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# If positive integer x is divided by 2, the remainder is 1. What is the

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Re: If positive integer x is divided by 2, the remainder is 1. What is the [#permalink]
If positive integer x is divided by 2, the remainder is 1. What is the remainder when x is divided by 4 ?

(1) 31 < x < 35
(2) x is a multiple of 3.

A
According to the question, the positive integer x is defined as 2n + 1 i.e an odd number.

Statement 1: The only odd number between 31 and 35, excluding the two extremes is 33. Sufficient
Statement 2: Looks at odd numbers that are multiples of 3. Different remainders possible. Insufficient.

hence, A - Statement 1 alone is sufficient, statement 2 is not.
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Re: If positive integer x is divided by 2, the remainder is 1. What is the [#permalink]
A -gives only one possibility ie.. 33 (sufficient)
B - when 9/4, rem = 1
when 12/4, rem - 0 (not suff)

ans - A
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Re: If positive integer x is divided by 2, the remainder is 1. What is the [#permalink]
Bunuel wrote:

Tough and Tricky questions: Remainders.

If positive integer x is divided by 2, the remainder is 1. What is the remainder when x is divided by 4 ?

(1) 31 < x < 35
(2) x is a multiple of 3.

Kudos for a correct solution.

Note : If any number is even it must be divisible by 2 , otherwise the number is odd. So, x is ODD.

Statement 1: only odd in the given range : 33 . So, remainder when 33 is divided by 4 is 1. Sufficient.

Statement 2; unlimited multiples we have . Different multiples , different reminder . NOT sufficient.

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Re: If positive integer x is divided by 2, the remainder is 1. What is the [#permalink]
One thing that many are not discussing in this question is that for statement 2), we already know that x = odd since x = 2q + 1. This means that from multiples of 3:
3, 6, 9, 12, 15, 18, ...
Only odd numbers should be tested. Thus the remainder cannot be 0 as some propose but only 3 or 1.
3 = 0*4 + 3
9 = 2*4 + 1
15 = 3*4 + 3
21 = 5*4 + 1
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Re: If positive integer x is divided by 2, the remainder is 1. What is the [#permalink]
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Re: If positive integer x is divided by 2, the remainder is 1. What is the [#permalink]
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