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Question

Write whether every positive integer can be of the form 4q+2, where q is an integer.

A
Yes
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B
No
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C
Ambiguous
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D
Data Insufficient
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Solution

The correct option is B No
No, all positive integers cannot be written in the form of 4q+2
Because, 4q+2=2(2q+1)
Therefore, 4q+2 is an even number.
So, we can't write odd numbers in the form 4q+2 (where q is an integer)
Also 2q+1 is an odd number, hence the maximum power of 2 that divides 4q+1 is 1. Therefore, we can't represent the numbers divisible by 4 this form.

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