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.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
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
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
25 Jun 2017, 04:02
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:
56% (02:32) correct
44%
(02:30)
wrong
based on 189
sessions
History
Date
Time
Result
Not Attempted Yet
What is the remainder when positive integer 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.
25 Jun 2017, 06:47
Kudos
Bookmarks
(1) \(p^{11} + 11^p\), when divided by 10, leaves remainder 4.
Whatever the value of p, \(11^p\) will always have an units digit of 1.
Also, \(p^{11}\) will have a units digit of 3 only when p=7
Hence p=7 will have a remainder of 7 when divided by 10(Sufficient)
(2)\(p^3\), when divided by 10, leaves remainder 3.
The only number which has a remainder of 3 in its cube is 7.
Hence sufficient(Option D)
Please find below the cyclicity of all the numbers :
Number---^1---^2---^3---^4------Cyclicity
2----------- 2-----4------8-----6----------4
3----------- 3-----9------7-----1----------4
4----------- 4-----6------4-----6----------2
5----------- 5-----5------5-----5----------1
6----------- 6-----6------6-----6----------1
7----------- 7-----9------3-----1----------4
8----------- 8-----4------2-----6----------4
9----------- 9-----1------9-----1----------2
Whatever the value of p, \(11^p\) will always have an units digit of 1.
Also, \(p^{11}\) will have a units digit of 3 only when p=7
Hence p=7 will have a remainder of 7 when divided by 10(Sufficient)
(2)\(p^3\), when divided by 10, leaves remainder 3.
The only number which has a remainder of 3 in its cube is 7.
Hence sufficient(Option D)
Please find below the cyclicity of all the numbers :
Number---^1---^2---^3---^4------Cyclicity
2----------- 2-----4------8-----6----------4
3----------- 3-----9------7-----1----------4
4----------- 4-----6------4-----6----------2
5----------- 5-----5------5-----5----------1
6----------- 6-----6------6-----6----------1
7----------- 7-----9------3-----1----------4
8----------- 8-----4------2-----6----------4
9----------- 9-----1------9-----1----------2
25 Jun 2017, 06:48
Kudos
Bookmarks
Solution:
Statement 1: The only value of p that satisfies this condition is p=7. Therefore as we are getting a unique value this is sufficient.
Statement 2: The only value of p that satisfies this condition is p^3=343, p=7. Sufficient.
Therefore the answer is Option D.
Statement 1: The only value of p that satisfies this condition is p=7. Therefore as we are getting a unique value this is sufficient.
Statement 2: The only value of p that satisfies this condition is p^3=343, p=7. Sufficient.
Therefore the answer is Option D.
