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If S is a set of distinct positive multiples of 5, what is the smalles

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Bunuel
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If S is a set of distinct positive multiples of 5, what is the smalles [#permalink] New post   24 Aug 2015, 23:42
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If S is a set of distinct positive multiples of 5, what is the smallest element of S?

(1) The mean of S and the median of S both equal 20.
(2) The largest element of S is 40.

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C
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VenoMfTw
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Re: If S is a set of distinct positive multiples of 5, what is the smalles [#permalink] New post   26 Aug 2015, 08:45
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Bunuel wrote:
If S is a set of distinct positive multiples of 5, what is the smallest element of S?

(1) The mean of S and the median of S both equal 20.
(2) The largest element of S is 40.

Kudos for a correct solution.


IMO: C

St 1: The mean of S and the median of S both equal 20.

Different sets are possible - {20} , {15,20,25}, {10,15,20,25,30}, {5,10,15,20,25,30,35}
Hence Not suff

St 2: The largest element of S is 40.

Different Sets are possible - {40} , {10,40} .....

Combined: The mean of S and the median of S both equal 20. & largest element of S is 40

Only one possible combination : {5, 10, 20, 25, 40}.
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If S is a set of distinct positive multiples of 5, what is the smalles [#permalink] New post   25 Aug 2015, 00:31
Bunuel wrote:
If S is a set of distinct positive multiples of 5, what is the smallest element of S?

(1) The mean of S and the median of S both equal 20.
(2) The largest element of S is 40.


Ans: NOT A Not B Not D ------------- C or E not sure
1) (20) (5,20,35) (10,20,30)(15,25) [Not Sufficient]
2) (40) (5,40) (10,40) (20,40) [Not Sufficient]

I know statement A and B alone are not sufficient
but there are so many possibilities with even number of elements and odd number of elements in set and calculating median and avg for all are too time consuming.
What is the trick here.. ? How to solve this in 2 min?
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If S is a set of distinct positive multiples of 5, what is the smalles [#permalink] New post   28 Aug 2015, 07:23
VenoMfTw
Quote:
IMO: C

St 1: The mean of S and the median of S both equal 20.

Different sets are possible - {20} , {15,20,25}, {10,15,20,25,30}, {5,10,15,20,25,30,35}
Hence Not suff

St 2: The largest element of S is 40.

Different Sets are possible - {40} , {10,40} .....

Combined: The mean of S and the median of S both equal 20. & largest element of S is 40

Only one possible combination : {5, 10, 20, 25, 40}


Agree with everything except the final sentence. What if 0(which is also a multiple of 5) is considered. Then we have another set possible:{0,10,20,30,40},{0,15,20,25,40}. There are still at least two possible answers.
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Re: If S is a set of distinct positive multiples of 5, what is the smalles [#permalink] New post   29 Aug 2015, 22:40
hb4100 wrote:
VenoMfTw

Agree with everything except the final sentence. What if 0(which is also a multiple of 5) is considered. Then we have another set possible:{0,10,20,30,40},{0,15,20,25,40}. There are still at least two possible answers.


hb4100
0 is not a positive integer. In question stem it is stated "positive integers".
Hence 0 is not possible.
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Re: If S is a set of distinct positive multiples of 5, what is the smalles [#permalink] New post   27 Jan 2021, 09:57
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Re: If S is a set of distinct positive multiples of 5, what is the smalles [#permalink]
27 Jan 2021, 09:57
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