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

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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

Source: www.gmatprepnow.com
Answer: B
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[email protected] wrote:
Thu Jul 14, 2022 7:34 am
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

Source: www.gmatprepnow.com
Answer: B
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
Brent Hanneson - Creator of GMATPrepNow.com
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