|
|
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.
16 Dec 2024, 10:43
Kudos
Bookmarks
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
0% (00:00) wrong based on 0 sessions
History
Date
Time
Result
Not Attempted Yet
\(A_{n} = 2^n - 1\) for all integers \(n ≥ 1\)
Quantity A
The units digit of \(A_{26}\)
Quantity B
The units digit of \(A_{34}\)
Quantity A
The units digit of \(A_{26}\)
Quantity B
The units digit of \(A_{34}\)
30 Dec 2024, 20:43
Kudos
Bookmarks
Given that \(A_n=2^n-1\) for all integers \(n \geq 1\)
Quantity A
The unit digit of \(A_{26}\) = Unit's digit of (\(2^{26} - 1\))
Unit's digit of \(2^1\) = 2
Unit's digit of \(2^2\) = 4
Unit's digit of \(2^3\) = 8
Unit's digit of \(2^4\) = 6
Unit's digit of \(2^5\) = 2
So, unit's digit of power of 2 repeats after every \(4^{th}\) number.
=> We need to divided 26 by 4 and check what is the remainder
=> 26 divided by 4 gives 2 remainder
=> \(2^{26}\) will have the same unit's digit as \(2^2\) = 4
=> Unit's digits of \(2^{26}\) = 4
=> Unit's digit of \(2^{26} - 1\) = 4 - 1 = 3
Quantity B
The unit digit of \(A_{34}\) = Unit's digit of (\(2^{34} - 1\))
34 divided by 4 gives 2 remainder
=> \(2^{34}\) will have the same unit's digit as \(2^2\) = 4
=> Unit's digits of \(2^{34}\) = 4
=> Unit's digit of \(2^{34} - 1\) = 4 - 1 = 3
Clearly, Quantity A(3) = Quantity B(3)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to find Unit's digit
Quantity A
The unit digit of \(A_{26}\) = Unit's digit of (\(2^{26} - 1\))
Unit's digit of \(2^1\) = 2
Unit's digit of \(2^2\) = 4
Unit's digit of \(2^3\) = 8
Unit's digit of \(2^4\) = 6
Unit's digit of \(2^5\) = 2
So, unit's digit of power of 2 repeats after every \(4^{th}\) number.
=> We need to divided 26 by 4 and check what is the remainder
=> 26 divided by 4 gives 2 remainder
=> \(2^{26}\) will have the same unit's digit as \(2^2\) = 4
=> Unit's digits of \(2^{26}\) = 4
=> Unit's digit of \(2^{26} - 1\) = 4 - 1 = 3
Quantity B
The unit digit of \(A_{34}\) = Unit's digit of (\(2^{34} - 1\))
34 divided by 4 gives 2 remainder
=> \(2^{34}\) will have the same unit's digit as \(2^2\) = 4
=> Unit's digits of \(2^{34}\) = 4
=> Unit's digit of \(2^{34} - 1\) = 4 - 1 = 3
Clearly, Quantity A(3) = Quantity B(3)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to find Unit's digit
