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Which of the following series of numbers, if added to the

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Which of the following series of numbers, if added to the set {1, 6, 11, 16, 21}, will not change the set’s mean?

I. 1.5, 7.11 and 16.89
II. 5.36, 10.7 and 13.24
III. -21.52, 23.3, 31.22

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) None
[Reveal] Spoiler: OA
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Re: set’s mean [#permalink]

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New post 26 Jan 2012, 12:46
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rohitgoel15 wrote:
Which of the following series of numbers, if added to the set {1, 6, 11, 16, 21}, will not change the set’s mean?
I. 1.5, 7.11 and 16.89
II. 5.36, 10.7 and 13.24
III. -21.52, 23.3, 31.22

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) None


Mean of the given set is (1+6+11+16+21)/5=11.

Now, in order the mean not to change, the mean of the new set we add to the old one should also be equal to 11 (or as in all 3 new sets there are 3 numbers, then their sum must be 3*11=33). Let's check:

I. 1.5, 7.11 and 16.89 --> will end with 0.5 son not 33. Discard.
II. 5.36, 10.7 and 13.24 --> will end with 0.3 son not 33. Discard.
III. -21.52, 23.3, 31.22 --> -21.52+23.3+31.22=-21.52+54.52=33. Correct.

Answer: C (III only).
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Re: Which of the following series of numbers, if added to the [#permalink]

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New post 17 Apr 2015, 05:07
Straightforward. The mean of the current set is (1+6+11+16+21)/5=11. Set has 5 numbers. So keep the mean the same after new numbers are added we need to find the sum that will be added. We can set up equation (55+x)/8=11. 8 is because we add 3 numbers. Hence x=33. Only set III has numbers that sum up to 33. Hope it is clear
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Re: Which of the following series of numbers, if added to the [#permalink]

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New post 17 Apr 2015, 11:03
Expert's post
Hi All,

This question has some great Number Property shortcuts built into it (which you can take advantage of to save some time and avoid some of the math "work").

We're given the set {1, 6, 11, 16, 21}. We're asked which set of additional numbers, when added into this set, will NOT change the set’s mean.

In the original set of numbers, notice how the 5 terms are 'evenly spaced'; this means that the average MUST be the 'middle term' --> the average is 11.

Looking at the three options, notice how each has 3 terms. To add 3 terms to the given set and NOT change the average, we need the average of the 3 terms to be 11. By extension, we need the SUM to = 33.

A quick estimate of Roman Numerals 1 and 2 proves that neither has a sum of 33 (the sums are both TOO SMALL). Eliminate Answers A, B and D.

Adding up the terms in Roman Numeral 3 gives us a sum of 33, so this set 'fits' what we're looking for.

Final Answer:
[Reveal] Spoiler:
C


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Re: Which of the following series of numbers, if added to the   [#permalink] 17 Apr 2015, 11:03
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