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Average Problem

by coolhabhi » Sat Oct 19, 2013 3:02 am
The average age of 40 women decreases by 1/8th of a year when one of them whose age is 50 years is replaced by a new woman. Find the age of the new woman.
a)36 years
b)42 years
c)45 years
d)43 years

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Got the answer but need a simple and quick solution.
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by theCodeToGMAT » Sat Oct 19, 2013 3:35 am
Let total Weight = x

x/40 - 1/8 = (x - 50 + A)/40

x/40 = (x - 50 + A)/40 + 1/8

x/40 = (x - 50 + A + 5)/40

LHS will be equal to RHS when A = 45

So, [spoiler]{C}[/spoiler]
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by Brent@GMATPrepNow » Sat Oct 19, 2013 6:59 am
coolhabhi wrote:The average age of 40 women decreases by 1/8th of a year when one of them whose age is 50 years is replaced by a new woman. Find the age of the new woman.
a)36 years
b)42 years
c)45 years
d)43 years
We're told that the new average age is 1/8 years less than the original average age.
Let's start with a "word equation"
(original average age) - (new average age) = 1/8
So, (original sum of 40 women)/40 - (new sum of 40 women)/40 = 1/8
Multiply both side by 40 to get: (original sum of 40 women) - (new sum of 40 women) = 5

IMPORTANT: Notice that the two sums both have the same 39 ages. All that changes is that we replace the 50-year old, with a woman who is x years old.

In other words, (sum of 39 ages + 50) - (sum of 39 ages + x) = 5
Simplify to get: 50 - x = 5
x = [spoiler]45 = C[/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Gurpreet singh » Sun May 22, 2016 10:37 pm
avg=sum/total no of units
question stem says age has decreased by 1/8th of a year when 50 year women is replaced by another women.

The total no of years reduced is 1/8*40=5 years.

Only one women is replaced whose age was 50 by some one whose age is less by 5 years hence age of replaced women is 45(c)
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by bubai800 » Mon May 23, 2016 1:02 am
The average is reduced by 1/8 th of an year. That means total age of 40 women is reduced by 40 * 1/8 = 5 years.

because of the new woman replacing 50 year old woman the age is reduced by 5 years. Which can happen only if the new woman is 5 years younger.
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by Matt@VeritasPrep » Fri May 27, 2016 2:34 pm
Those are nice ideas - anything that involves less computational time is a great strategy on test day.
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by danielle07 » Sun Sep 03, 2017 2:50 am
Simple solution

The average is reduced by 1/8 a year. That means total age of 40 women is reduced by 40 * 1/8 = 5 years.
50 - 5 = 45

The answer is = C 45
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Re: Average Problem

by Scott@TargetTestPrep » Thu Feb 13, 2020 6:00 am
coolhabhi wrote: ↑
Sat Oct 19, 2013 3:02 am
 The average age of 40 women decreases by 1/8th of a year when one of them whose age is 50 years is replaced by a new woman. Find the age of the new woman.
a)36 years
b)42 years
c)45 years
d)43 years

OAC

Got the answer but need a simple and quick solution.
We can let a = the average age of the original 40 women and x = the age of the new woman. We can create the equation:

(40a - 50 + x) / 40 = a - 1/8

40a - 50 + x = 40(a - 1/8)

40a - 50 + x = 40a - 5

x = 45

Answer: C

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