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.
Aug 2610:00 AM EDT
-11:59 PM EDT
Save up to $1,000 on select GMAT prep now. This Fall, achieve your most ambitious goals with millions of student success stories behind you.
Aug 2710:00 AM EDT
-11:00 AM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Sep 0609:30 AM EDT
-12:30 PM EST
Top scores are possible when you enroll in a powerful EA course, taught live online + 6 months access to TTP OnDemand video courses included! Perfect class schedule and easy course access for working professionals. Class starts Sept. 6, 9:30am-12:30pm EST
Sep 0907:00 AM PDT
-10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2108:00 PM EDT
-10:00 PM EDT
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Oct. 13, 2026 - Jan. 7, 2027, 8:00pm-10:00pm EST
28 Aug 2024, 03:02
Kudos
Bookmarks
Mbappe withdraws \(\frac{100}{x}\%\) of the amount in his account each time he visits the bank, where \(x\) is an integer greater than 1. If, after 5 visits, he has less than \(\frac{1}{x}^{th}\) of the initial amount left in the bank, what is the range of possible values for \(x\)?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
28 Aug 2024, 03:02
Kudos
Bookmarks
Official Solution:
Mbappe withdraws \(\frac{100}{x}\%\) of the amount in his account each time he visits the bank, where \(x\) is an integer greater than 1. If, after 5 visits, he has less than \(\frac{1}{x}^{th}\) of the initial amount left in the bank, what is the range of possible values for \(x\)?
A. 1
B. 2
C. 3
D. 4
E. 5
Since \(\frac{100}{x}\%\) of the money is withdrawn each time, after each visit, \((1 - \frac{100}{x}*\frac{1}{100})= (1 - \frac{1}{x})\) of the previous amount will remain in the bank. For example, if 10% is withdrawn each time, after each visit, \((1 - 10*\frac{1}{100})= (1 - \frac{1}{10})=\frac{9}{10}\) of the previous amount will remain in the bank.
Assuming the initial amount in the bank is A, then after 5 visits, the amount would be \(A(1 - \frac{1}{x})^5\). We are told that this is less than \(\frac{1}{x}\) of the initial amount, so we have:
\(A(1 - \frac{1}{x})^5 < A*\frac{1}{x}\)
\((1 - \frac{1}{x})^5 < \frac{1}{x}\)
\((\frac{x-1}{x})^5 < \frac{1}{x}\)
\(\frac{(x-1)^5}{x^5} < \frac{1}{x}\)
\((x-1)^5 < x^4\)
As \(x\) increases, the left-hand side of the inequality grows faster than the right-hand side, so the inequality will only hold for smaller values of \(x\). Let's test some values. For \(x = 5\), the inequality does not hold: \(4^5 > 5^4\). However, if \(x\) is 4 or less, it does hold. Since \(x\) is an integer greater than 1, it can be 2, 3, or 4, making the range of possible values for \(x\) equal to \(4 - 2 = 2\).
Answer: B
Mbappe withdraws \(\frac{100}{x}\%\) of the amount in his account each time he visits the bank, where \(x\) is an integer greater than 1. If, after 5 visits, he has less than \(\frac{1}{x}^{th}\) of the initial amount left in the bank, what is the range of possible values for \(x\)?
A. 1
B. 2
C. 3
D. 4
E. 5
Since \(\frac{100}{x}\%\) of the money is withdrawn each time, after each visit, \((1 - \frac{100}{x}*\frac{1}{100})= (1 - \frac{1}{x})\) of the previous amount will remain in the bank. For example, if 10% is withdrawn each time, after each visit, \((1 - 10*\frac{1}{100})= (1 - \frac{1}{10})=\frac{9}{10}\) of the previous amount will remain in the bank.
Assuming the initial amount in the bank is A, then after 5 visits, the amount would be \(A(1 - \frac{1}{x})^5\). We are told that this is less than \(\frac{1}{x}\) of the initial amount, so we have:
\(A(1 - \frac{1}{x})^5 < A*\frac{1}{x}\)
\((1 - \frac{1}{x})^5 < \frac{1}{x}\)
\((\frac{x-1}{x})^5 < \frac{1}{x}\)
\(\frac{(x-1)^5}{x^5} < \frac{1}{x}\)
\((x-1)^5 < x^4\)
As \(x\) increases, the left-hand side of the inequality grows faster than the right-hand side, so the inequality will only hold for smaller values of \(x\). Let's test some values. For \(x = 5\), the inequality does not hold: \(4^5 > 5^4\). However, if \(x\) is 4 or less, it does hold. Since \(x\) is an integer greater than 1, it can be 2, 3, or 4, making the range of possible values for \(x\) equal to \(4 - 2 = 2\).
Answer: B
02 Sep 2024, 05:50
Kudos
Bookmarks
\(\frac{100}{x}\)% = \(\frac{1}{x}\)
M: original amount in the account
=> \(M * (1-\frac{1}{x})^5 < M * \frac{1}{x}\)
=> \(\frac{(x-1)^5}{x^5} < \frac{1}{x}\)
=> \((x-1)^5 < x^4\)
If x = 2 => \(1^5 = 1 < 2^4\) => ok
If x = 3 => \(2^5 = 32 < 3^4 = 81\)
If x = 4 => \(3^5 = 243 < 4^4 = 2^8 = 256\) => ok
\((x-1)^5\) is coming really close so x = 5 won't work
=> Range: 4 - 2 = 2
M: original amount in the account
=> \(M * (1-\frac{1}{x})^5 < M * \frac{1}{x}\)
=> \(\frac{(x-1)^5}{x^5} < \frac{1}{x}\)
=> \((x-1)^5 < x^4\)
If x = 2 => \(1^5 = 1 < 2^4\) => ok
If x = 3 => \(2^5 = 32 < 3^4 = 81\)
If x = 4 => \(3^5 = 243 < 4^4 = 2^8 = 256\) => ok
\((x-1)^5\) is coming really close so x = 5 won't work
=> Range: 4 - 2 = 2
