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Word problem - ratio disorder

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Word problem - ratio disorder

by jnellaz » Mon Nov 03, 2008 6:52 am
Can someone help with this? I thought it was a straight forward problem but I ended up getting snagged on terminology. (Please see my comments below after you read the problem)

At a nearby college, 50% of the men have a GPA above 3.5 while 25% of the women do not have a GPA above 3.5. If the ratio of men to women is 2/5, what percent of the student body is comprised of women with GPAs not above 3.5?
A) 60%
B) 40%
C) 20%
D) 15%
E) 10%

If you notice above, the question says the ratio of men to women is 2/5. To me - this has always translated to a RATIO of 2 : 5, meaning the number of men/total student body would = to 2/7 and women/total student body would = to 5/7. I guess this way of thinking is wrong because here it explicityly means that men comprise of 60% of the total student population, while women are 40%. This is very different from my assumption that men/stutdent body = 2/7 or 28%. Can someone explain my error in thinking?

Thanks in advance!
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by jimmiejaz » Mon Nov 03, 2008 8:37 am
so i guess according to the comments provided by you, the answer given is 10%? Please post the ans too as this would be helpful. Also, would like to suggest that there is nothing wrong in your approach.
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by jnellaz » Mon Nov 03, 2008 10:01 am
Sorry - the answer is D!
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by jimmiejaz » Mon Nov 03, 2008 11:48 am
jnellaz wrote:Sorry - the answer is D!
hi according to the question, the ans comes to 17.8, but as per the soln provided by you, the ratio should be 2:3.
can you please post the official explanation.It will be helpful. as if the ratio of men to women is 2:5, it is a part n part ratio. so ratio of men to total should be 2:2+5 = 2:7
but if the ratio of men to toal population is 2:5, then the ans is correct as D.

Hope it helps.
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by jnellaz » Mon Nov 03, 2008 1:01 pm
This was the official answer. It is interesting to see that you too got 17.8 as the answer. Please read this explanation and let me know where we went wrong!


Set up a 2x2 Matrix, inputting the given information. (Note that a ratio of men to women of 2/5 means that men comprise 40% of the student population while women comprise 60% of the student population.) Also, note that the 50% is out of the number of men, not the total number of students. Likewise, the 25% is out ot the total number of women, not the total number of students. Also, let x = total number of students. Men Women Total
Above 3.5 GPA 50% of 40% = 20% of total
Not Above 3.5 GPA 25% of 60% = 15% of total
40% 60% x

Simplify the information from above. Men Women Total
Above 3.5 GPA 20%x
Not Above 3.5 GPA 15%x
40%x 60%x x

Fill in other information. Men Women Total
Above 3.5 GPA 20%x 45%x 65%x
Not Above 3.5 GPA 20%x 15%x 35%x
40%x 60%x x

We are now ready to answer the original question ("what percent of the student body is comprised of women with GPAs not above 3.5?") The answer will be (the percent of women with GPAs not above 3.5)/(total student body) = 15%x/x = 15%
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by codesnooker » Mon Nov 03, 2008 1:20 pm
To solve such question, always use the matrix. See the attached image.

Other way is, think total students = 100.
Now 2/5 are men.

Therefore, Male Students = 40
and female Students = 60

Now 25% does not score more than 3.5, therefore, 25% of 60 = 15.

Now 15 is 15% of 100. That is your real answer.

Hope this helps.
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by jnellaz » Mon Nov 03, 2008 2:19 pm
Thanks Code Snooker BUT the problem says the ratio of men to women is 2/5. Doesn't this mean that the percentage of men is 2/7 - which is equal to 28.5%????
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by cramya » Tue Nov 04, 2008 2:21 am
Received a PM to respond.


hi according to the question, the ans comes to 17.8, but as per the soln provided by you, the ratio should be 2:3.
can you please post the official explanation.It will be helpful. as if the ratio of men to women is 2:5, it is a part n part ratio. so ratio of men to total should be 2:2+5 = 2:7
but if the ratio of men to toal population is 2:5, then the ans is correct as D.

Hope it helps.

I agree with Jimmie. Either there is a typo in the problem or I must be missing something.

If its 2/3 then 15% makes sense but its 2/5 then 17.8 is what one should get.

Hoping I am not missing anything.
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by cramya » Tue Nov 04, 2008 2:22 am
Let me see if I can PM a few others and see how they respond :-)
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by vishubn » Tue Nov 04, 2008 5:16 am
number of men M=200
number of Women=500

50% of the men is 100 >3.5
25% of women ie 125 W<=3.5

m/w=200/500

so wat makes 125/700 ie 125 uis wat percent of 700 ! which is 17.78%

so approx is either 15%/20% .....

So wat is it ???

Vishu
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by jnellaz » Tue Nov 04, 2008 5:46 am
I guess there is a split decision on the interpretation of this problem - which probably means that it was probably worded poorly.

The issue with this problem comes into play with phrase "THE RATIO OF MEN TO WOMEN IS 2/5". If you interpret that phrase to mean that 40% of the total are men, then you got the question correct. If you interpret that phrase to mean 2/7 - which is equal to 28.5%, then you get thrown off.

I was trying to figure out why my way of thinking was wrong and does not lead me to one of the answer choices.
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by Stacey Koprince » Tue Nov 04, 2008 3:00 pm
Yeah, something's wrong here. If you say a "ratio of men to women is 2/5" then you're saying:

....men...2
women...5

That's a part-to-part relationship and the "whole" is 2+5=7.

I would suggest there was a typo, except someone also posted the explanation and that sentence explaining how ratios work is just... not how ratios actually work. Perhaps this isn't the best source from which to get study material. :)
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by cramya » Tue Nov 04, 2008 3:19 pm
Thanks Stacey!

Jimmie,

Just curious; whats the source because things like these can mislead one's understanding of ratios (or any concept in general)

Regards,
Cramya
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by jimmiejaz » Tue Nov 04, 2008 3:50 pm
cramya wrote:Thanks Stacey!

Jimmie,

Just curious; whats the source because things like these can mislead one's understanding of ratios (or any concept in general)

Regards,
Cramya
First of all,

Thanks Stacey for clearing the doubt!!! It really helped. I was getting confused.

Cramya,

I just browsed through the forum and saw this thread. I have not posted this question. But, when i got too confused, i thought that i shall take help from the experts. :) I tried by two or three methods but every time i got the same answer of 17.8 which is not thr in any of the answer choices. So, i thought let me double chk with all the experts if my reasoning or concepts are flawed..

Rajiv
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by Stacey Koprince » Tue Nov 04, 2008 3:56 pm
jnellaz was the original poster. jnellaz, can you let us know where you found this question? Thanks!
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