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
