If x is an integer, what is the value of x? (1) : GMAT Data Sufficiency (DS)
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# If x is an integer, what is the value of x? (1)

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If x is an integer, what is the value of x? (1) [#permalink]

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02 May 2011, 04:00
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If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5
[Reveal] Spoiler: OA

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02 May 2011, 04:52
If sqrt(x) is integer then x is integer

From 1) x can be 12,13,14,15,16

Only sqrt(16) is integer. Hence sqrt(x) = 4. Sufficient.

From 2) sqrt(x) can be 3 or 4. x can be 9 or 16. Not sufficient.

Hence A.

If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5
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02 May 2011, 05:22
Thanks. i was bit confused with (2). sqrt(x) is an integer not x itself hence sqrt(x) can be 3 or 4 with x non-integer and integer respectively.
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03 May 2011, 20:04
for B, x^(1/2) = 3,4. Hence POE.
thus A.
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Re: If x is an integer, what is the value of x? (1) [#permalink]

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22 May 2016, 02:39
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Re: If x is an integer, what is the value of x? (1) [#permalink]

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22 May 2016, 12:00
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5

√x is an integer or x is square of an integer.

(1) 11<x<17
In the given range, only 16 is a number that is square of an integer. Sufficient

(2) 2<√x<5

integers 3 and 4 are between 2 and 5. So possible values van be √9 or √16. Not sufficient.

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Re: If x is an integer, what is the value of x? (1) [#permalink]

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04 Aug 2016, 11:51
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5

√x is an integer or x is square of an integer.

(1) 11<x<17
In the given range, only 16 is a number that is square of an integer. Sufficient

(2) 2<√x<5

integers 3 and 4 are between 2 and 5. So possible values van be √9 or √16. Not sufficient.

if x = 16, why are we not considering \sqrt{x} = -4?
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Re: If x is an integer, what is the value of x? (1) [#permalink]

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04 Aug 2016, 13:35
ajiteshdas wrote:
if x = 16, why are we not considering \sqrt{x} = -4?

In the GMAT, the square root refers to only the positive solution. This does not apply to the inverse.

$$\sqrt{16} = 4\\x^2 = 16 \implies x \in \{4,-4\}$$
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Re: If x is an integer, what is the value of x? (1)   [#permalink] 04 Aug 2016, 13:35
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