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amina.shaikh309
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Mitch provides a nice solution here: https://qa.www.beatthegmat.com/og-questi ... 84191.html
Cheers,
Brent
OG16- DS 88
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Brent@GMATPrepNow
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Matt@VeritasPrep
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Here's an alternative that gets us there directly with algebra: it's quicker and requires a lot less guessing and checking.
Suppose we have w women and m men. Since (Sum of Scores) = Average * (# of Scores), we know that
(Sum of all scores) = 80*(m + w)
Let's also say that the average female score is a and the average male score is b. Then we have
w*a + m*b = 80*(m + w)
or
w*a + m*b = 80m + 80w
or
w*(a - 80) = m*(80 - b)
We want to know if a > 85.
S1:
b < 75
That means that m * (80 - b) > m * (80 - 75), or m * (80 - b) > 5m.
Since w*(a - 80) = m * (80 - b), we must also have
w*(a - 80) > 5m
Since we're looking to find a, let's rearrange everything in terms of a.
w*a - 80w > 5m
w*a > (5m + 80w)
a > (5m + 80w)/w
a > 5*(m/w) + 80
So close!
S2::
(m/w) > 1
By itself this is useless.
S1 + S2
We have
a > 5*(m/w) + 80
and
(m/w) > 1
so
a > 5*1 + 80
or
a > 85
Touchdown!
Suppose we have w women and m men. Since (Sum of Scores) = Average * (# of Scores), we know that
(Sum of all scores) = 80*(m + w)
Let's also say that the average female score is a and the average male score is b. Then we have
w*a + m*b = 80*(m + w)
or
w*a + m*b = 80m + 80w
or
w*(a - 80) = m*(80 - b)
We want to know if a > 85.
S1:
b < 75
That means that m * (80 - b) > m * (80 - 75), or m * (80 - b) > 5m.
Since w*(a - 80) = m * (80 - b), we must also have
w*(a - 80) > 5m
Since we're looking to find a, let's rearrange everything in terms of a.
w*a - 80w > 5m
w*a > (5m + 80w)
a > (5m + 80w)/w
a > 5*(m/w) + 80
So close!
S2::
(m/w) > 1
By itself this is useless.
S1 + S2
We have
a > 5*(m/w) + 80
and
(m/w) > 1
so
a > 5*1 + 80
or
a > 85
Touchdown!
