Is n an integer?
(1) n^2 is an integer.
(2) (rad n) is an integer.
My problem here is how would you know what to investigate for statement 2?
Is n an integer?
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statement 2)gamecomplete wrote:Is n an integer?
(1) n^2 is an integer.
(2) (rad n) is an integer.
My problem here is how would you know what to investigate for statement 2?
n^0.5 = x
(n^0.5)^2 = x^2
n = x^2
x = integer
integer x integer = integer
therefore n= integer
sufficent
statement 1)
n^2 = x
n = x^0.5
x can be any integer .... if x=2, n is not an integer
insufficent
ans = b
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Statement 1: n² is an integerIs n an integer ?
(1) n² is an integer
(2) √n is an integer
Case 1: n=1, with the result that n² = 1² = 1.
In this case, n is an integer.
Case 2: n=√2, with the result that n² = (√2)² = 2.
In this case, n is NOT an integer.
INSUFFICIENT.
Statement 2: √n is an integer
Since √n = integer, n = (integer)².
In other words, n is a PERFECT SQUARE.
Thus, n is an integer.
SUFFICIENT.
The correct answer is B.
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Don't worry about that notation. On the actual GMAT, questions will feature square root symbols.nikhilgmat31 wrote:is rad n means n ^ 1/2 ?
Cheers,
Brent
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Concept/rule tested:Is n an integer ?
(1) n² is an integer
(2) √n is an integer
(integer)(integer) = integer
Similar concepts:
(integer) + (integer) = integer
(integer) - (integer) = integer
Target question: Is n an integer?
Statement 1: The median of the numbers is 30
This statement doesn't FEEL sufficient, so I'm going to TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 3 (notice that 3² = 9, and 9 is an integer). In this case, n IS an integer
Case b: n = √2 (notice that (√2)² = 2, and 2 is an integer). In this case, n is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: √n is an integer
If √n is an integer, then n > 0
If n > 0, then (√n)² = n
If √n is an integer, we can write: (some integer)² = n
In other words, (some integer)(some integer) = n
By the above rule, n must be an integer.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
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(1) n can be integer 1 or non-integer sqrt(2)gamecomplete wrote:Is n an integer?
(1) n^2 is an integer.
(2) (rad n) is an integer.
Insufficient
(2) sqrt(n) is integer.
n = sqrt(n) * sqrt(n)
So, n = integer * integer
n must be integer.
ANswer = B