BTGModeratorVI wrote: ↑Sun Jul 19, 2020 1:44 pm
If p is a positive integer, is p even?
(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
Answer:
B
Source: Economist GMAT
Target question: Is p even?
Statement 1: p divided by 3 leaves a remainder of 1
In other words, p is 1 greater than some multiple of 3
There are several values of p that satisfy this condition. Here are two:
Case a: p = 4. In this case, the answer to the target question is
YES, p is even
Case b: p = 7. In this case, the answer to the target question is
NO, p is not even
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: p divided by 4 leaves a remainder of 1
In other words, p is 1 greater than some multiple of 4
So, we can say that: p = 4k + 1 for some integer k
Since 4k must be EVEN, we can conclude that 4k+1 must be ODD
In other words,
p MUST be ODD
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
