tracyyahoo wrote:

if N=p/q, where p and q are nozero integers, is n an integer?

1) N^2 is an integer

2) 2n+4/2 is an integer

why? pls tell me, thank you.

It is said that n=p/q, so n is a rational number. what is rational number?

Tracy - No need of knowing rational numbers and all - It is separate Maths concept.

Is 2) 2n+4/2 or (2n+4)/2

Anyway either case the answer will be D

Let us walk through the thought process

N=p/q, where p,q are integers

1) N^2 is an integer -

Take N^2 as 3, now N=sqr. root(3)/1 --> It does not satisfy our case

Take N^2 as 9, now N=3/1 --> It satisfies our case

The point is our scenario will be satisfied only when N is a perfect square ( 4,9,25,36,49)

When N is not a perfect square, N will never be an integer, so it will not get satisfied.

So (1) is sufficient

2)

If 2n+4/2 is an integer ==> 2n+2 is an integer ==> 2(n+1) is an integer

This means 2(n+1) is an even integer

So cancelling out 2 on both sides

(n+1) is an integer ==> n will be an integer

If (2n+4)/2 is an integer ==> (n+2) is an integer ==> n is an integer

So (2) is sufficient

So the Ans. is D

Let me know if you are not able to follow the steps.

---- Now going to sleep, bye

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