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# If the average of 5 numbers is 36 and the average of four

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Retired Moderator
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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If the average of 5 numbers is 36 and the average of four [#permalink]  08 Dec 2017, 20:57
Expert's post
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Question Stats:

99% (00:45) correct 0% (00:00) wrong based on 7 sessions
If the average of 5 numbers is 36 and the average of four of those numbers is 34, then what is the value of the fifth number?

A. 2
B. 34
C. 35
D. 36
E. 44

Drill 4
Question: 6
Page: 532

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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 163

Kudos [?]: 2740 [0], given: 394

Re: If the average of 5 numbers is 36 and the average of four [#permalink]  29 Dec 2017, 16:38
Expert's post
Explanation

Use the Average Pie to solve each part of the problem. If the average of 5 numbers is 36, then the sum of those numbers is 180. If the average of four of the numbers is 34, then the sum of those numbers is 136.

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If five numbers add up to 180 and four of those five numbers add up to 136, then the fifth number is the difference between those two sums: 180 – 136 = 44. If you picked choice (A), you found the difference between the two averages, not the fifth number. If you picked choice (C), you found the average of the averages. If you picked either choice (B) or choice (D), you resolved for the average after determining the sum.
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Sandy
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Re: If the average of 5 numbers is 36 and the average of four [#permalink]  19 Jan 2020, 07:13
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Expert's post
sandy wrote:
If the average of 5 numbers is 36 and the average of four of those numbers is 34, then what is the value of the fifth number?

A. 2
B. 34
C. 35
D. 36
E. 44

Drill 4
Question: 6
Page: 532

Let the five numbers be a, b, c, d, and e

The average of 5 numbers is 36

We can write: $$\frac{a+b+c+d+e}{5}=36$$

Multiply both sides by 5 to get: $$a+b+c+d+e=180$$

The average of four of those numbers is 34

We can write: $$\frac{a+b+c+d}{4}=34$$

Multiply both sides by 4 to get: $$a+b+c+d=136$$

What is the value of the fifth number?
At the moment we have two equations:
$$a+b+c+d+e=180$$
$$a+b+c+d=136$$

When we subtract the bottom equation from the top equation we get: $$e = 44$$

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Re: If the average of 5 numbers is 36 and the average of four   [#permalink] 19 Jan 2020, 07:13
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