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04 Jul 2009, 05:04
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I'm pretty sure the answer given in one of my review books is incorrect, but thought I'd check with the legions of quant wizards on the forum before jumping to any unwarranted conclusions:
What is the sum of the numbers in a list of m even integers?
(1) The largest integer on the list is 12.
(2) The list consists of 6 consecutive multiples of 4.
Solutions, please!
What is the sum of the numbers in a list of m even integers?
(1) The largest integer on the list is 12.
(2) The list consists of 6 consecutive multiples of 4.
Solutions, please!
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04 Jul 2009, 06:37
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carriedinterest
Statement 1 alone: we don't know anything about the other numbers in the list besides the fact that they are even and no larger than 12. Insufficient.
Statement 2 alone: we don't know where the list starts or ends. Insufficient.
Statements 1+2 together: 'consists of' means 'is entirely made up of', so we know that there are exactly six numbers in the list, and they are consecutive multiples of 4. Since the largest is 12, we can reconstruct the entire list (it is 12, 8, 4, 0, -4, -8), and therefore find the sum. Sufficient. C.
What answer does the book give? If their answer is not C, I'd be curious to know the source. It's an odd question regardless, since the fact that the numbers are even isn't ever used in the solution, and authentic GMAT DS questions rarely provide extraneous information in the stem.
Updated on: 04 Jul 2009, 10:21
Originally posted by carriedinterest on 04 Jul 2009, 09:46.
Last edited by carriedinterest on 04 Jul 2009, 10:21, edited 1 time in total.
Last edited by carriedinterest on 04 Jul 2009, 10:21, edited 1 time in total.
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IanStewart
The book gives the same response (C). For me, the issue is that there is an ambiguity around the word 'consecutive' in the context of the question. Are the multiples themselves consecutive or are the members of the set consecutive? If the former is true, the latter is necessarily true and we arrive at the set you provided (12, 8, 4, 0, -4, -8). But if statement (2) only implies that the members of the set are BOTH consecutive AND multiples of 4, there are other sets that satisfy both conditions (e.g., 12, 0, -12, -24, -36, -48). It seems clear to me that the members of the set in the proceeding example are both consecutive and multiples of 4. My answer: E.
Phrased differently:
- Consecutive integers are defined as integers that are evenly spaced. It follows that the intervals themselves are irrelevant.
- x is a multiple of y if and only if x/y is an integer. Thus, 12 is a multiple of 4, 36 is a multiple of 4, etc.
From the above, it is certainly true that (12, 8, 4, 0, -4, -8) is a set of "6 consecutive multiples of 4". But the set (12, 0, -12, -24, -36, -48) also satisfies these conditions: each of the members of the set are evenly spaced (consecutive) and is a multiple of 4.
