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Is n an integer

Expert replies
Source: — Data Sufficiency |

by GMATGuruNY » Sun Jul 17, 2016 1:48 am
Needgmat wrote:Is n an integer?

1) n^2 is an integer.

2) under root n is an integer.
Statement 1:
n² = 1, 2, 3, 4...

If we take the square root of both sides, we get the following options for n:
n = 1, √2, √3, 2...

If n=1, then n is an integer.
If n=√2, then n is NOT an integer.
INSUFFICIENT.

Statement 2:
√n = 1, 2, 3, 4...

If we square both sides, we get the following options for n:
n = 1, 4, 9, 16...
In every case, n is an integer.
SUFFICIENT.

The correct answer is B.
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by OptimusPrep » Sun Jul 17, 2016 8:54 pm
Needgmat wrote:Is n an integer?

1) n^2 is an integer.

2) under root n is an integer.

OAB

Please explain.
Required: Is n an integer?

Statement 1: n^2 is an integer
If n = 2, n^2 = 4
If n = √2, n^2 = 2
INSUFFICIENT

Statement 2: √n is an integer.
If √n is an integer, then (√n)^2 = n
This will also be an integer.
SUFFICIENT

Correct Option: B
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by Matt@VeritasPrep » Fri Jul 22, 2016 1:55 am
We could also do algebra:

S1:

n² = integer

n = √integer

So n is the ROOT of an integer, not necessarily an integer itself; NOT SUFFICIENT

S2:

√n = integer

n = integer²

So n is the SQUARE of an integer, which must always be an integer. SUFFICIENT
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