Search found 82 matches


Possible values: x = 1,3,5,7,9,11,13,15,17,19 Write values as products of prime factors: x = 1,3,5,7,3^2,11,13,(3*5),17,19 1) (2^4)x is divisible by (2^3)*3 simplified becomes 2x is divisible by 3, so x is divisible by 3, so x =3,9,15 2) (2*7)x is not divisible by 3*5 simplified becomes x is not div...

by DrMaths

Wed Jan 31, 2018 9:58 am
Forum: GMAT Math
Topic: If x < 20, How many distinct factors does odd number x ha
Replies: 2
Views: 3209

consistency

Let m = number of multiples of 77
and p = number of multiples of 7
Note that 77 = 70 + 7, so 77m = 70m + 7m
Therefore 350 = 70m + 7m + 7p = 70m + 7(m+p)
As 350 is a multiple of 10, then (m+p) must be a multiple of 10 too
Only Answer C gives n = 40 = m+p = multiple of 10

by DrMaths

Wed Jan 31, 2018 9:44 am
Forum: Problem Solving
Topic: If each term in the sum a1+a2+a3+.....+an is either 7 or...
Replies: 6
Views: 2350

No need to consider summing or subtracting rates; just look at comparing ratios in a simple equation: L/R = 10/40 = 1/4 = L/(L+6) Rearranged gives L+6 = 4L 3L= 6 L = 2 (no. of revolutions) as L makes 10 revs per minute, then 2 revs is 2/10 of a minute = 1/5 of a minute 1/5 of 60 seconds = 12 seconds...

by DrMaths

Wed Jan 31, 2018 9:35 am
Forum: Problem Solving
Topic: Circular gears L and R start to rotate at the same time...
Replies: 6
Views: 948

Alternative method: We should know that the difference of 2 squares x^2-y^2 = (x+y)(x-y) Now substitute x=m^2+n^2, and y=2mn: (x+y)(x-y) = (m^2+n^2+2mn)(m^2+n^2-2mn) This gives a result that includes negative terms, so only answers D and E are valid. Also, the factor (m^2+n^2+2mn)>0 since all negati...

by DrMaths

Wed Jan 31, 2018 9:16 am
Forum: Problem Solving
Topic: If m<n<0, x=m^2+n^2, and y=2mn,
Replies: 2
Views: 840

Watch out for negative values!

Test by using simple integers such as n = -1, m = -2 x=m^2+n^2 = 2^2 + 1^2 = 5 y = 2mn = 2 * 2 * 1 = 4 Now substitute... x^2-y^2 = 25 - 16 = 9 So sqrt(x^2-y^2) = 3 (This is what we are looking for) Now test the options: A. m^2+n^2 = 4 + 1 = 5 B. 2m^2+n^2 = 8 + 1 = 9 C.m^2+2n^2 = 4 + 2 D. m^2-n^2 = 4...

by DrMaths

Wed Jan 31, 2018 8:57 am
Forum: Problem Solving
Topic: If m<n<0, x=m^2+n^2, and y=2mn,
Replies: 2
Views: 840

Note that (a+b)^2-2ab = a^2 + b^2 Therefore a⊙b = a^2 + b^2 Now look at the options: Ⅰ. a⊙b=b⊙a is TRUE because a^2 + b^2 is commutative Ⅱ. (a⊙b)⊙c=a⊙(b⊙c) FALSE LHS: (a⊙b)⊙c = [a^2 + b^2]^2 + c^2 which results in a^4 +... RHS: a⊙(b⊙c) = a^2 + [[b^2 + c^2]^2] which results ...

by DrMaths

Wed Jan 31, 2018 8:45 am
Forum: Problem Solving
Topic: If a⊙b=(a+b)^2-2ab, which of the following is(are) true?
Replies: 2
Views: 529

X = 4/3Y (because 1 + 1/3 = 4/3)
Y = 3/4Z (because 1 - 1/4 = 3/4)
Substituting Y into X gives X = 4/3*3/4Z = Z

Therefore X = Z = 24000

by DrMaths

Wed Jan 31, 2018 8:31 am
Forum: Problem Solving
Topic: In a mayoral election
Replies: 3
Views: 723

We only need to regard last digit of everything! The last digit of both 07 and 77 is 7. Now multiply this 7 by the last digit of each given answer: A. 8 x 7 = 56 B. 9 x 7 = 63 C. 0 x 7 = 0 D. 1 x 7 = 7 E. 2 x 7 = 14 Only answer C has a last digit that matches the last digit of 350. None of the other...

by DrMaths

Wed Jan 31, 2018 8:22 am
Forum: Problem Solving
Topic: If each term in the sum a1+a2+a3+.....+an is either 7 or...
Replies: 6
Views: 2350

I. a-14, a, a, a, a+14 II. b, b+1, b+2, b+3, b+4 III. c, c, c, c, c The data sets I, II and III above are ordered from greatest standard deviation to least standard deviation in which of the following? A. I, II, III B. I, III, II C. II, III, I D. III, I, II E. III, II, I The OA is A . Please, can a...

by DrMaths

Wed Jan 31, 2018 8:13 am
Forum: Problem Solving
Topic: The data sets I, II, and III above are ordered from...
Replies: 2
Views: 765

If a person purchases 15 of the 3,000 tickets sold in a raffle that awards one prize, what is the probability that this person will not win? A. 0 B. 1/200 C. 1/2 D. 199/200 E. 1 Two solutions, same answer: (1) Pure method: P = P(winning ) = 15/3000 = 5/1000 = 1/200 P' = (P of not winning) = 1 - P = ...

by DrMaths

Wed Jan 31, 2018 7:50 am
Forum: Problem Solving
Topic: If a person purchases 15 of the 3,000 tickets sold in a...
Replies: 3
Views: 897

Pythagoras' Theorem works in 3D as well as 2D. In 2D, hypotenuse^2 = a^2 + b^2 In 3D, hypotenuse^2 = a^2 + b^2 + c^2 Where a, b and c are the orthogonal triangle sides or edges. With a cube of unit length, AC = 1 AB = SQRT(1 + 1) = SQRT(2) BC = SQRT(1 + 1 + 1 = SQRT(3) So (BC - AB)/AC = (SQRT(3) - S...

by DrMaths

Wed Jan 31, 2018 7:43 am
Forum: Problem Solving
Topic: What fraction of the distance from A to C?
Replies: 2
Views: 545

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. 4 B. 3 C. 2 $$D.\sqrt{3}$$ $$E.\sqrt{2}$$ For speed, ignoring the proportionality consta...

by DrMaths

Wed Jan 31, 2018 7:23 am
Forum: Problem Solving
Topic: How many times the circumference of the smaller circle?
Replies: 3
Views: 803

The smallest Pythagorean triples are:
(3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25)
None of these include 11
Answer A is 11^2 = 121

As 11 is not in the list of triples, then A is impossible.
All the other values are not squares, so non-integer solutions are possible.

by DrMaths

Thu Jan 25, 2018 7:41 am
Forum: Problem Solving
Topic: If x and y are integers, which of the following CANNOT be th
Replies: 6
Views: 1220

If the number x is obtained by reversing the order of the digits in the positive 3-digit integer y, is x > y? (1) The tens digit of y is 3. (2) The rightmost digit of x is 1 and the rightmost digit of y is 9. The OA is the option B . How can I use the statement (2) to get an answer here? Experts, c...

by DrMaths

Thu Jan 25, 2018 7:35 am
Forum: Data Sufficiency
Topic: If the number x is obtained by reversing the.....
Replies: 2
Views: 674

(x−1)(1−y)=-(x-1)(y-1) = -(xy - x - y + 1) = 1 - xy + x + y

(1) Substitute x+y=xy to get 1 - xy + xy = 1 SUFFICIENT
(2) Substitute x=y to get 1 - x^2 + 2x INSUFFICIENT

by DrMaths

Thu Jan 25, 2018 7:32 am
Forum: Data Sufficiency
Topic: (x−1)(1−y)=?
Replies: 1
Views: 641