BTGModeratorVI wrote: ↑Mon Sep 07, 2020 6:53 am
Is a^5 divisible by 4?
(1) a^5 – 8 is divisible by 4.
(2) a is divisible by 6.
Answer:
D
Source: Official guide
Target question: Is a^5 divisible by 4?
Statement 1: a^5 - 8 is divisible by 4.
In other words, a^5 – 8 is a MULTIPLE OF 4
So, we can say that: a^5 – 8 = 4k for some integer k
Add 8 to both sides to get: a^5 = 4k + 8 (for some integer k)
Factor the right side: a^5 =
4(k + 2) (for some integer k)
This tells us that a^5 is a MULTIPLE of
4
Another way to express this is to say that
a^5 IS divisible by 4
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: a is divisible by 6
In other words, a is a MULTIPLE OF 6
So, we can say that: a = 6j for some integer j
Rewrite this as: a = (2)(3j)
So, a^5 = (2)(3j)(2)(3j)(2)(3j)(2)(3j)(2)(3j)
Simplify to get: a^5 = (
4)(3j)(2)(3j)(2)(3j)(2)(3j)(3j)
This tells us that a^5 is a MULTIPLE of
4
Another way to express this is to say that
a^5 IS divisible by 4
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
