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When n is divided by 5, what is the remainder?

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When n is divided by 5, what is the remainder?

by Max@Math Revolution » Thu Mar 01, 2018 2:38 am
[GMAT math practice question]

When n is divided by 5, what is the remainder?

1) When n is divided by 3, the remainder is 2
2) When n+1 is divided by 5, the remainder is 3
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Mar 04, 2018 6:16 pm
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.
It is suggested we plug in numbers for the remainder questions.

Condition 1): n=3p+2=2,5,8........
n = 2 : The remainder of n is 2 when it is divided by 5.
n = 5 : The remainder of n is 0 when it is divided by 5.

Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2):
We have n + 1 = 5q + 3 for some integer, since n + 1 has the remainder 3 when it is divided by 5.
It is equivalent to n = 5q + 2=2,7,12,17,....
The remainder is 2 when n is divided by 5.
Thus condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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