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05 Apr 2022, 05:30
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Difficulty:
45%
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66% (01:37) correct
34%
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wrong
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What is the remainder when positive integer n is divided by 6?
(1) When n is divided by 4, the remainder is 3.
(2) When n is divided by 12, the remainder is 3.
(1) When n is divided by 4, the remainder is 3.
(2) When n is divided by 12, the remainder is 3.
09 Apr 2022, 12:35
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Step 1: Analyse Question Stem
n is a positive integer.
We need to find the remainder when n is divided by 6.
Let us say the remainder is R. Then, as per the basic property of remainders, 0 ≤ R < 6; this means that the remainder can be any integer from 0 to 5.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1:When n is divided by 4, the remainder is 3.
Thus, n can be expressed as n = 4x + 3, where x is any non-negative integer.
If x = 0, n = 3. The remainder when n is divided by 6, is 3.
If x = 1, n = 7. The remainder when n is divided by 6, is 1.
Since we do not have a unique value for the remainder, statement 1 alone is insufficient.
Answer options A and D can be eliminated.
Statement 2: When n is divided by 12, the remainder is 3.
Similar to the process followed in evaluating Statement 1, we can say that n can be expressed as, n = 12y + 3, where y is any non-negative integer.
Since 12 is completely divisible by 6, 12y will also be completely divisible by 6.
Therefore, if 12y + 3 is divided by 6, as per remainder rules, the first part will yield a remainder of ZERO, while the second part will yield a remainder of 3; the final remainder will therefore be 3.
Note that the value of y does not affect the remainder in any way, so we do not have to plug in values like we did in the analysis of Statement 1.
Statement 2 alone is sufficient to say that the remainder is 3, when n is divided by 6.
Answer options C and E can be eliminated.
The correct answer option is B.
n is a positive integer.
We need to find the remainder when n is divided by 6.
Let us say the remainder is R. Then, as per the basic property of remainders, 0 ≤ R < 6; this means that the remainder can be any integer from 0 to 5.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1:When n is divided by 4, the remainder is 3.
Thus, n can be expressed as n = 4x + 3, where x is any non-negative integer.
If x = 0, n = 3. The remainder when n is divided by 6, is 3.
If x = 1, n = 7. The remainder when n is divided by 6, is 1.
Since we do not have a unique value for the remainder, statement 1 alone is insufficient.
Answer options A and D can be eliminated.
Statement 2: When n is divided by 12, the remainder is 3.
Similar to the process followed in evaluating Statement 1, we can say that n can be expressed as, n = 12y + 3, where y is any non-negative integer.
Since 12 is completely divisible by 6, 12y will also be completely divisible by 6.
Therefore, if 12y + 3 is divided by 6, as per remainder rules, the first part will yield a remainder of ZERO, while the second part will yield a remainder of 3; the final remainder will therefore be 3.
Note that the value of y does not affect the remainder in any way, so we do not have to plug in values like we did in the analysis of Statement 1.
Statement 2 alone is sufficient to say that the remainder is 3, when n is divided by 6.
Answer options C and E can be eliminated.
The correct answer option is B.
Fisayofalana
21 Nov 2025, 15:55
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When N is divided by 6, the remainder is R ------> N=6Q+R
1) N=4Q+3
When Q is :
0, N = 3
1, N = 7
2, N = 11
3, N = 15
When you divide 6 by any two, you get different remainders. Not sufficient
2) N=12Q+3
When Q is :
0, N = 3
1, N = 15
2, N = 27
3, N = 39
When you divide 6 by any two, you get the same remainder. Sufficient. Answer choice B.
This method took me 2 minutes and 3 seconds to do.
1) N=4Q+3
When Q is :
0, N = 3
1, N = 7
2, N = 11
3, N = 15
When you divide 6 by any two, you get different remainders. Not sufficient
2) N=12Q+3
When Q is :
0, N = 3
1, N = 15
2, N = 27
3, N = 39
When you divide 6 by any two, you get the same remainder. Sufficient. Answer choice B.
This method took me 2 minutes and 3 seconds to do.
Bunuel
