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Find an average of ages of eight students.

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Find an average of ages of eight students.  [#permalink]

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New post 29 Mar 2019, 10:32
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E

Difficulty:

  65% (hard)

Question Stats:

47% (01:19) correct 53% (01:25) wrong based on 15 sessions

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Find an average of ages of eight students.

a) If you remove the youngest student, the average will increase by thirty-one years.

b) If you remove the oldest student, the average will decrease by twenty-five years.
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Re: Find an average of ages of eight students.  [#permalink]

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New post 29 Mar 2019, 13:08
Question: calculate average (\(Av\)) of sum of ages (\(S\)) of 8 students.

from statement 1: let youngest age be "\(a\)"
\(\frac{S - a}{8-1}\) = \(\frac{S}{8}\) + 31
\(8S-8a = 7S + (31*7*8)\)
\(S - 8a = (31*7*8)\)
\(\frac{S}{8} = Av = a + (31*7)\) --> we have two unknowns, so insufficient

from statement 2: let eldest age be "\(b\)"
\(\frac{S - b}{8-1}\) = \(\frac{S}{8}\) - 25
\(8S-8b = 7S - (25*7*8)\)
\(S - 8b = -(25*7*8)\)
\(\frac{S}{8} = Av = b - (25*7)\) --> we have two unknowns, so insufficient

by combining,
only an equation relating the difference between "\(a\)" and "\(b\)" can be formed: \(b - (25*7) = a + (31*7)\) , and \(b-a = (56*7)\)
while \(Av\) is still unknown

E
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Re: Find an average of ages of eight students.  [#permalink]

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New post 29 Mar 2019, 13:33
Let the avg of 8 student is x, and the age of the youngest is a & the age of the oldest one is b.

i. 7(31+x)+a=8x ... 2 variable 1 eqn.... x can not be determined. ------NS
ii. 7(x-25)+b=8x ... 2 variable 1 eqn.... x can not be determined. ------NS

Hence Ans is E.
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Re: Find an average of ages of eight students.   [#permalink] 29 Mar 2019, 13:33
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