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: â… . a⊙b=b⊙a is TRUE because a^2 + b^2 is commutative â…¡. (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