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 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
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.
28 May 2024, 06:30
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:24) correct
29%
(01:55)
wrong
based on 112
sessions
History
Date
Time
Result
Not Attempted Yet
When (23^7)(12^8)(516^22) is divided by 10, what is the remainder?
A. 0
B. 2
C. 4
D. 6
E. 8
A. 0
B. 2
C. 4
D. 6
E. 8
28 May 2024, 06:52
Kudos
Bookmarks
Bunuel
When (23^7)(12^8)(516^22) is divided by 10
(23^7)/10 = 3^7 /10 checking divisibility of 10 for powers of 3, 3/10 = rem 3, 9/10 = rem 9, 27/10 = rem 7 and 81/10 = rem 1
after this you will see that this number will get repeated again so 3^5 (i.e 243)/10 = rem 3, 3^6/10 = 729/10 = rem 9.
Hence for 3^7/10 = rem 7
similarly for 12^8 / 10 if we check divisibility of 10 for powers of 2 we will get remainder as 6.
and for 516^22 / 10 if we check for power of 6 we will get remainder as 6.
now multiplying all these remainders we will get number 7*6*6 = 252 and dividing that number by 10 we will get 2 as answer
Hence B.
29 May 2024, 06:12
Kudos
Bookmarks
Bunuel
Remainder on divison by 10 is nothing but the units digit of the term.
\((23^7)(12^8)(516^{22}) \)
Using cyclicity in the units digit, which is that as we increase power, the units digit will repeat and will follow pattern after every four powers for sure. It could happen after every second power too.
\(23^7 =23^{4+3}\) will give the same units digit as \(3^3\) or 7
\(12^8=12^{2*4}\) will give the same units digit as \(2^4\) or 6
6 to any power will always give 6.
Thus, \((23^7)(12^8)(516^{22}) \) can be written as \(7*6*6 \ \ or \ \ 2\) for the purpose of units digit.
Answer: 2
