BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:50 am

W, X, Y, and Z represent distinct digits such that WX * YZ = 1995. What is the value of W?

(1) X is a prime number
(2) Z is not a prime number

Answer: D
Source: Veritas Prep

Target question: What is the value of W?

Given: W, X, Y, and Z represent distinct digits such that (WX)(YZ) = 1995
Let's take a close look at what we can conclude from this info.
Whenever I see a big number like 1995, I consider finding its PRIME FACTORIZATION
1995 = (3)(5)(7)(19)
In what ways can we take this and rewrite 1995 as the product of two 2-digit integers?
We get 4 possible cases;
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995
c) (35)(57) = 1995
d) (57)(35) = 1995

HOWEVER, since all 4 digits must be DISTINCT, we must eliminate cases c and c, which leaves us with only 2 possible cases.
(WX)(YZ) = 1995
a) (21)(95) = 1995
b) (95)(21) = 1995

Statement 1: X is a prime number
Since 1 is not prime, we can rule out case a.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Z is not a prime number
1 is the only NON-PRIME number, so this rules out case a.
This leaves only case b, which means W must equal 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent