BTGmoderatorDC wrote: ↑Tue Jan 25, 2022 5:42 pm
If z is an integer, is z even?
(1) z/2 is even.
(2) 3z is even.
OA
D
Source: Manhattan Prep
Target question: Is z an even integer?
Aside: Integer n is even if we can express n as n = 2k for some integer k
Statement 1: z/2 is an even integer.
This means z/2 =2k for some integer k
Multiply both sides by 2 to get: z = 4k
This tells us that z is a multiple of 4, which means
z is definitely even
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: 3z is even .
Since 3 is ODD, the only way that 3z can be even is if
z is EVEN.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
