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KarishmaB
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Tackling Ratios 14 Oct 2012, 21:05
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Responding to a pm:

When you come across a ratio e.g. ratio of men to women is 2:3, say to yourself, ok, so there could be 2 men and 3 women or 4 men and 6 women etc. Alternatively, if you see yourself using algebra to solve the question, you say that there are 2x men and 3x women. Thereafter, it's just a matter of making equations and solving. Try to stick to using a single variable. Let's discuss what we will do in the questions given by you:

Question 1: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?

Generally, in such questions, one can quickly arrive at the desired numbers. Difference given between the number is small (4 more men and 6 more women) I rarely use algebra here.

Snyder men:women = 4:5
Leigh men:women = 5:6

Focus on men. We want to have 4 more men in Snyder than in Leigh. One quick pair I can see is 24 (6th multiple of 4) and 20 (4th multiple of 5).
Snyder men, women = 24, 30
Leigh men, women = 20, 24
Here the difference between the women is 6 and when you add them, you get 44, 54 which is a ratio of 22:27. So there are 30 women in the Snyder choir.

or if this is not intuitive, use algebra.

Snyder men, women = 4x, 5x
Leigh men, women = 4x-4, 5x - 6 (instead of saying 5y and 6y, try to use x only)

Given, (4x-4)/(5x - 6) = 5/6
Solving for x, you get x = 6

No of Snyder women = 5*6 = 30


Question 2: The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B?

This is a weighted average problem.

A Junior:Senior = 4:5
B Junior:Senior = 3:17
Together Junior:Senior = 5:7

Let's focus on juniors only.
Juniors in A = 4/9 = 80/180
Juniors in B = 3/20 = 27/180
Junior in the combined class = 5/12 = 75/180

Students in A/Students in B = (27 - 75)/(75 - 80) = 48/5

Check these posts for detailed discussion on weighted average and mixtures:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -averages/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -mixtures/

For discussion on ratios, check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... of-ratios/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... os-in-tsd/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -problems/



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Tackling Ratios 16 Oct 2012, 14:19
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VeritasPrepKarishma
Responding to a pm:

When you come across a ratio e.g. ratio of men to women is 2:3, say to yourself, ok, so there could be 2 men and 3 women or 4 men and 6 women etc. Alternatively, if you see yourself using algebra to solve the question, you say that there are 2x men and 3x women. Thereafter, it's just a matter of making equations and solving. Try to stick to using a single variable. Let's discuss what we will do in the questions given by you:

Question 1: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?

Generally, in such questions, one can quickly arrive at the desired numbers. Difference given between the number is small (4 more men and 6 more women) I rarely use algebra here.

Snyder men:women = 4:5
Leigh men:women = 5:6

Focus on men. We want to have 4 more men in Snyder than in Leigh. One quick pair I can see is 24 (6th multiple of 4) and 20 (4th multiple of 5).
Snyder men, women = 24, 30
Leigh men, women = 20, 24
Here the difference between the women is 6 and when you add them, you get 44, 54 which is a ratio of 22:27. So there are 30 women in the Snyder choir.

or if this is not intuitive, use algebra.

Snyder men, women = 4x, 5x
Leigh men, women = 4x-4, 5x - 6 (instead of saying 5y and 6y, try to use x only)

Given, (4x-4)/(5x - 6) = 5/6
Solving for x, you get x = 6

No of Snyder women = 5*6 = 30


Question 2: The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B?

This is a weighted average problem.

A Junior:Senior = 4:5
B Junior:Senior = 3:17
Together Junior:Senior = 5:7

Let's focus on juniors only.
Juniors in A = 4/9 = 80/180
Juniors in B = 3/20 = 37/180
Junior in the combined class = 5/12 = 75/180

Students in A/Students in B = (37 - 75)/(75 - 80) = 38/5

/
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Thanks for the post....This makes sense now! I guess the approach you describe for the first questions looks more organic and less cumbersome. I think I may have jumped to algebra straight away and made a careless mistake somewhere along the line; Must get familiar with this approach rather than sticking to algebra every time.

Thanks for covering this.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!