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If x, y, and z are different positive integers, is x prime?

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Feb 03, 2019 11:38 pm
BTGmoderatorDC wrote:If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y

OA C

Source: Veritas Prep
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GMAT/MBA Expert

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by Jay@ManhattanReview » Sun Feb 03, 2019 11:46 pm
BTGmoderatorDC wrote:If x, y, and z are different positive integers, is x prime?

(1) xyz = 30
(2) z < x < y

OA C

Source: Veritas Prep
Given: x, y, and z are different positive integers.

We have to determine whether x is prime.

Let's take each statement one by one.

(1) xyz = 30

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Case 1: Say xyz = 30 = 1*2*15; x = 1 is non-prime.
Case 2: Say xyz = 30 = 2*1*15; x = 2 is prime.

No unique answer. Insufficient.

(2) z < x < y

Certainly insufficient.

(1) and (2) together

Given x < y < z, we can write xyx = 30 only in the following four ways.

1. xyx = yxz = 30 = 1*2*15; x = 2 is prime.
2. xyx = yxz = 30 = 2*3*5; x = 3 is prime.
3. xyx = yxz = 30 = 1*3*10; x = 3 is prime.
4. xyx = yxz = 30 = 1*5*6; x = 5 is prime.

The answer is Yes. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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