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Making ratio problems more difficult

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Making ratio problems more difficult

by topspin20 » Thu Aug 01, 2013 5:37 pm
The ratio of men to women taking a certain class is 3:5. How many students are taking the class?


1) If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10.

2) The ratio of men to women is the same as it was last semester, when 6 women took the class.

Answer: A

What are some things the GMAT question writers would do to make a question like this more difficult?
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by Brent@GMATPrepNow » Fri Aug 02, 2013 6:19 am
topspin20 wrote:The ratio of men to women taking a certain class is 3:5. How many students are taking the class?

1) If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10.

2) The ratio of men to women is the same as it was last semester, when 6 women took the class.
Target question: How many students are taking the class?

Given: The ratio of men to women taking a certain class is 3:5
Let M = # of men taking the class
Let W = # of women taking the class
So, M/W = 3/5
Cross multiply to get 5M = 3W
Rearrange to get 5M - 3W = 0

Statement 1: If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10
If 2 women join, then there will be W + 2 women
So, we get: M/(W+2) = 7/10
Cross multiply to get 10M = 7(W + 2)
Expand: 10M = 7W + 14
Rearrange to get 10M - 7W = 14
Since we also know that 5M - 3W = 0, we COULD solve this system for M and W, in which case we COULD determine the number of students taking the class
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The ratio of men to women is the same as it was last semester, when 6 women took the class.
This doesn't help us determine the number of students PRESENTLY taking the class.
This only tells us that 6 women and 10 men took the class LAST year.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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Brent
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by Brent@GMATPrepNow » Fri Aug 02, 2013 6:49 am
topspin20 wrote: What are some things the GMAT question writers would do to make a question like this more difficult?
One option is to throw in an inequality. For example . . .
The ratio of men to women taking a certain class is 3:5. How many students are taking the class?
1) If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10.
2) If 5 more men join the class, and the number of women stays the same, the ratio of men to women will be greater than 11/10
Here, the answer is D.
Can anyone show why?

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by topspin20 » Fri Aug 02, 2013 5:23 pm
Brent,

The answer is now D because:

(m+5)/w>(11/10) - cross multiply to get:

10m+50>11w - plug in m=(3/5)w from the ratio in the question stem to get:

10(3w/5)+50>11w = 6w+50>11w = 10>w = w<10

Since w<10, and men and women can only be counted with integers, w can only be 5, given the ratio of 3m/5w. So there would be 8 students in the class.

Thank you for that Brent-very interesting!

Also I should point out an error I made in the original question: the first clue should read 'If two more men join the class, the ratio will be 7:10. As written, the question is impossible to answer. My bad![/b][/spoiler]
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by Uva@90 » Sat Aug 03, 2013 9:32 pm
Brent@GMATPrepNow wrote:
topspin20 wrote:The ratio of men to women taking a certain class is 3:5. How many students are taking the class?

1) If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10.

2) The ratio of men to women is the same as it was last semester, when 6 women took the class.
Target question: How many students are taking the class?

Given: The ratio of men to women taking a certain class is 3:5
Let M = # of men taking the class
Let W = # of women taking the class
So, M/W = 3/5
Cross multiply to get 5M = 3W
Rearrange to get 5M - 3W = 0

Statement 1: If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10
If 2 women join, then there will be W + 2 women
So, we get: M/(W+2) = 7/10
Cross multiply to get 10M = 7(W + 2)
Expand: 10M = 7W + 14
Rearrange to get 10M - 7W = 14
Since we also know that 5M - 3W = 0, we COULD solve this system for M and W, in which case we COULD determine the number of students taking the class
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The ratio of men to women is the same as it was last semester, when 6 women took the class.
This doesn't help us determine the number of students PRESENTLY taking the class.
This only tells us that 6 women and 10 men took the class LAST year.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent,
I have a doubt in your solution,
In statement 1, if we solve the equations
10M-7W = 14
5M-3W = 0
we get W = -14
Since number of women can't be negative,this statement shouldn't help us am I right ?

correct me if I am wrong.

Thanks & Regards,
Uva
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by Brent@GMATPrepNow » Sun Aug 04, 2013 6:25 am
Uva@90 wrote: Brent,
I have a doubt in your solution,
In statement 1, if we solve the equations
10M-7W = 14
5M-3W = 0
we get W = -14
Since number of women can't be negative,this statement shouldn't help us am I right ?

correct me if I am wrong.

Thanks & Regards,
Uva
Good point, Uva. I never actually bothered to solve the system since the GMAT would never construct a sentence about a negative number of people.

As topspin20 pointed out in the above post, the original wording should have been such that 2 men (not 2 women) joined the class. This would have created a question with positive numbers of people.

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Brent
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by lunarpower » Mon Aug 05, 2013 3:17 am
Brent@GMATPrepNow wrote:
topspin20 wrote:The ratio of men to women taking a certain class is 3:5. How many students are taking the class?

1) If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10.

2) The ratio of men to women is the same as it was last semester, when 6 women took the class.
Target question: How many students are taking the class?

Given: The ratio of men to women taking a certain class is 3:5
Let M = # of men taking the class
Let W = # of women taking the class
So, M/W = 3/5
Cross multiply to get 5M = 3W
Rearrange to get 5M - 3W = 0

Statement 1: If 2 more women join the class, and the number of men stays the same, the ratio of men to women will be 7:10
If 2 women join, then there will be W + 2 women
So, we get: M/(W+2) = 7/10
Cross multiply to get 10M = 7(W + 2)
Expand: 10M = 7W + 14
Rearrange to get 10M - 7W = 14
Since we also know that 5M - 3W = 0, we COULD solve this system for M and W, in which case we COULD determine the number of students taking the class
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
this works, of course, but it's ... just so. much. work.

this is all you have to do:

* the original ratio of m:w is 3:5. so, forget the two-variable approach.
original # of men = 3x
original # of women = 5x

* once you have this... statement 2 is 3x/(5x + 2) = 7/10.
well, if you cross-multiply this, the x's don't cancel out. so, you can solve it.

done!

you should almost always be able to solve multiple-choice ratio problems with 1 variable.
if you can, then, as you see here, using a second variable will squander a significant amount of time.

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and, yes, as "uva90" points out, these numbers are screwy.
this can actually be seen without doing any algebra at all: according to the statements, the original ratio of men to women is 0.6. then, after women are added, it's 0.7?
that's absurd; clearly, adding women will make the m:w ratio go even further down, not up.
Ron has been teaching various standardized tests for 20 years.

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