Data Sufficiency

BTGModeratorVI wrote: ↑

Sat Mar 28, 2020 9:51 am

If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

(1) The remainder is 3 when x + 1 is divided by 4.
(2) The remainder is 0 when 2x is divided by 4.

Answer: A
Source: Official guide

Target question: What is the remainder when x is divided by 4 ?

Statement 1: The remainder is 3 when x + 1 is divided by 4.
------ASIDE----------------------
There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
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We don't know how many times 4 divides into x+1. So, let's just say 4 divides into x+1 k times.
So, we can write: x + 1 = 4k + 3 (for some integer k)
Subtract 1 from both sides to get x = 4k + 2
Since 4k is a multiple of 4, we can see that x is 2 greater than some multiple of 4
So, when we divide x by 4, the remainder will be 2
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The remainder is 0 when 2x is divided by 4.
We can write: 2x = 4k (for some integer k)
Divide both sides by 2 to get: x = 2k
This tells us that x is an even integer.
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 2. In this case, the answer to the target question is when we divide x by 4, the remainder will be 2
Case b: : x = 4. In this case, the answer to the target question is when we divide x by 4, the remainder will be 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent