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When positive integer n is divided by 7, the remainder is 2. What is

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Bunuel
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When positive integer n is divided by 7, the remainder is 2. What is [#permalink] New post   04 May 2022, 01:30
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When positive integer n is divided by 7, the remainder is 2. What is the value of n?

(1) n is less than 20.
(2) When n is divided by 8, the remainder is 0.




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ramonbhadauria
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Re: When positive integer n is divided by 7, the remainder is 2. What is [#permalink] New post   04 May 2022, 07:32
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When n is divided by 7, the remainder is 2.

Statement 1 tells us that n is less than 20. Therefore n can be 9 or 16. Inconclusive.

Statement 2 tells us that n is a multiple of 8. Since there is no upper bound, n can be 16, 72, any other number which is a multiple of 56 greater than 16. Inconclusive.

Using 1 and 2 together, we see only 16 is a possible option. Therefore, choice should be C.
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Re: When positive integer n is divided by 7, the remainder is 2. What is [#permalink] New post   04 May 2022, 11:01
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Pre-thinking
n can be 2, 9, 16, 23, ...

(1) Only
n can be 2, 9, 16
Not sufficient

(2) Only
n can be 16
and n can be 16 + 56 = 72 (56 is LCM of 7 and 8)
Not sufficient

(1)(2) together
n is 16
Sufficient.

The answer is thus (C).
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Re: When positive integer n is divided by 7, the remainder is 2. What is [#permalink] New post   05 May 2022, 22:19
IMO C

From statement 1 : we can assume the required integer to be 2,9 or 16. Hence Insufficient
From Statement 2: we can assume the required integer to be 8,16,24...... Hence Insufficient

Combining both we have unique value i.e. 16 as it is restricted to 20 only. Hence, sufficient
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Re: When positive integer n is divided by 7, the remainder is 2. What is [#permalink]
05 May 2022, 22:19
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