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If p is a positive integer, is p even? (1) p divided by 3 leaves a re

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Bunuel
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If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink] New post   02 May 2021, 03:45
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If p is a positive integer, is p even?

(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1
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B
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Bunuel
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Re: If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink] New post   09 May 2021, 03:45
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If p is a positive integer, is p even?

(1) p divided by 3 leaves a remainder of 1 --> p = 3q + 1 --> p could be 1, 4, 7, ... So, as you can see p can be odd as well as even. Not sufficient.

(2) p divided by 4 leaves a remainder of 1 --> p = 4m + 1 = even + odd = odd (p could be 1, 5, 9, ...). Sufficient.

Answer: B.
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Re: If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink] New post   02 May 2021, 04:19
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If p is a positive integer, is p even?

(1) p divided by 3 leaves a remainder of 1
So p=3x+1. P could be 4, 7, 10..
Insufficient

(2) p divided by 4 leaves a remainder of 1
p=4K+1=even+odd=odd.
p could be 1, 5, 9, and so on. But it will always be odd.
Sufficient

B
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Re: If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink] New post   02 May 2021, 04:39
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Bunuel wrote:
If p is a positive integer, is p even?

(1) p divided by 3 leaves a remainder of 1
(2) p divided by 4 leaves a remainder of 1


1)\(\frac{p}{3}, r = 1\)

So, p could be 1, 4, 7...
1 is odd, 4 is even. Insufficient.

2)\(\frac{p}{4}, r = 1\)

So, p could be 1, 5, 9...
Always odd as odd + even = odd. Sufficient.
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Re: If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink] New post   07 May 2021, 19:59
B is ans as with option A - It can be odd/even. So not sufficient.
Option B --> It will be ODD always.. So sufficient
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Re: If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink] New post   09 May 2021, 03:39
1) make patterns of 3 1-2-3 and 4-5-6 and 7-8-9 etc.. and you will notice that in every pattern only the first number gives a remainder of 1 when divided by 3 and it can be both even or odd THUS NOT SUFFICIENT

2) make patterns of 4 1-2-3-4 and 5-6-7-8 and 9-10-11-12 etc.. and you will notice that in every pattern only the first number gives a remainder of 1 when divided by 3 and it is always an odd number THUS SUFFICIENT
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Re: If p is a positive integer, is p even? (1) p divided by 3 leaves a re [#permalink]
09 May 2021, 03:39
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