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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
