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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 theCodeToGMAT
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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]
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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We're told that the new average age is 1/8 years less than the original average age.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
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 50year 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

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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)
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)
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.
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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Those are nice ideas  anything that involves less computational time is a great strategy on test day.

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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
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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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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