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 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 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
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.
14 Jul 2023, 07:45
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:
60% (01:34) correct
40%
(01:23)
wrong
based on 308
sessions
History
Date
Time
Result
Not Attempted Yet
If a positive integer t is not divisible by 5, how many possible different remainders can t^4 have when it is divided by 5?
A. one
B. two
C. three
D. four
E. five
A. one
B. two
C. three
D. four
E. five
14 Jul 2023, 08:13
Kudos
Bookmarks
Given:
* t is a positive integer
* t is not divisible by 5 OR t/5 doesn't equal a whole number
Rephrasing of the question:
How many possible different remainders can t^4 have when it is divided by 5?
OR
Find all the possible remainders of t^4/5 and how many of them are they?
Applicable number properties:
* All multiples of 5 have ones place digits of 5 or 0.
* 1-4 & 6-9 are the set of possible ones place digits not divisible by 5.
Ones place digits for integers (not 5) to the 4th power:
- Ones place digit for 1^4 = 1
- Ones place digit for 2^4 = 6
- Ones place digit for 3^4 = 1
- Ones place digit for 4^4 = 6
- Ones place digit for 6^4 = 6
- Ones place digit for 7^4 = 1
- Ones place digit for 8^4 = 6
- Ones place digit for 9^4 = 1
Thus, all possible remainders for t^4/5 will have a ones place digit of 6 or 1 and because all multiples of 5 end in 5 or 0, we can conclude that all remainders of t^4/5 will have a remainder of 1 because all numbers with a ones digit place of 6 or 1 to be divided by 5 will have 1 as the remainder.
Answer is A, just the one single remainder answer.
* t is a positive integer
* t is not divisible by 5 OR t/5 doesn't equal a whole number
Rephrasing of the question:
How many possible different remainders can t^4 have when it is divided by 5?
OR
Find all the possible remainders of t^4/5 and how many of them are they?
Applicable number properties:
* All multiples of 5 have ones place digits of 5 or 0.
* 1-4 & 6-9 are the set of possible ones place digits not divisible by 5.
Ones place digits for integers (not 5) to the 4th power:
- Ones place digit for 1^4 = 1
- Ones place digit for 2^4 = 6
- Ones place digit for 3^4 = 1
- Ones place digit for 4^4 = 6
- Ones place digit for 6^4 = 6
- Ones place digit for 7^4 = 1
- Ones place digit for 8^4 = 6
- Ones place digit for 9^4 = 1
Thus, all possible remainders for t^4/5 will have a ones place digit of 6 or 1 and because all multiples of 5 end in 5 or 0, we can conclude that all remainders of t^4/5 will have a remainder of 1 because all numbers with a ones digit place of 6 or 1 to be divided by 5 will have 1 as the remainder.
Answer is A, just the one single remainder answer.
