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If n is a 2-digit positive integer and its tens digit is 4 t

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If n is a 2-digit positive integer and its tens digit is 4 t

by Max@Math Revolution » Mon Aug 06, 2018 11:50 pm

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[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Aug 09, 2018 12:19 am

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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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

n = 10a + b and a = 4b
The possible pairs ( a, b ) are ( 4, 1 ) and ( 8, 2 ) by the original condition.
Thus, n = 41 or n = 82.

Since we have 3 variables and 2 equations, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
Since a = 8, we must have n = 82.
Thus, condition 1) is sufficient.

Condition 2)
Since 4 + 1 = 5 is not a 2-digit integer and 8 + 2 = 10 is a 2-digit integer, n = 82.
Thus, condition 2) is sufficient.

Therefore, D is the answer.

Answer: D

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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