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by Ashetty » Wed Sep 14, 2011 6:34 am
At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?


A.80
B.90
C.100
D.110
E.120

Ans:120
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by shankar.ashwin » Wed Sep 14, 2011 6:45 am
Let the ratio of juniors to seniors be 3x/4x.
Now 10 juniors and 20 seniors leave the school, so the ratio becomes (3x-10)/(4x-20)
this is given to be 4/5 (the new ratio),

So solve for x,

(3x-10)/(4x-20)=4/5
x=30.

Number of seniors is asked, so 4x = 120
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by GMATGuruNY » Wed Sep 14, 2011 7:41 am
Ashetty wrote:At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?


A.80
B.90
C.100
D.110
E.120

Ans:120
We can plug in the answers, which represent the number of seniors at the beginning of the year.
Since the ratio of juniors to seniors is 3:4, the number of seniors must be a multiple of 4.
Eliminate B and D.

Answer choice C: 100 seniors
Since 3:4 = 75:100, there are 75 juniors.
After 10 juniors leave, remaining juniors = 75-10 = 65.
Since the ratio of juniors to seniors changes to 4:5, the remaining number of juniors must be a multiple of 4.
65 is not a multiple of 4.
Eliminate C.

Answer choice D: 120 seniors
Since 3:4 = 90:120, there are 90 juniors.
After 10 juniors leave, remaining juniors = 90-10 = 80.
After 20 seniors leave, remaining seniors = 120-20 = 100.
80:100 = 4:5. Success!

The correct answer is E.
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by Scott@TargetTestPrep » Fri Dec 15, 2017 11:43 am
Ashetty wrote:At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?


A.80
B.90
C.100
D.110
E.120
We are given that the original ratio of juniors to seniors was 3x : 4x.

Since 10 juniors and 2(10) = 20 seniors transferred, we have a new ratio of 4 : 5. Thus:

(3x - 10)/(4x - 20) = 4/5

5(3x - 10) = 4(4x - 20)

15x - 50 = 16x - 80

30 = x

Thus, there were 4(30) = 120 seniors at the school at the beginning of the year.

Answer: E

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