Problem Solving

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?

A) 29/12
B) 59/10
C) 65/8
D) 48/5
E) 29/3

I had a difficult time with this question on a Kaplan CAT. The explanation given was not great.

jjf wrote: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?

A) 29/12
B) 59/10
C) 65/8
D) 48/5
E) 29/3

I had a difficult time with this question on a Kaplan CAT. The explanation given was not great.

This is a weighted average question.

(4/9)A = juniors in A
(3/20)B = juniors in B
(5/12)(A+B) = juniors in A+B combined

Since (juniors in A) + (juniors in B) = (juniors in A+B), we can set up the following equation:

(4/9)A + (3/20)B = (5/12)(A+B)
(80/180)A + (27/180)B = (75/180)(A+B)
80A + 27B = 75A + 75B
5A = 48B
A/B = 48/5

The correct answer is D.

GMATGuruNY wrote:

jjf wrote: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?

A) 29/12
B) 59/10
C) 65/8
D) 48/5
E) 29/3

I had a difficult time with this question on a Kaplan CAT. The explanation given was not great.

This is a weighted average question.

(4/9)A = juniors in A
(3/20)B = juniors in B
(5/12)(A+B) = juniors in A+B combined

Since (juniors in A) + (juniors in B) = (juniors in A+B), we can set up the following equation:

(4/9)A + (3/20)B = (5/12)(A+B)
(80/180)A + (27/180)B = (75/180)(A+B)
80A + 27B = 75A + 75B
5A = 48B
A/B = 48/5

The correct answer is D.

It's Great to see the solution, Can we also find the minimum value for the Number of students in Class A and Class B, I know problem is solved but is it possible to find the minimum integral value for A and B, considering all the situations,

Solution using Allegation Approach

Junior in A..............Juniors in B

4/9.............M=5/12...........3/20

Using Allegation Approach:
Ratio of a:b = B-M/M-A

Hence a:b = (3/20 -5/12) / (5/12 -4/9)

= 48:5 Choice D