Is n an integer?
1) n^2 is an integer.
2) under root n is an integer.
OAB
Please explain.
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Is n an integer
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GMATGuruNY
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Statement 1:Needgmat wrote:Is n an integer?
1) n^2 is an integer.
2) under root n is an integer.
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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Required: Is n an integer?Needgmat wrote:Is n an integer?
1) n^2 is an integer.
2) under root n is an integer.
OAB
Please explain.
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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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
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
