = \limits^? \,\,\operatorname{int}$ $\left( 1 \right)\,\,\,\frac{{5x}}{{11}}\,\, = \operatorname{int} \,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,x = 0\,\,\,\,\, \Rightarrow \,\,\,\,\frac{x}{{11}} = \,\,0\,\,\,\, \Rightarrow \,\,\,\left\langle ...” October 10, 2018 fskilnik@GMATH posted a reply to The terminal zeros of a number are the zeros to the right of in the Data Sufficiency forum “\[?\,\,\,:\,\,\,{\text{number}}\,\,{\text{of}}\,\,{\text{terminal}}\,\,{\text{zeros}}\,\,{\text{of}}\,\,n\,{\text{!}}$ $\left( 1 \right)\,\,\,{n^2} - 15n + 50 < 0\,\,\,\, \Leftrightarrow \,\,\,\,5 < n < 10$ \[\left. \begin{gathered} n! = 6! = 6 \cdot \boxed5 \cdot 4 \cdot 3 \cdot 2 ...”
October 10, 2018
fskilnik@GMATH posted a reply to If Jim drives k miles in 50 minutes, how many minutes will in the Problem Solving forum
“\licit converter. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.”
October 10, 2018
fskilnik@GMATH posted a reply to If 2 numbers are selected from the first 8 prime numbers, wh in the Problem Solving forum
“\[{\rm{first}}\,\,{\rm{8}}\,\,{\rm{primes}}\,\,\left\{ \matrix{ \,{\rm{first}} = 2 = {\rm{even}} \hfill \cr \,{\rm{7}}\,{\rm{others}}\,\, = \,\,{\rm{odd}}\,\,\,\,\,\left( {{\rm{it}}\,\,{\rm{does}}\,\,{\rm{not}}\,\,{\rm{matter}}\,{\rm{who}}\,\,{\rm{they}}\,\,{\rm{are}}!} \right) \hfill \cr} ...”
October 10, 2018
GMATGuruNY posted a reply to Hard Assumption - Manhattan in the Critical Reasoning forum
“Premise: All of the applicants given babies far surpassed the adoption criteria. Conclusion: In placing 8 of the 10 babies with friends, the staff was not guilty of favoritism. Apply the NEGATION TEST. When the correct answer is negated, the conclusion will be invalidated. B, negated: Of ...”
October 10, 2018