If x and y are positive integers, and x³ 10x²y 24xy² = 0, which of

Question

If x and y are positive integers, and x3 – 10x2y – 24xy2 = 0, which of the following could be true?

I. x = 0
II. x - 12y = 0
III. x + 2y = 0

A) I only 
B) II only
C) I and III only
D) II and III only
E) I, II and III

Regor60 · Answer

I is out since X is positive.

III is out because both X and Y are positive

This leaves II as the only remaining choice, B

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truplayer257 · Answer

x³ – 10x²y – 24xy² = 0
Attempt to factor:
 x³ – 12x²y + 2x²y – 24xy² = 0
x²(x - 12y) + 2xy(x - 12y) = 0
x(x + 2y)(x - 12y) = 0
So we have:
x = 0 (Not possible since x is a POSITIVE integer)
x + 2y = 0 (Could be possible)
x - 12y = 0 (Could be possible)

The answer is D

Edit: good point about x = -2y leading to a negative value therefore it can’t be true.

So answer can only be x -12y = 0

BrentGMATPrepNow · Answer

This question is proving to be pretty difficult!

Key property: If ABC = 0, then A = 0, B = 0, or C = 0

Given:  x³ – 10x²y – 24xy² = 0 
First factor out the x on the left side to get:  x(x² – 10xy – 24y²) = 0 
Now factor the quadratic:  x(x - 12y)(x + 2y) = 0 
From the  property  above, we know that  x = 0 ,  x - 12y = 0  or  x + 2y = 0 
However, before we select answer choice E, we must remember that we're told that  x and y are  positive  integers

If x is  positive , x can't equal 0, since 0 is neither positive nor negative. So, statement I can't be true. 
Similarly, if  x and y are  positive  , then x is  positive  and 2y is  positive , which means the sum x + 2y must  positive , which means x + 2y CANNOT equal 0. So, statement III can't be true.

Since statement II is the only statement that can be true, the  correct answer is B

samarpan.g28 · Answer

If we take x common at the beginning, we get x=0, (x-12y)=0, and (x+2y)=0.
x and y are positive integers, so x cannot be 0. I is omitted.
x-12y=0 i.e. x=12y. If x is +ve then y is +ve too, so II is correct.
x+2y=0 i.e. x=-2y. If x is +ve then y is -ve and vice-versa. III is incorrect.
Only II is right so correct answer is (B).

If x and y are positive integers, and x³ 10x²y 24xy² = 0, which of

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GMAT Problem Solving (PS) Questions

If x and y are positive integers, and x³ 10x²y 24xy² = 0, which of

Prep Toolkit

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