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Is n an integer?

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by Jay@ManhattanReview » Sun Mar 19, 2017 10:53 pm

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vikkimba17 wrote:Is n an integer?

(1) n^2 is an integer.
(2) SQROOT(n)is an integer.

PLS HELP
Hi vikkimba17,

Let's discuss each statement one by one.

S1: n^2 is an integer.

Let's take two cases.

Case 1: If say n^2 = 1, 4, 9, etc, n = +/-1, +/-2, +/-3. It means that n is an integer.

Case 2: If say n^2 = 2, 3, 5, etc. It means that n is not an integer. No unique result.

S2: SQROOT(n)is an integer.

Say sqrt (n) = k, where k is an integer

=> n = k^2 = integer; since square of an integer is an integer. Sufficient.

The correct answer: B

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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by vikkimba17 » Sun Mar 19, 2017 11:04 pm

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Hi jay i understand

case 1 in statement 1
but in case 2: If say n^2 = 2, 3, 5, etc. It means that n is not an integer. No unique result.

how n^2 will be 2,3,5, etc... for what values of n will they yield that result.
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by Jay@ManhattanReview » Sun Mar 19, 2017 11:38 pm

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vikkimba17 wrote:Hi jay i understand

case 1 in statement 1
but in case 2: If say n^2 = 2, 3, 5, etc. It means that n is not an integer. No unique result.

how n^2 will be 2,3,5, etc... for what values of n will they yield that result.
Hi vikkimba17,

Since it is given that n^2 is an integer, we can choose any integer value for n^2 such as 1, 2, 3, 4, 5, etc.

1. If n^2 = 1, n = sqrt(1) = 1... An integer. The answer is YES.
1. If n^2 = 2, n = sqrt(2) = 1.414... Not an integer. The answer is NO.
2. If n^2 = 3, n = sqrt(3) = 1.732... Not an integer. The answer is NO.
1. If n^2 = 4, n = sqrt(4) = 2... An integer. The answer is YES.
3. If n^2 = 5, n = sqrt(5) = 2.65... Not an integer. The answer is NO.

No unique result.

Hope this helps!

-Jay
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by vikkimba17 » Mon Mar 20, 2017 12:06 am

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Got you. Thanks for the post. :)
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by GMATGuruNY » Mon Mar 20, 2017 3:33 am

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vikkimba17 wrote:Is n an integer?

(1) n^2 is an integer.
(2) SQROOT(n)is an integer.
Statement 1:
Since n² must be an integer, make a list of options for n²:
n² = 1, 2, 3, 4...
To get a list of options for n, take the square root of every value in the list above:
n = 1, √2, √3, 2...
If n=1, then the answer to the question stem is YES.
If n=√2, then the answer to the question stem is NO.
Since the answer could be YES or NO, INSUFFICIENT.

Statement 2:
Since √n must be an integer, make a list of options for √n:
√n = 1, 2, 3, 4...
To get a list of options for n, square every value in the list above:
n = 1, 4, 9, 16...
In every case, n is an integer, implying that the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Mon Mar 20, 2017 6:21 am

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Is n an integer ?

(1) n² is an integer
(2) √n is an integer
Concept/rule tested:
(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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by Jeff@TargetTestPrep » Thu Mar 23, 2017 3:32 pm

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vikkimba17 wrote:Is n an integer?
(1) n^2 is an integer.
(2) √n is an integer.
We need to determine whether n is an integer.

Statement One Alone:

n^2 is an integer.

If n^2 is an integer, n may or may not be an integer. For instance, if n^2 = 4, then n is an integer (since n = 2 or -2). However, if n^2 = 5, then n is not an integer (since n = √5 or -√5). Statement one is not sufficient to answer the question.

Statement Two Alone:

√n is an integer.

In order for √n to be an integer, n must be an integer. This is because n = (√n)^2, and any integer squared is also an integer. Statement two is sufficient to answer the question.

Answer: B

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