Seven friends went to an art festival and each spent a different sum of money. If the friends' totals were

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Oct 06, 2020 7:06 am

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Seven friends went to an art festival and each spent a different sum of money. If the friends' totals were $\$127, \$135, \$129, \$138, \$126, \$142,$ and $\$134,$ what was the average sum of money that a friend spent?

A. $\$128$
B. $\$133$
C. $\$138$
D. $\$141$
E. $\$145$

Answer: B

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Source: Beat The GMAT — Problem Solving | Tue Oct 06, 2020 7:06 am

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Re: Seven friends went to an art festival and each spent a different sum of money. If the friends' totals were

by Scott@TargetTestPrep » Sat Oct 10, 2020 2:31 pm

Vincen wrote: ↑
Tue Oct 06, 2020 7:06 am
Seven friends went to an art festival and each spent a different sum of money. If the friends' totals were $\$127, \$135, \$129, \$138, \$126, \$142,$ and $\$134,$ what was the average sum of money that a friend spent?

A. $\$128$
B. $\$133$
C. $\$138$
D. $\$141$
E. $\$145$

Answer: B

Solution:

Sum/quantity = average, so we have:

(127 + 135 + 129 + 138 + 126 + 142 + 134) / 7 = 931/7 = $133

Alternate Solution:

Let’s pick a value that is close to all the sums, such as 130. We will add the signed differences between the sums and 130:

(127 - 130) + (135 - 130) + (129 - 130) + (138 - 130) + (126 - 130) + (142 - 130) + (134 - 130)

-3 + 5 + (-1) + 8 + (-4) + 12 + 4 = +21

So, the average of all the sums differs from 130 by 21/7 = +3; therefore, the average is 130 + 3 = $133. Note that we would have obtained the same answer had we calculated the differences with a different number, such as 125 or 135.

Answer: B

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