## If z is an integer, is z even?

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### If z is an integer, is z even?

by BTGmoderatorDC » Tue Jan 25, 2022 5:42 pm

00:00

A

B

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D

E

## Global Stats

If z is an integer, is z even?

(1) z/2 is even.
(2) 3z is even.

OA D

Source: Manhattan Prep

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### Re: If z is an integer, is z even?

by [email protected] » Wed Jan 26, 2022 7:33 am

00:00

A

B

C

D

E

## Global Stats

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