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Senior Manager  D
Joined: 29 Oct 2019
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If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 20% (01:56) correct 80% (01:20) wrong based on 169 sessions

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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
Director  V
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Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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$$y^2 = \frac{-12x}{5}$$
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
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Target Test Prep Representative V
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Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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sjuniv32 wrote:
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

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.)

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# Scott Woodbury-Stewart

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Director  D
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Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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

Posted from my mobile device

If x=0 then y=0 and 0 is an integer
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Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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sjuniv32 wrote:
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

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 = [-(2^2).3.x]/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)
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Target Test Prep Representative V
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Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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Raksat wrote:

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).

Posted from my mobile device

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".
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# Scott Woodbury-Stewart

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Scott@TargetTestPrep.com

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Intern  Joined: 23 Dec 2019
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Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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

Posted from my mobile device
Senior Manager  D
Joined: 29 Oct 2019
Posts: 317
Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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sjuniv32 wrote:
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

Veritas solution to this hard problem: https://www.youtube.com/watch?v=fxJBwPCEMUA&t=918s
Manager  P
Joined: 20 Feb 2017
Posts: 186
Location: India
Concentration: Operations, Strategy
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If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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ScottTargetTestPrep wrote:
sjuniv32 wrote:
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

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.)

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).

Posted from my mobile device
Director  D
Joined: 12 Dec 2015
Posts: 500
Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus  [#permalink]

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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 Re: If x and y are integers and 12x + 5y^2 = 0. Which of the following mus   [#permalink] 04 Mar 2020, 07:16

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