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# Seven friends went to an art festival and each spent a different sum

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Math Expert
Joined: 02 Sep 2009
Posts: 52343
Seven friends went to an art festival and each spent a different sum  [#permalink]

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30 Aug 2018, 20:53
00:00

Difficulty:

15% (low)

Question Stats:

89% (01:18) correct 11% (02:03) wrong based on 44 sessions

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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

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Re: Seven friends went to an art festival and each spent a different sum  [#permalink]

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30 Aug 2018, 22:15
Bunuel wrote:
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

Average of $127,$135, $129,$138, $126,$142, and $134=$$\frac{127+135+129+138+126+142+134}{7}$$=$$\frac{700}{7}$$+$$\frac{27+35+29+38+26+42+34}{7}$$=100+33=$133

Ans. (B)
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Re: Seven friends went to an art festival and each spent a different sum  [#permalink]

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30 Aug 2018, 23:50
Bunuel wrote:
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

average = $$\frac{sum}{7}$$ = $$\frac{931}{7}$$ =133
Math Expert
Joined: 02 Aug 2009
Posts: 7212
Re: Seven friends went to an art festival and each spent a different sum  [#permalink]

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31 Aug 2018, 00:27
1
1
Bunuel wrote:
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

the choices are spread so may not require calculations..
arrange in ascending order.. 126,127,129,134,135,138,142
the numbers are generally even spaced, so the average should be close to median..
so close to 133
B

C,D and E are clearly out as they are close to largest and also A is close to the lowest

B
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Re: Seven friends went to an art festival and each spent a different sum  [#permalink]

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04 Sep 2018, 11:24
1
Bunuel wrote:
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

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.

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Re: Seven friends went to an art festival and each spent a different sum &nbs [#permalink] 04 Sep 2018, 11:24
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