Is positive integer z greater than 275?

This topic has expert replies
Moderator
Posts: 6595
Joined: 07 Sep 2017
Followed by:20 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Is positive integer z greater than 275?

(1) z is a multiple of 21

(2) z is a multiple of 39


OA E

Source: Veritas Prep

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16086
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

BTGmoderatorDC wrote:
Tue Apr 19, 2022 1:52 am
Is positive integer z greater than 275?

(1) z is a multiple of 21

(2) z is a multiple of 39


OA E

Source: Veritas Prep
Target question: Is positive integer z greater than 275?

Statement 1: z is a multiple of 21
Let's TEST some values.
There are several values of z that satisfy statement 1. Here are two:
Case a: z = 21, in which case, the answer to the target question is NO, z is NOT greater than 275
Case b: z = 2100, in which case, the answer to the target question is YES, z IS greater than 275
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: z is a multiple of 39
Let's TEST values again.
Case a: z = 39, in which case, the answer to the target question is NO, z is NOT greater than 275
Case b: z = 3900, in which case, the answer to the target question is YES, z IS greater than 275
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that z is a multiple of 21, which means we can write z = 21k for some integer k
Statement 2 tells us that z is a multiple of 39, which means we can write z = 39j for some integer j
Saying that z = 21k is the same as saying that z = (3)(7)(k)
Saying that z = 39j is the same as saying that z = (3)(13)(j)
When we write z is these two ways, we can see that (3)(7)(13) will be a multiple of 21 AND a multiple of 39
(3)(7)(13) = 273, so z COULD equal 273, in which case, the answer to the target question is NO, z is NOT greater than 275
Or it could be the case that z = (3)(7)(13)(2) = 546, in which case, the answer to the target question is YES, z IS greater than 275
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image