BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:35 am

Is integer k a prime number?

(1) k = 10! + m, where 1 < m < 8
(2) k is a multiple of 7


Answer: A
Source: Veritas Prep

Target question: Is integer k a prime number?

Statement 1: k = 10! + m, where 1 < m < 8
Let's check a few values of m and look for a pattern.

m = 2
k = 10! + 2
k = (10)(9)(8)(8)(6)(5)(4)(3)(2)(1) + 2
k = 2[(10)(9)(8)(8)(6)(5)(4)(3)(1) + 1]
Since k is a multiple of 2, k is NOT prime

m = 3
k = 10! + 3
k = (10)(9)(8)(8)(6)(5)(4)(3)(2)(1) + 3
k = 3[(10)(9)(8)(8)(6)(5)(4)(2)(1) + 1]
Since k is a multiple of 3, k is NOT prime

m = 4
k = 10! + 4
k = (10)(9)(8)(8)(6)(5)(4)(3)(2)(1) + 4
k = 4[(10)(9)(8)(8)(6)(5)(3)(2)(1) + 1]
Since k is a multiple of 4, k is NOT prime

As you can see, we can perform the same operations with m = 5, 6 and 7, and EVERY TIME we will conclude that k is NOT prime
Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Statement 2: k is a multiple of 7
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 7, in which case k IS prime [yes, 7 is a multiple of 7]
Case b: k = 14, in which case k is NOT prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent