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Averages

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by SaraLotfy » Thu Sep 19, 2013 12:04 am
Set S consists of integers 7,8,10,12,13. If the integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. what is the value of integer n?

A) 10
B) 12
C) 16
D) 22
E) 24
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by theCodeToGMAT » Thu Sep 19, 2013 12:12 am
Is ANSWER [spoiler][D][/spoiler]

(7 + 8 + 10 + 12 + 13 + x)
___________________________ = 10 (1.2)
6

50 + x = 12 x 6
x = 22
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by vinay1983 » Thu Sep 19, 2013 12:15 am
SaraLotfy wrote:Set S consists of integers 7,8,10,12,13. If the integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. what is the value of integer n?

A) 10
B) 12
C) 16
D) 22
E) 24
Average now is 50/5 = 10
New average is (120/100)*10 = 12, but his average will be for 6 numbers, hence sum of the six numbers is 6*12=72
So the new number is 72-50 = 22

D


Hope this helps!
Last edited by vinay1983 on Thu Sep 19, 2013 12:21 am, edited 1 time in total.
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by SaraLotfy » Thu Sep 19, 2013 12:15 am
Yes that's what I got too :)
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by SaraLotfy » Thu Sep 19, 2013 12:17 am
Yes that's what I got too :)
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by theCodeToGMAT » Thu Sep 19, 2013 12:21 am
Great :) ..
SaraLotfy wrote:Yes that's what I got too :)
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by GMATGuruNY » Thu Sep 19, 2013 12:58 am
SaraLotfy wrote:Set S consists of integers 7,8,10,12,13. If the integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. what is the value of integer n?

A) 10
B) 12
C) 16
D) 22
E) 24
Original set:
When a set of values is SYMMETRICAL about the median, the average = the median.
The original set is SYMMETRICAL about the median of 10.
Thus:
Original average = 10.
Original sum = (original number of integers)(original average) = 5*10 = 50.

New set:
Since the new average is 20% greater, the new average = 10 + .2(10) = 12.
Thus, the new sum = (new number of integers)(new average) = 6*12 = 72.

Since the sum increases from 50 to 72, n = 72-50 = 22.

The correct answer is D.
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by GMATGuruNY » Thu Sep 19, 2013 12:58 am
SaraLotfy wrote:Set S consists of integers 7,8,10,12,13. If the integer n is included in the set, the average (arithmetic mean) of set S will increase by 20%. what is the value of integer n?

A) 10
B) 12
C) 16
D) 22
E) 24
Original set:
When a set of values is SYMMETRICAL about the median, the average = the median.
The original set is SYMMETRICAL about the median of 10.
Thus:
Original average = 10.
Original sum = (original number of integers)(original average) = 5*10 = 50.

New set:
Since the new average is 20% greater, the new average = 10 + .2(10) = 12.
Thus, the new sum = (new number of integers)(new average) = 6*12 = 72.

Since the sum increases from 50 to 72, n = 72-50 = 22.

The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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by [email protected] » Thu Sep 19, 2013 12:17 pm
Hi SaraLotfy,

It appears that everyone else in this post has provided the appropriate "algebra" solution to this prompt. Here's another method to solve this question that you might find useful (and possibly faster). It is based on TESTing THE ANSWERS.

The set 7,8,10,12,13 has a sum of 50 and an average of 50/5 = 10

To raise this average by 20%, we're likely going to need to add in a larger number. With the 5 answer choices provided, it's probably NOT going to be A or B.

Let's test D. If it's correct, then we're done. If it leads to an answer that's too big or too small, then we'll know which of the other 2 answers to pick.

7,8,10,12,13,22 has a sum of 72 and an average of 72/6 = 12

12 is 20% more than 10, so this is a PERFECT MATCH for what we're looking for.

Final Answer: D

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