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.
May 2008:00 AM PDT
-08:30 AM PDT
What’s in it for you- Live Profile Evaluation Chat Session with Jenifer Turtschanow, CEO, ARINGO. Come with your details prepared and ARINGO will share insights! Pre-MBA Role/Industry, YOE, Exam Score, C/GPA, ECs Post-MBA Role/ Industry & School List.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
07 May 2020, 00:51
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (02:06) correct
23%
(02:13)
wrong
based on 56
sessions
History
Date
Time
Result
Not Attempted Yet
If \(u=2^{5}-2\), \(v=3^{5}-3\) and \(w=4^{5}-4\), what is the greatest common divisor of u,v and w?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
07 May 2020, 03:07
Kudos
Bookmarks
Ravixxx
\(u=2^{5}-2 = 32-2 = 30\)
i.e. answer can NOT be options C, D and E which we can eliminate now
Also, Option A can be eliminated because 20 is not the factor of u so it can NOT be HCF of u, v and w
Hence, Answer: Option B
However, with confusing options we need to do the following calculations
\(v=3^{5}-3= 3*(3^4-1) = 3*(3^2+1)*(3^2-1) = 3*10*8 \)
\(w=4^{5}-4= 4*(4^4-1) = 4*(4^2+1)*(4^2-1) = 4*17*15 \)
so GCD of u, v and w = 30
07 May 2020, 05:23
Kudos
Bookmarks
Ravixxx
we can individually simplify each term also.
u = \(2^5 - 2 = 2(2^4 - 1) = 2(2^2 + 1)(2^2 - 1) = 2*5*3 = 2^1 * 3^1 * 5^1\)
v = \(3^5 - 3 = 3(3^4 - 1) = 3(3^2 + 1)(3^2 - 1) = 3*10*8 = 2^4 * 3^1 * 5^1\)
w = \(4^5 - 4 = 4(4^4 - 1) = 4(4^2 + 1)(4^2 - 1) = 4*17*15 = 2^2 * 3^1 * 5^1 * 17^1\)
therefore, the GCD(u, v, w) = \(2^1 * 3^1 * 5^1 = 30\) (option B)
