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

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

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

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