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# Is the average (arithmetic mean) of a, b, and c greater than 12?

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
Is the average (arithmetic mean) of a, b, and c greater than 12?  [#permalink]

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01 Jan 2018, 01:30
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Difficulty:

35% (medium)

Question Stats:

78% (01:30) correct 22% (02:11) wrong based on 23 sessions

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Is the average (arithmetic mean) of a, b, and c greater than 12?

(1) c > a + b
(2) ac = 48

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Re: Is the average (arithmetic mean) of a, b, and c greater than 12?  [#permalink]

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02 Jan 2018, 13:12
Bunuel wrote:
Is the average (arithmetic mean) of a, b, and c greater than 12?

(1) c > a + b
(2) ac = 48

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 3 variables (x and y) and 0 equations, E is most likely to be the answer. So, we should consider 1) & 2) first.

Case 1: a = 1, b = 2 c = 48
( a + b + c ) / 3 = 51 / 3 > 12 : Yes

Case 2: a = 6, b = 1, c = 8
( a + b + c ) / 3 = 15 / 3 = 5 < 12 : No

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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Re: Is the average (arithmetic mean) of a, b, and c greater than 12?   [#permalink] 02 Jan 2018, 13:12
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