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If p is a positive odd integer, what is the remainder when p is divide

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Bunuel
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If p is a positive odd integer, what is the remainder when p is divide [#permalink] New post   30 Jun 2023, 01:30
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If p is a positive odd integer, what is the remainder when p is divided by 3 ?

(1) When p is divided by 12, the remainder is 7.
(2) p = n(n + 1) + 1, where n is an integer.


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Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink] New post   30 Jun 2023, 01:53
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(1)Only
p=7+12k where k=0,1,2,...
When p is divided by 3, the quotient is (2+3k) and the remainder is 1
Sufficient

(2)Only
When n=0, p=1 (When p is divided by 3, its remainder is 1)
When n=1, p=3 (When p is divided by 3, its remainder is 0)
Not sufficient.

The answer is thus (A)
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If p is a positive odd integer, what is the remainder when p is divide [#permalink] New post   30 Jun 2023, 02:48
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Statement 1 :
p can we 7, 19, ... etc, The remainder will come 1. Sufficient

Statement 2 :
When n=1, p=3 [When p is divided by 3, remainder is 0]
When n=2, p=7 [When p is divided by 3, remainder is 1] .Not Sufficient

A is the answer
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If p is a positive odd integer, what is the remainder when p is divide [#permalink] New post   01 Jul 2023, 07:37
Using statement 1, p = 12k+7, which is a sufficient condition. Remember you need to remove indefiniteness in answer, no need to find exact answer. Thus statement 1 is sufficient.

For statement 2, p =n(n+1)+1, since one out of n and n+1 has to be an even number so p is simply any random odd number. This statement does not introduce definite odd number and hence insufficient.

Therefore A is the answer.

Bunuel wrote:
If p is a positive odd integer, what is the remainder when p is divided by 3 ?

(1) When p is divided by 12, the remainder is 7.
(2) p = n(n + 1) + 1, where n is an integer.


This is a Data Sufficiency Butler Question



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If p is a positive odd integer, what is the remainder when p is divide [#permalink]
01 Jul 2023, 07:37
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Bunuel
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