BTGModeratorVI wrote: ↑

Tue Mar 31, 2020 5:10 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

Given that W, X, Y, and Z represent distinct digits, we have WX and YZ, two-digit numbers.

Let's take WX * YZ = 1995 = 3*5*7*19

There are few possibilities, keeping in mind that W, X, Y, and Z are distinct digits and WX and YZ are two-digit numbers.

1. WX = 3*5 = 15 and YZ = 7*133; however this is not possible since Y and Z are single digits.

2. WX = 3*7 = 21 and YZ = 5*19 = 95; we have W = 2.

3. WX = 5*19 = 95 and YZ = 3*7 = 21; we have W = 5.

4. WX = 3*19 = 57 and YZ = 5*7 = 35; however this is not possible since W, X, Y and Z are distict digits.

So, we have to ascertain a unique value between the two values of W = {2, 9}.

Let's take each statement one by one.

(1) X is a prime number.

Case 2 above is invalid since WX = 21, and X = 1, non-prime; thus, only Case 3 is applicable as WX - 95 and X = 5, prime number. So, we have W = 9. Sufficient.

(2) Z is not a prime number.

Again, Case 2 above is invalid since YZ = 95, and Z = 5, prime; thus, only Case 3 is applicable as YZ = 21 and Z = 1, non-prime number. So, we have W = 9. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Tue Mar 31, 2020 5:10 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