Is n an integer

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deepak_free: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sat Feb 21, 2009 8:02 am; Thanked: 1 times

by deepak_free » Fri Jun 25, 2010 11:42 am

Is n an integer?

1) n^2 is an integer
2)sqroot(n) is an integer

Please explain

Source OG 11

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 25, 2010 11:42 am

tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Fri Jun 25, 2010 1:20 pm

The problem deals with the issue of square roots - and how they relate to integers. When you think of integers you have to consider integers, fractions, decimals and square roots.

if n^2 is an integer then n could be an integer or a square root - for instance (SQRT2)^2=2 so you can't be sure that n is an integer.

however if SQRT(n) is an integer that means that n is a perfect square - which means that n is the product of 2 integers therefor you know that n must be an integer.

Answer is B.

Last edited by tpr-becky on Fri Jun 25, 2010 3:46 pm, edited 1 time in total.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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deepak_free: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sat Feb 21, 2009 8:02 am; Thanked: 1 times

by deepak_free » Fri Jun 25, 2010 2:03 pm

[quote="tpr-becky"]The problem deals with the issue of square roots - and how they relate to integers. When you think of integers you have to consider integers, fractions, decimals and square roots.

if n^2 is an integer then n could be an integer or a square root - for instance (SQRT2)^2=2 so you can't be sure that n is an integer.

however if SQRT(n) is an integer that means that n is a perfect square - which means that n is the product of 2 integers therefor you know that n must be an integer.

Answer is D.[/quote]

Thanks for the explanation. I think you mean the answer is B and not D.

Now the question,which I have.

I understand that sqrt(2) is not an integer but I thought in the following way.

value of sqrt(2) in terms of decimal will be

1.4142135623730950488016887242097 in fact it will contain some other digits as well and if we do a square of the same then it will result in 1.999999999999999999,which is not an integer and the same will be true for the sqrt of all the numbers

Am I wrong

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tpr-becky: GMAT Instructor; Posts: 509; Joined: Wed Apr 21, 2010 1:08 pmFollowed by: 85 members; Location: Irvine, CA; Thanked: 199 times; GMAT Score:750

by tpr-becky » Fri Jun 25, 2010 3:46 pm

you are correct for my answer (typo) but on the other fact you are only wrong because you have rounded off the number - yes the SQRT of 2 is a long decimal but by the very fact of it being the SQRT of 2 when you square it you will get 2. That is why when you are dealing with these type of questions it is important to think about integers, fractions, decimals and square roots - becuase square roots act in a different manner.

Becky
Master GMAT Instructor
The Princeton Review
Irvine, CA

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deepak_free: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Sat Feb 21, 2009 8:02 am; Thanked: 1 times

by deepak_free » Sat Jun 26, 2010 6:42 am

Thanks

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