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When n is divided by 4, what is the remainder?

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by Vincen » Wed Sep 27, 2017 6:23 pm
When n is divided by 4, what is the remainder?

1) When n is divided by 3, the remainder is 1
2) When n+1 is divided by 4, the remainder is 2

The OA is B.

Why statement (2) is sufficient? I couldn't get this conclusion.
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Source: — Data Sufficiency |

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by [email protected] » Fri Sep 29, 2017 10:05 am
Hi Vincen,

We're asked for the remainder when N is divided by 4. We can solve this question by TESTing VALUES.

1) When n is divided by 3, the remainder is 1

With this Fact, we know that N could be 1, 4, 7, 10, 13, etc.
IF....
N=1, then 1/4 = 0 r 1 --> the answer is 1.
N=4, then 4/4 = 1 r 0 --> the answer is 0.
Fact 1 is INSUFFICIENT

2) When (N+1) is divided by 4, the remainder is 2

With this Fact, we know that N could be 1, 5, 9, 13, 17, etc.
IF....
N=1, then 1/4 = 0 r 1 --> the answer is 1.
N=5, then 5/4 = 1 r 1 --> the answer is 1.
N=9, then 9/4 = 2 r 1 --> the answer is 1.
Since the value of N increases by 4 each time, and the calculation divides by 4, the remainder will ALWAYS be 1.
Fact 2 is SUFFICIENT

Final Answer: B

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Rich
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