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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