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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
02 Oct 2010, 04:44
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
59% (01:35) correct
41%
(01:45)
wrong
based on 1635
sessions
History
Date
Time
Result
Not Attempted Yet
If \(243^x*463^y =n\) , where x and y are positive integers, what is the units digit of n?
(1) x + y = 7
(2) x = 4
(1) x + y = 7
(2) x = 4
02 Oct 2010, 04:56
Kudos
Bookmarks
If \(243^x*463^y =n\), where x and y are positive integers, what is the units digit of n?
The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).
(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power is \(4\), units digit of \(3^7\) would be the same as of units digit of \(3^3\) which is \(7\))
(2) \(x=4\). No info about \(y\). Not sufficient.
Answer: A.
Hope it helps.
The units digit of \(243^x\) is the same as the units digit of \(3^x\) and similarly the units digit of \(463^y\) is the same as the units digit of \(3^y\), so the units digit of \(243^x*463^y\) equals to the units digit of \(3^x*3^y=3^{x+y}\). So, knowing the value of \(x+y\) is sufficient to determine the units digit of \(n\).
(1) \(x + y = 7\). Sufficient. (As cyclicity of units digit of \(3\) in integer power is \(4\), units digit of \(3^7\) would be the same as of units digit of \(3^3\) which is \(7\))
(2) \(x=4\). No info about \(y\). Not sufficient.
Answer: A.
Hope it helps.
General Discussion
03 Mar 2014, 05:18
Kudos
Bookmarks
I have a doubt. Cyclicity of unit digit of 3 is 4. Hence we know that every fourth power of 3 (3^4, 3^8, 3^12) will have the same unit digit, 1. Hence when option B says x = 4, knowing that x and y are positive integers, we know that xy will be a multiple of 4. Unit digit of 3^4k is always 1 isn't it? Shouldn't this be sufficient information?
Shouldn't the answer be D?
Shouldn't the answer be D?
