MathRevolution wrote:
[GMAT math practice question]
When a positive integer n is divided by 5, the remainder is 2. What is the remainder when n is divided by 3?
1) n is divisible by 2
2) When n is divided by 15, the remainder is 2.
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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.
We have 1 variable (n) and 1 equation. So, D is most likely to be the answer, and we should consider each of the conditions on its own first.
Plugging-in numbers is the suggested approach to remainder questions.
Condition 1)
The possible values of n are
n = 2, 4, 6, 8, …
When these are divided by 3, the remainders are 0, 1 and 2.
Since the answer is not unique, condition 1) is not sufficient.
Condition 2)
The possible values of n are
n = 17, 32, 47, 62, …
When these are divided by 3, the remainder is always 2.
Since the answer is unique, 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.
How can we take such values of n in condition 1?
If divided by 5, they don't give remainder of 2!