If n is an integer, which of the following CANNOT be a factor of 3n+4?

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?

by Brent@GMATPrepNow » Sun Jun 28, 2020 5:31 am

BTGModeratorVI wrote: ↑
Sat Jun 27, 2020 6:49 am
If n is an integer, which of the following CANNOT be a factor of 3n+4?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: C
Source: GMAT paper tests

KEY CONCEPTS
If a number is divisible by 6 it MUST also be divisible by 3
Conversely, if a number is NOT divisible by 3, then that number is NOT divisible by 6

3n + 4 = 3n + 3 + 1
= 3(n + 1) + 1
We can see that 3n+4 is 1 greater than some multiple of 3
This tells us that 3n+4 is NOT divisible by 3
This means (from the rules above) that 3n+4 is NOT divisible by 6

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?

by Brent@GMATPrepNow » Sun Jun 28, 2020 5:32 am

BTGModeratorVI wrote: ↑
Sat Jun 27, 2020 6:49 am
If n is an integer, which of the following CANNOT be a factor of 3n+4?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: C
Source: GMAT paper tests

Another approach is to plug in integer values for n and start ELIMINATING answer choices..

Try n = 0
So, 3n + 4 = 3(0) + 4 = 4
4 IS a factor of 4
ELIMINATE A

Try n = 1
So, 3n + 4 = 3(1) + 4 = 7
7 IS a factor of 7
ELIMINATE D

Try n = 2
So, 3n + 4 = 3(2) + 4 = 10
5 IS a factor of 10
ELIMINATE B

Try n = 3
So, 3n + 4 = 3(3) + 4 = 13
Doesn't help...

Try n = 4
So, 3n + 4 = 3(4) + 4 = 16
8 IS a factor of 16
ELIMINATE E

By the process of elimination, the correct answer is C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: If n is an integer, which of the following CANNOT be a factor of 3n+4?

by Scott@TargetTestPrep » Sat Jul 04, 2020 12:03 pm

BTGModeratorVI wrote: ↑
Sat Jun 27, 2020 6:49 am
If n is an integer, which of the following CANNOT be a factor of 3n+4?

A. 4
B. 5
C. 6
D. 7
E. 8

Answer: C
Source: GMAT paper tests

Solution:

Since 3n + 4 will never be a multiple of 3, it will never be a multiple of 6. In other words, 6 cannot be a factor of 3n + 4.

Answer: C

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