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Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and

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Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and  [#permalink]

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New post 30 Jan 2016, 02:55
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Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and y are both prime numbers and 0 < x < 40 and 0 < y < 40, which of the following MUST be true?

I. The maximum possible range of the set is greater than 33.
II. The median can never be an even number.
III. If y = 37, the average of the set will be greater than the median.

A. I only
B. I and II only
C. I and III only
D. III only
E. I, II, and III

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Re: Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and  [#permalink]

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New post 30 Jan 2016, 05:55
1
1
S = {2, 4, 6, 8, x, y}
x and y are both prime numbers and 0 < x < 40 and 0 < y < 40
I. The maximum possible range of the set is greater than 33.
The biggest prime number < 40 is 37 . To obtain the max possible range either x or y has to be 37
Range = 37-2 = 35
True
II. The median can never be an even number.
S = {2, 4, 6, 8, x, y}
If x and y are prime numbers greater than 8 , then median will be (6+8)/2 = 7
If x and y are 3 and 5 , then set S = {2,3,4,5,6,8} , then median will be = 9/2
If x = 3 , then set S = { 2,3,4,6,8, y} , then median will be = 5
If x = 5 , then set S = { 2,4,5,6,8,y} , then median will be = 11/2
If x = 7 , then set S ={ 2,4,6,7,8,y} , then median will be = 13/2
Median will either be an odd number or a decimal .
True
III. If y = 37, the average of the set will be greater than the median.
S = {2, 4, 6, 8, x, 37}
The average will be least when x is smallest
S = {2, 3, 4, 6, 8, 37}
If x=3 , then average will be 60/6 = 10 and median will be 5 .
The median will be highest when x>8 , median = 7 , now the average will be more than 10 .
True
Answer E
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Re: Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and  [#permalink]

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New post 29 Jun 2017, 13:17
how to solve this within 2 mins---- seems hard to do this within 2 mins ?

any suggestions on cutting above steps perhaps ?
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Re: Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and  [#permalink]

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New post 02 Jul 2017, 11:33
I have a question, the first line say "with distinct elements", and for me means that x and y are totally different from the numbers of the set. For this reason the statement III does not fix.

Could you clarify it please or why do you consider x=3?
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Re: Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and  [#permalink]

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New post 03 Jul 2017, 09:21
leysbals wrote:
I have a question, the first line say "with distinct elements", and for me means that x and y are totally different from the numbers of the set. For this reason the statement III does not fix.

Could you clarify it please or why do you consider x=3?



in the given set they have mentioned all the numbers are distinct and x and y are prime number, now considering that, 3 is the number not included in the set given and is the smallest prime number so x taken as 3 to get least possible mean
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Re: Consider a set S = {2, 4, 6, 8, x, y} with distinct elements. If x and   [#permalink] 03 Jul 2017, 09:21
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