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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