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The average weight of 5 students in a class was reported to

by Max@Math Revolution » Mon Dec 09, 2019 11:44 pm
[GMAT math practice question]

The average weight of 5 students in a class was reported to be 60kg. However, the average seems to be too low. So after re-examination, it was found that one student was actually 80kg and was recorded incorrectly. After this correction, the actual average was 70kg. What was the weight which was recorded incorrectly?

A. 20kg
B. 25kg
C. 30kg
D. 50kg
E. 80kg
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by Max@Math Revolution » Thu Dec 12, 2019 1:31 am
=>

Assume a, b, c, d, and e are the weights of the 5 students.
Since their average is reported as 60kg, we have (a + b + c + d + e) / 5 = 60 or a + b + c + d + e = 300.
If a is the incorrectly recorded weight, then (80 + b + c + d + e) / 5 = 70 or 80 + b + c + d + e = 350. We have b + c + d + e = 270.
Then, a = (a + b + c + d + e) - (b + c + d + e) = 300 - 270 = 30.

Therefore, C is the answer.
Answer: C
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by Scott@TargetTestPrep » Sun Dec 15, 2019 6:33 pm
Max@Math Revolution wrote:[GMAT math practice question]

The average weight of 5 students in a class was reported to be 60kg. However, the average seems to be too low. So after re-examination, it was found that one student was actually 80kg and was recorded incorrectly. After this correction, the actual average was 70kg. What was the weight which was recorded incorrectly?

A. 20kg
B. 25kg
C. 30kg
D. 50kg
E. 80kg
Letting n = the incorrectly recorded weight, we can create the equation:

(60 x 5 - n + 80)/5 = 70

380 - n = 350

n = 30

Alternate Solution:

Using the corrected average, we find that the correct sum of the weights of the five students is 70 x 5 = 350 kg. Since the student whose weight was misreported weighs 80kg, the sum of the weights of the remaining four students is 350 - 80 = 270 kg.

Using the incorrect average, we find that the incorrect sum of the weights of the five students is 60 x 5 = 300kg. Since the sum of the weights of the four students, besides the one whose weight was misreported, is 270kg, we find the weight that was reported incorrectly is 300 - 270 = 30kg.

Answer: C

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