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 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.
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
30 Jan 2024, 02:30
Kudos
Bookmarks
C
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:
42% (01:43) correct
58%
(01:45)
wrong
based on 91
sessions
History
Date
Time
Result
Not Attempted Yet
If x is an integer greater than 1, what is the remainder when x^4 is divided by 10?
(1) x is not a multiple of 5.
(2) x is a multiple of 2.
(1) x is not a multiple of 5.
(2) x is a multiple of 2.
Updated on: 30 Jan 2024, 18:07
Originally posted by crimson_king on 30 Jan 2024, 02:48.
Last edited by crimson_king on 30 Jan 2024, 18:07, edited 1 time in total.
Last edited by crimson_king on 30 Jan 2024, 18:07, edited 1 time in total.
Kudos
Bookmarks
The answer for this should be C.
If we look at option A, if the number is not a multiple of 5 then it can be a multiple of 2,3 or 7
If it is a multiple of 2 that is not divisible by 5, the remainder will always be 6 if divided by 10 as all the multiples of 2 not divisible by 5 when raised to the power of 4 will end with the unit's digit being 6 & the remainder will be 6 when divided by 10.
If it's a multiple of 3 or 7, the unit's digit will be 1 & the remainder will hence be 1 when divided by 10
Since we cannot determine the remainder with definite proof, (A) is incorrect & by default (D) is also incorrect.
If we only consider (B), we saw that the multiples of 2 that are not divisible by 5 will give the value of the remainder as 6. But 10 is also a multiple of 2 & the remainder will be 0 in this case. So (B) alone is also not sufficient.
If we combine both (A) & (B), then we get a clear answer as the multiples of 10 will not be considered & we will always have our remainder as 6. The correct option hence is (C)
Posted from my mobile device
If we look at option A, if the number is not a multiple of 5 then it can be a multiple of 2,3 or 7
If it is a multiple of 2 that is not divisible by 5, the remainder will always be 6 if divided by 10 as all the multiples of 2 not divisible by 5 when raised to the power of 4 will end with the unit's digit being 6 & the remainder will be 6 when divided by 10.
If it's a multiple of 3 or 7, the unit's digit will be 1 & the remainder will hence be 1 when divided by 10
Since we cannot determine the remainder with definite proof, (A) is incorrect & by default (D) is also incorrect.
If we only consider (B), we saw that the multiples of 2 that are not divisible by 5 will give the value of the remainder as 6. But 10 is also a multiple of 2 & the remainder will be 0 in this case. So (B) alone is also not sufficient.
If we combine both (A) & (B), then we get a clear answer as the multiples of 10 will not be considered & we will always have our remainder as 6. The correct option hence is (C)
Posted from my mobile device
30 Jan 2024, 12:44
Kudos
Bookmarks
Answer Option C should be Correct
If any number is divided by 10, the remainder is the unit's digit. First Let us see what are the unit's digits for different cases of unit
digits of a number.
1^4=1
2^4=6
3^4=1
4^4=6
5^4=5
6^4=6
7^4=1
8^4=6
9^4=1
For Statement (1) X>1 and x not a multiple of 5
Now we have 2 different cases of unit's digit (1 and 6); so can't reach to a conclusion. Hence, not sufficient.
For statement (2) x>1 and x is an even number
The leftovers, all of them have unit's digit of 6 except 0. So can't reach conclusion. Hence, statement
2 is not Sufficient
If 1 and 2 are clubbed, we get
So only remainder is 6.
Correct option should be C
If any number is divided by 10, the remainder is the unit's digit. First Let us see what are the unit's digits for different cases of unit
digits of a number.
1^4=1
2^4=6
3^4=1
4^4=6
5^4=5
6^4=6
7^4=1
8^4=6
9^4=1
For Statement (1) X>1 and x not a multiple of 5
| Unit's Digit | Unit's digit after ^4 |
| 1 | 1 ❌ |
| 2 | 6 |
| 3 | 1 |
| 4 | 6 |
| 5 | 5 ❌ |
| 6 | 6 |
| 7 | 1 |
| 8 | 6 |
| 9 | 1 |
| 0 | 0 ❌ |
Now we have 2 different cases of unit's digit (1 and 6); so can't reach to a conclusion. Hence, not sufficient.
For statement (2) x>1 and x is an even number
| Unit's Digit | Unit's digit after ^4 |
| 1 | 1 ❌ |
| 2 | 6 |
| 3 | 1 ❌ |
| 4 | 6 |
| 5 | 5 ❌ |
| 6 | 6 |
| 7 | 1 ❌ |
| 8 | 6 |
| 9 | 1 ❌ |
| 0 | 0 |
The leftovers, all of them have unit's digit of 6 except 0. So can't reach conclusion. Hence, statement
2 is not Sufficient
If 1 and 2 are clubbed, we get
| Unit's Digit | Unit's digit after ^4 |
| 1 | 1 ❌ |
| 2 | 6 |
| 3 | 1 ❌ |
| 4 | 6 |
| 5 | 5 ❌ |
| 6 | 6 |
| 7 | 1 ❌ |
| 8 | 6 |
| 9 | 1 ❌ |
| 0 | 0 ❌ |
So only remainder is 6.
Correct option should be C
