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The number of elements in set K is an odd number. The minimum value of

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The number of elements in set K is an odd number. The minimum value of [#permalink]

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New post 29 Mar 2017, 22:13
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E

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Question Stats:

24% (02:24) correct 76% (03:02) wrong based on 62 sessions

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The number of elements in set K is an odd number. The minimum value of set K is 22, the maximum value is 40, and the median value is 37. Is the number of elements in set K at least 13?

1) The total average of elements in set K is greater than 37.
2) The sum of the elements in set K is greater than 407.
Spoiler: OA

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Re: The number of elements in set K is an odd number. The minimum value of [#permalink]

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New post 06 Apr 2017, 10:07
Can somebody help with how A is sufficient?
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Re: The number of elements in set K is an odd number. The minimum value of [#permalink]

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New post 06 Apr 2017, 13:15
What is a minimum value ( of ) set k , do u mean (in) ?


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Re: The number of elements in set K is an odd number. The minimum value of [#permalink]

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New post 06 Apr 2017, 14:26
We have a set {22,_ _ _, 37, _ _ _ ,40}. We need to check minimum and maximum scenarios to calculate the number of elements in the set.
Currently we have 3 elements and according to the scenario we can add elements in pairs (since the number of elements is odd): one between 22 to 37 and the other between 37 to 40 inclusive.

1) The total average of elements in set K is greater than 37.
22 is 15 less than 37. 40 is only 3 above 37.We need to add elements that will raise the average to 37. In order to get the minimum elements scenario we will add pairs with maximum value (37,40). We get a set {22,37,37,37,37,37,40,40,40,40,40}. That's 11 elements, but we need average greater than 37, so we need an additional pair of elements which makes it at least 13 elements. Sufficient.

2) The sum of the elements in set K is greater than 407.
The minimum scenario from the previous statement fit for this statements as well. Again we need a sum which is greater than 407, which makes it at least 13 elements. Sufficient.

The answer is D.

By the way I selected E, since I missed the part of the "greater". LOL
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Re: The number of elements in set K is an odd number. The minimum value of [#permalink]

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New post 06 Apr 2017, 20:29
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Number of elements = odd
Min = 22, Median = 37 and Max = 40

Question: Number of elements >= 13?

St1: Average > 37
Our goal is to find the minimum number of elements for which the max possible average is greater than 37.
Let's assume the number of elements = 13
Set = {22, 37, 37, 37, 37, 37, 37, 40, 40, 40, 40, 40, 40}
Average = 37 + (-15 + 18)/13 = 37 + 3/13 > 37
So max possible average for 13 elements just crosses 37 and hence the number of elements must be atleast 13. If you lower the values we need more number of elements for the average to cross 37.
Sufficient

St2: Sum > 407
Lets consider only 11 elements and maximize the value of the set
22 + 37*5 + 40*5 = 22 + 185 + 200 = 407
Since sum > 407, the set should have one more element. But the set contain odd number of elements.
Hence number of elements in the set must be atleast 13
Sufficient

Answer: D
Re: The number of elements in set K is an odd number. The minimum value of   [#permalink] 06 Apr 2017, 20:29
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