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 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
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.
30 Jul 2017, 22:43
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:20) correct
47%
(02:14)
wrong
based on 154
sessions
History
Date
Time
Result
Not Attempted Yet
What is the remainder when p is divided by 10?
(1) p^11 + 11^p, when divided by 10, leaves remainder 4.
(2) p^3, when divided by 10, leaves remainder 3.
(1) p^11 + 11^p, when divided by 10, leaves remainder 4.
(2) p^3, when divided by 10, leaves remainder 3.
31 Jul 2017, 10:40
Kudos
Bookmarks
Bunuel
stat2: last digit of p^3 is 3
only number ending with 7 when cubed will give u last digit as 3.... hence p divided by 10 will give 7 as remainder..
suff
stat1: no matter what number 11 is raised to,,,it will always be 1 and 7^11 gives 3 as last digit..
hence the sum has 4 as the last digit...
suff
ans D
15 Nov 2019, 11:24
Kudos
Bookmarks
A number is divisible by 10 if its units digit is ZERO. So, we focus on finding the unit digit of the number in order to find the remainder.
The unit digit of 'p' will represent the remainder when 'p' is divided by 10.
In statement 1, 11^p + p^11 gives a remainder of 4, when divided by 10. This means units digit of the expression should be 4.
But 11^p always ends with 1, so units digit of p^11 should be 3. There are only 2 unit digit cycles which have a 3 in them - the cycles of numbers ending with 3 and 7. For both these cycles, the frequency of the cycle is 4. Since the power of p is 11 and it's giving unit digit 3, p should definitely be a number ending with 7 since 7^(4x+3) always ends with 3.
Unit digit of p is 7 is sufficient to tell the remainder when p is divided by 10.
In statement 2, p^3 gives a remainder of 3 when divided by 10. This means p^3 ends with 3.
Units digit of perfect cubes always have a one-to-one relationship with their cube roots. So, we can surely say that, if p^3 ends with 3, then p ends with 7.
This is also sufficient to answer the question.
Correct answer is D, since each statement alone is sufficient to answer the question.
Cheers
The unit digit of 'p' will represent the remainder when 'p' is divided by 10.
In statement 1, 11^p + p^11 gives a remainder of 4, when divided by 10. This means units digit of the expression should be 4.
But 11^p always ends with 1, so units digit of p^11 should be 3. There are only 2 unit digit cycles which have a 3 in them - the cycles of numbers ending with 3 and 7. For both these cycles, the frequency of the cycle is 4. Since the power of p is 11 and it's giving unit digit 3, p should definitely be a number ending with 7 since 7^(4x+3) always ends with 3.
Unit digit of p is 7 is sufficient to tell the remainder when p is divided by 10.
In statement 2, p^3 gives a remainder of 3 when divided by 10. This means p^3 ends with 3.
Units digit of perfect cubes always have a one-to-one relationship with their cube roots. So, we can surely say that, if p^3 ends with 3, then p ends with 7.
This is also sufficient to answer the question.
Correct answer is D, since each statement alone is sufficient to answer the question.
Cheers
