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28 Mar 2021, 09:16
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:17) correct
28%
(01:46)
wrong
based on 72
sessions
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What is the remainder when positive integer \(n\) is divided by 6?
1) When \(n\) is divided by 12 the remainder is 9.
2) When \(n\) is divided by 15 the remainder is 6.
1) When \(n\) is divided by 12 the remainder is 9.
2) When \(n\) is divided by 15 the remainder is 6.
28 Mar 2021, 21:35
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What is the remainder when positive integer \(n\) is divided by 6?
1) When \(n\) is divided by 12 the remainder is 9.
So \(n=12q+9=12q+6+3=6(2q+1)+3\)
When we divide 6(2q+1)+3 by 6, only 3 remains as the remainder.
Sufficient
2) When \(n\) is divided by 15 the remainder is 6.
So \(n=15q+6=12q+6+3q=6(2q+1)+3q\)
When we divide 6(2q+1)+3q by 6, 3q remains as the remainder.
If q is even, 3q is divisible by 6 and remainder is 0.
If q is odd, there is a remainder of 3.
Insufficient
A
1) When \(n\) is divided by 12 the remainder is 9.
So \(n=12q+9=12q+6+3=6(2q+1)+3\)
When we divide 6(2q+1)+3 by 6, only 3 remains as the remainder.
Sufficient
2) When \(n\) is divided by 15 the remainder is 6.
So \(n=15q+6=12q+6+3q=6(2q+1)+3q\)
When we divide 6(2q+1)+3q by 6, 3q remains as the remainder.
If q is even, 3q is divisible by 6 and remainder is 0.
If q is odd, there is a remainder of 3.
Insufficient
A
30 Mar 2021, 13:14
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TheUltimateWinner
Statement 1:
We may write n as \(n = 12*i + 9\) where \(i\) is any positive integer. Then if we divide by 6 we get \(\frac{n}{6} = 2*i + 1 + \frac{3}{6}\). Which means the remainder must be 3. Sufficeint.
Statement 2:
\(n = 15*i + 6\). However dividing \(15*i\) by 6 does not guarantee an integer, so insufficient.
Ans: A
