Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
23 Sep 2021, 08:07
Kudos
Bookmarks
The ratio of the number of marbles in boxes X and Y was 5 to 8. After some number of marbles were transferred from box Y to box X, the ratio of the number of marbles in boxes X and Y became 7 to 6. What is the total number of marbles in the two boxes?
(1) Initially the number of marbles in box Y was between 45 and 100.
(2) After the transfer, the number of marbles in box X became between 45 and 100.
(1) Initially the number of marbles in box Y was between 45 and 100.
(2) After the transfer, the number of marbles in box X became between 45 and 100.
23 Sep 2021, 08:07
Kudos
Bookmarks
Official Solution:
The ratio of the number of marbles in boxes X and Y was 5 to 8. After some number of marbles were transferred from box Y to box X, the ratio of the number of marbles in boxes X and Y became 7 to 6. What is the total number of marbles in the two boxes?
Initial ratio: \(\frac{X}{Y}=\frac{5a}{8a}\), for some positive integer \(a\).
Final ratio: \(\frac{X'}{Y'}=\frac{5a+k}{8a-k}=\frac{7b}{6b}\), for some positive integers \(b\) and \(k\).
The total number of marbles \(= 5a+8a=7b+6b\), which gives \(a=b\).
Thus:
Initial ratio: \(\frac{X}{Y}=\frac{5a}{8a}\)
Final ratio: \(\frac{X'}{Y'}=\frac{7a}{6a}\) (the number of marbles transferred from Y to X is \(2a\))
The question asks to find the number of total marbles, which is \(5a+8a=13a\)
(1) Initially the number of marbles in box Y was between 45 and 100.
\(45 < 8a < 100\)
\(a\) could be 6, 7, 8, 9, 10, 11, or 12. Not sufficient.
(2) After the transfer, the number of marbles in box X became between 45 and 100.
\(45 < 7a < 100\)
\(a\) could be 7, 8, 9, 10, 11, 12, 13, or 14. Not sufficient.
(1)+(2) \(a\) still could take more than one value: 7, 8, 9, 10, 11, or 12. Not sufficient.
Answer: E
The ratio of the number of marbles in boxes X and Y was 5 to 8. After some number of marbles were transferred from box Y to box X, the ratio of the number of marbles in boxes X and Y became 7 to 6. What is the total number of marbles in the two boxes?
Initial ratio: \(\frac{X}{Y}=\frac{5a}{8a}\), for some positive integer \(a\).
Final ratio: \(\frac{X'}{Y'}=\frac{5a+k}{8a-k}=\frac{7b}{6b}\), for some positive integers \(b\) and \(k\).
The total number of marbles \(= 5a+8a=7b+6b\), which gives \(a=b\).
Thus:
Initial ratio: \(\frac{X}{Y}=\frac{5a}{8a}\)
Final ratio: \(\frac{X'}{Y'}=\frac{7a}{6a}\) (the number of marbles transferred from Y to X is \(2a\))
The question asks to find the number of total marbles, which is \(5a+8a=13a\)
(1) Initially the number of marbles in box Y was between 45 and 100.
\(45 < 8a < 100\)
\(a\) could be 6, 7, 8, 9, 10, 11, or 12. Not sufficient.
(2) After the transfer, the number of marbles in box X became between 45 and 100.
\(45 < 7a < 100\)
\(a\) could be 7, 8, 9, 10, 11, 12, 13, or 14. Not sufficient.
(1)+(2) \(a\) still could take more than one value: 7, 8, 9, 10, 11, or 12. Not sufficient.
Answer: E
22 Oct 2025, 21:58
Kudos
Bookmarks
I like the solution - it’s helpful.
