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

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

Therefore, C is the answer.
Answer: C
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Re: The average weight of 5 students in a class was reported to be 60kg. [#permalink]
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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.

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