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# If set S consists of positive two-digit integers (m25#32)

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If set S consists of positive two-digit integers (m25#32) [#permalink]

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15 Feb 2012, 06:02
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If set $$S$$ consists of all positive two-digit integers divisible by 4, what is the mean of set $$S$$ ?

(A) 52.0
(B) 54.0
(C) 54.5
(D) 55.5
(E) 56.0
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Senior Manager
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Re: If set S consists of positive two-digit integers (m25#32) [#permalink]

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06 Jun 2012, 11:31
Hi all, can you pls explain why the mean is the max value plus minimum value divided by 2 from the set (96 + 12)/2?

I don't understand why its not the sum of all values in the set between 12 and 96 divided by the total number of values (21)?

Would appreciate the help.
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Re: If set S consists of positive two-digit integers (m25#32) [#permalink]

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06 Jun 2012, 14:36
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Aximili85 wrote:
Hi all, can you pls explain why the mean is the max value plus minimum value divided by 2 from the set (96 + 12)/2?

I don't understand why its not the sum of all values in the set between 12 and 96 divided by the total number of values (21)?

Would appreciate the help.

I thought there was 22 values in the set. (4 - 100 is 25 values, subtract out 4, 8, 100 to get only 2-digit values is 22).

I didn't know any short hand trick to the problem, so the way I did it was:

There's 22 numbers in the set

12, 16, . . . 92, 96

Basically each low-high sums to 108 (12+96=108, 16+92=108), and there are 11 pairs of this (22 numbers divided by 2).

So the mean would be (108 * 11)/22 which simplifies to (108)/2 = 54.
Senior Manager
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Kudos [?]: 129 [1] , given: 134

Re: If set S consists of positive two-digit integers (m25#32) [#permalink]

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06 Jun 2012, 14:43
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Swoosh617 wrote:
Aximili85 wrote:
Hi all, can you pls explain why the mean is the max value plus minimum value divided by 2 from the set (96 + 12)/2?
numbers divided by 2).

So the mean would be (108 * 11)/22 which simplifies to (108)/2 = 54.

oh hell.. ok that's complex.. appreciate the help though but that won't come to me intuitively in that time-frame. I was googling around, apparently the rule is that if the numbers are equally spaced in any set of numbers, then the average ends up being the sum of the first and the last # divided by 2. Tried it on sample set of numbers and it worked.

A rule to learn for me I guess since my intuitive sense isn't the best.

Really appreciate your prompt response though amigo!
A.
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Re: If set S consists of positive two-digit integers (m25#32) [#permalink]

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06 Jun 2012, 14:45
Aximili85 wrote:
Swoosh617 wrote:
Aximili85 wrote:
Hi all, can you pls explain why the mean is the max value plus minimum value divided by 2 from the set (96 + 12)/2?
numbers divided by 2).

So the mean would be (108 * 11)/22 which simplifies to (108)/2 = 54.

oh hell.. ok that's complex.. appreciate the help though but that won't come to me intuitively in that time-frame. I was googling around, apparently the rule is that if the numbers are equally spaced in any set of numbers, then the average ends up being the sum of the first and the last # divided by 2. Tried it on sample set of numbers and it worked.

A rule to learn for me I guess since my intuitive sense isn't the best.

Really appreciate your prompt response though amigo!
A.

And that rule was exactly what I was hoping to get from this thread. Good to know the short way to the answer now. Kudos!
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Re: If set S consists of positive two-digit integers (m25#32) [#permalink]

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06 Jun 2012, 14:47
gotta love this forum
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Re: If set S consists of positive two-digit integers (m25#32) [#permalink]

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14 Jun 2012, 02:56
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dzyubam wrote:
If set $$S$$ consists of all positive two-digit integers divisible by 4, what is the mean of set $$S$$ ?

(A) 52.0
(B) 54.0
(C) 54.5
(D) 55.5
(E) 56.0

Hi,

For an AP (12, 16,....,96),
the mean as well as median would be equal to average of first and last term.
Hence, (12+96)/2=54

Proof: lets consider an AP,
a, a+d, a+2d,...., a+(n-1)d
sum of AP =$$\frac n2 (2a+(n-1)d)$$
mean value = $$\frac{\frac n2 (2a+(n-1)d)}n$$
=2a+(n-1)d= a + a+(n-1)d
= first term + last term

Other properties which you may remember:
average of even number of consecutive natural numbers will never be an integer.
average of odd number of consecutive natural numbers will always be an integer.

Regards,
Re: If set S consists of positive two-digit integers (m25#32)   [#permalink] 14 Jun 2012, 02:56
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# If set S consists of positive two-digit integers (m25#32)

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