Bunuel wrote:

For integers x and y, if 91x = 8y, which of the following must be true?

I. y > x

II. y/7 is an integer

III. The cube root of x is an integer

A) I only

B) II only

C) III only

D) I and II

E) II and III

Without actually solving the equation algebraically, we can see that x could be 8 and y could be 91, since 91(8) = 8(91). However, this is not the only possibility. We see that x could be 0 and y could be 0, since 91(0) = 8(0), or x could be -8 and y could be -91, since 91(-8) = 8(-91). In any event, we see that x is a multiple of 8 (including 0 and the negative multiples) and y is a multiple of 91 (including 0 and the negative multiples).

Let’s analyze each Roman numeral:

I. y > x

Since both x and y could be 0, y is not necessarily greater than x.

Roman numeral I is not true.

II. y/7 is an integer

Since y is a multiple of 91, y/7 is an integer.

Roman numeral II must be true.

III. The cube root of x is an integer

We’ve mentioned that x is a multiple of 8. If x = 8, then the cube root of x is an integer. However, if x = 16, then the cube root of x is not an integer.

Roman numeral III is not true.

Answer: B

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Scott Woodbury-Stewart

Founder and CEO

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