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# M14-15

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Math Expert
Joined: 02 Sep 2009
Posts: 47037

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16 Sep 2014, 00:53
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Difficulty:

25% (medium)

Question Stats:

82% (00:46) correct 18% (01:11) wrong based on 84 sessions

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The average weight of 15 items is 8 kilograms. If at least one item weighs exactly 5 kilograms, what is the maximum number of items that can have the same weight of 5 kilograms?

A. 3
B. 5
C. 6
D. 10
E. 14

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Math Expert
Joined: 02 Sep 2009
Posts: 47037

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16 Sep 2014, 00:53
Official Solution:

The average weight of 15 items is 8 kilograms. If at least one item weighs exactly 5 kilograms, what is the maximum number of items that can have the same weight of 5 kilograms?

A. 3
B. 5
C. 6
D. 10
E. 14

Total weight of these 15 items is $$15*8=120$$ kilograms.

We also know that at least one item weighs exactly 5 kilograms. Now, all 15 items cannot have the same weight of 5 kilograms since in this case average weight would be 5 kilograms and not 8.

Can 14 items have the same weight of 5 kilograms? Why not? In this case the total weight of these 14 items would be $$14*5=70$$ kilograms and the last item would be 50 kilograms $$(70+50=120)$$.

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Joined: 20 Aug 2017
Posts: 39
Location: United States (FL)
Schools: Stanford '20 (D)
GMAT 1: 750 Q49 V42
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15 Sep 2017, 17:13
Why all the complications in the question? Why not simply ask "The average weight of 15 items is 8 kilograms. What is the maximum number of items that can weigh exactly 5 kilograms?" I'm not sure how adding the phrase "If at least one item weighs exactly 5 kilograms" adds anything but confusion. Whether at least 1 item weighs 5 kilos is irrelevant.
Re: M14-15   [#permalink] 15 Sep 2017, 17:13
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# M14-15

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