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12 Nov 2021, 04:48
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If \(p\) is a positive integer divisible by 10, and \(r\) is the remainder when \(p\) is divided by 15, what is the value of \(r\)?
(1) \(p\) is not a multiple of 6
(2) When \(p + 7\) is divided by 15, the remainder is less than \(r\).
(1) \(p\) is not a multiple of 6
(2) When \(p + 7\) is divided by 15, the remainder is less than \(r\).
12 Nov 2021, 04:48
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Official Solution:
If \(p\) is a positive integer divisible by 10, and \(r\) is the remainder when \(p\) is divided by 15, what is the value of \(r\)?
\(p\) is a positive integer divisible by 10: 10, 20, 30, 40...
The remainder when \(p\) is divided by 15: 10, 5, 0, 10, ...
As we can see the remainder, \(r\), can be 10, 5, or 0.
(1) \(p\) is not a multiple of 6
If \(p\) is 10, the remainder is 10 but if \(p\) is 20, the remainder is 5. Not sufficient.
(2) When \(p + 7\) is divided by 15, the remainder is less than \(r\).
\(p + 7=\) 17, 27, 37, 47, ...
\(p + 7\) divided by 15 gives the following remainders: 2, 12, 7, 2, ... The corresponding values of \(r\) are 10, 5, 0, 10, ...
As we can see the remainder is less than \(r\) when \(r=10\). Sufficient.
Answer: B
If \(p\) is a positive integer divisible by 10, and \(r\) is the remainder when \(p\) is divided by 15, what is the value of \(r\)?
\(p\) is a positive integer divisible by 10: 10, 20, 30, 40...
The remainder when \(p\) is divided by 15: 10, 5, 0, 10, ...
As we can see the remainder, \(r\), can be 10, 5, or 0.
(1) \(p\) is not a multiple of 6
If \(p\) is 10, the remainder is 10 but if \(p\) is 20, the remainder is 5. Not sufficient.
(2) When \(p + 7\) is divided by 15, the remainder is less than \(r\).
\(p + 7=\) 17, 27, 37, 47, ...
\(p + 7\) divided by 15 gives the following remainders: 2, 12, 7, 2, ... The corresponding values of \(r\) are 10, 5, 0, 10, ...
As we can see the remainder is less than \(r\) when \(r=10\). Sufficient.
Answer: B
