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

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

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[email protected] wrote: ↑Thu Jul 14, 2022 7:34 amIf 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**