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What is the largest of three consecutive even integers?

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What is the largest of three consecutive even integers?

by Max@Math Revolution » Tue Jun 05, 2018 4:56 am

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[GMAT math practice question]

What is the largest of three consecutive even integers?

1) The smallest integer is 6.
2) Their average is 8.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Thu Jun 07, 2018 1:31 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.

Let 2k - 2, 2k, 2k + 2 be the 3 consecutive even integers. Since we have 1 variable (k) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
Since 2k - 2 = 6, we must have 2k = 8 or k = 4.
Then the largest integer is 2k + 2 = 10.
Thus, condition 1) is sufficient.

Condition 2)
The average of three consecutive even integers is their median.
Since 2k = 8, we must have k = 4.
Then, the largest integer is 2k + 2 = 10.
Thus, condition 2) is sufficient.

Therefore, the answer is D.

Answer: D

Note: Since both conditions give us the same information, the answer is D by tip 1).

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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