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Find an average of ages of eight students.

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Intern
Joined: 20 Jan 2019
Posts: 6
Find an average of ages of eight students.  [#permalink]

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29 Mar 2019, 10:32
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Difficulty:

65% (hard)

Question Stats:

50% (01:28) correct 50% (01:19) wrong based on 18 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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Joined: 27 Oct 2018
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Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: Find an average of ages of eight students.  [#permalink]

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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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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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