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# The average weight of 5 students in a class was reported to be 60kg.

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Re: The average weight of 5 students in a class was reported to be 60kg. [#permalink]
=>

Assume $$a, b, c, d,$$ and $$e$$ are the weights of the $$5$$ students.

Since their average is reported as $$60kg$$, we have $$\frac{(a + b + c + d + e) }{ 5} = 60$$ or $$a + b + c + d + e = 300.$$

If $$a$$ is the incorrectly recorded weight, then $$\frac{(80 + b + c + d + e) }{ 5} = 70$$ or $$80 + b + c + d + e = 350.$$ We have $$b + c + d + e = 270.$$

Then, $$a = (a + b + c + d + e) – (b + c + d + e) = 300 – 270 = 30.$$

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Re: The average weight of 5 students in a class was reported to be 60kg. [#permalink]
MathRevolution 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.