Is the interger K divisible by 4?
1) 8k is divisible by 16
2) 9k is divisible by 12
With the answer, can you all please explain how you came up with the answer thanks
Divisibility
This topic has expert replies
- DanaJ
- Site Admin
- Posts: 2567
- Joined: Thu Jan 01, 2009 10:05 am
- Thanked: 712 times
- Followed by:550 members
- GMAT Score:770
1. is insufficient, since if 8k is divisible by 16, this means that 8k = 16d (where d = quotient when you divide 8k by 16). This means that k = 2d, which means that k is even. However, we cannot tell if it is divisible by 4. If d is odd, then it sure isn't.
2. is sufficient, since if 9k is divisible by 12, this means that 9k = 12d (again, d = quotient). Since 9 is not divisible by 4 but it is divisible by 3, this means that k must be divisible by 12/3 = 4.
So k is divisible by 4.
Answer B.
2. is sufficient, since if 9k is divisible by 12, this means that 9k = 12d (again, d = quotient). Since 9 is not divisible by 4 but it is divisible by 3, this means that k must be divisible by 12/3 = 4.
So k is divisible by 4.
Answer B.