BTGModeratorVI wrote: ↑Thu Jun 18, 2020 5:44 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
