If x and y are integers and 12x + 5y^2 = 0. Which of the following mus

Question

If x and y are integers and 12x + 5y^2 = 0. Which of the following must be true?

(A) x is a multiple of 10

(B) x is a multiple of 15

(C) x is a multiple of 25

(D) x is not a multiple of 7

(E) x is negative

ScottTargetTestPrep · Accepted Answer

We see that 12x = -5y^2 and therefore, x = -5y^2/12. It’s tempting to conclude that x is negative, and if that were true, then choice E would be the correct answer. However, if y = 0, then x will also be 0, which is not negative. We can eliminate choice E.

Let’s take a closer look at x = -5y^2/12. Since 5 is not divisible by 12 and x is an integer, then y^2 must be divisible by 12. The smallest positive integer value of y such that y^2 is divisible by 12 is y = 6. And if y = 6, x = -5(36)/12 = -15, which is a multiple of 15. (Note: any other integer value of y must be a multiple of 6, so x will still be a multiple of 15.)

Answer: B

MahmoudFawzy · Answer

y^2 = \frac{-12x}{5} 
as the LHS must be non negative, so x is either (-ve) or zero --> E is incorrect

now, lets simply substitute x with (-10,-15,-25,-7),  y^2  will be (24,36,60,fraction)
only when x is substituted with -15, y is an integer -->  B

Rameshllll · Answer

If X is non negative i.e 0, how can y be an integer

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firas92 · Answer

If x=0 then y=0 and 0 is an integer

analytica233 · Answer

12x + 5y^2 = 0 <=> y^2 = (-12x)/5
- We can see that x = y = 0 satisfies the equation. --> Eliminate (E).
- Next, y^2 = (-12x)/5 =  /5 (factoring 12 into 2^2.3)
--> x's prime factors must include an ODD number of 5 AND include an ODD number of 3's 
--> x must be divisible by 15 (x = 0 is also divisible by 15) --> (B)

Russ19 · Answer

Veritas solution to this hard problem: https://www.youtube.com/watch?v=fxJBwPCEMUA&t=918s

Raksat · Answer

I had the impression that we should always consider positive multiple or factors in GMAT. I am not talking about mathematics in general but pertaining to GMAT. 
If we consider as above then if the question is like 
How many factors does 6 have?" The answer would be 8: (-6, -3, -2, -1, 1, 2, 3, 6).

So please clarify the doubt.

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ScottTargetTestPrep · Answer

It's not true that we always consider positive multiples or factors in GMAT, there are many examples where one has to consider negative multiples/factors to get the correct answer. On the other hand, questions in GMAT will always clarify whether you need to consider the negative factors or not. For instance, if the question wants you to consider {1, 2, 3, 6} as factors of 6, the question will most likely say "positive factors of 6" instead of just "factors of 6".

hiranmay · Answer

If x and y are integers and 12x + 5y^2 = 0. Which of the following must be true?

(A) x is a multiple of 10

(B) x is a multiple of 15 -->  correct

(C) x is a multiple of 25

(D) x is not a multiple of 7

(E) x is negative -->  wrong because x >=0 i.e. x is non-positive => so x can be 0 or negetive

Solution :
12x + 5y^2 = 0
=> y^2 = -12x/5 >=0
=> x <=0
y^2 = -2^2 * 3 * x / 5
=> x has to be multiple of 5 because y is an interger,
also x has to be multiple of 3 because right side has to be >= 2^2*3^2
so x = 3*5*n^2, n is an integer i.e x is multiple of 15

Crytiocanalyst · Answer

If x=0 then y=0 so the possibility of negstive can be eleminated and for the other cases so eleminate E

12x + 5y^2 = 0

=> y^2 = (-12x)/5

let us assume x to be -10 then 24 is not a perfect square eleminate A 
let us assume to be -25 since 60 is not a multiple hence eleminate C 
7 is not a factor of 5 so obviously eleminate 
and when -15 is substituted we recieve 36 which is a perfect square 
hence IMO B

maniknct · Answer

x can be zero or multiple of -15 to make y an integer . So answer is B

If x and y are integers and 12x + 5y^2 = 0. Which of the following mus

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GMAT Problem Solving (PS) Questions

If x and y are integers and 12x + 5y^2 = 0. Which of the following mus

Prep Toolkit

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