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If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4

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Bunuel
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If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4 [#permalink] If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4   11 Aug 2021, 06:00
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If x is a positive integer, is x even?

(1) The remainder of (x^2-1)/4 = 0
(2) x < 5
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A
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Re: If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4 [#permalink] If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4   11 Aug 2021, 06:09
1)for (x²-1) to be divisible by 4,x² has to be odd because
Odd-1=even
so, must be odd but NOT even.

SUFFICIENT.

2)x could be 1,2,3 or 4
INSUFFICIENT

A it is

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If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4 [#permalink] If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4   Updated on: 13 Aug 2021, 00:30
Correct the answer is A

For some reason I used Statement B with Statement A

Silly mistake

Originally posted by Shanil92 on 12 Aug 2021, 23:30.
Last edited by Shanil92 on 13 Aug 2021, 00:30, edited 1 time in total.
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Re: If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4 [#permalink] If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4   13 Aug 2021, 00:08
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Statement 1
(x^2 -1)/4 =0
x^2 -1 = 0
x = +1 or -1
As x is positive integer so x=1
Sufficient
Statement 2
x =1,2,3 or 4
Not sufficient
Hence answer is option A

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Re: If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4 [#permalink] If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4   13 Aug 2021, 00:46
A)x^2=4n+1
x^2=1,9,25,49..( as x is positive integer)
x=1,3,5,7..
x is odd
Sufficient
B)Not sufficient
1,2,3,4

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Re: If x is a positive integer, is x even? (1) The remainder of (x^2-1)/4 [#permalink]
13 Aug 2021, 00:46
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Bunuel
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