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# If x is an integer, what is the value of x?

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

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02 Jun 2010, 09:48
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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 Jun 2010, 11:41
ajitsah wrote:
If √x is an integer, what is the value of √x?

(1) 11 < x < 17
(2) 2 < √x < 5

If $$\sqrt{x}$$ is an integer, what is the value of $$\sqrt{x}$$?

$$\sqrt{x}$$ is an integer means that $$x$$ is a perfect square.

(1) $$11<x<17$$ --> the only perfect square in this range is 16. So $$\sqrt{x}=4$$. Sufficient.

(2) $$2<\sqrt{x}<5$$ --> $$\sqrt{x}$$ can be 3 or 4. Two answers, hence not sufficient.

Hope it's clear.
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02 Jun 2010, 11:59
i: The only perfect square in this range is 16, so $$sqrt x = 4$$; sufficient
ii: $$sqrt x$$ can be 3 or 4. insufficient.

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02 Jun 2010, 18:28
(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient.
(2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4.
Ans C

Am I missing something?
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If x is an integer, what is the value of x? [#permalink]

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02 Jun 2010, 18:43
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alokchaks wrote:
(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient.
(2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4.
Ans C

Am I missing something?

Square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.
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If x is an integer, what is the value of x? (1) [#permalink]

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02 May 2011, 05:00
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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, 05:52
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, 06:22
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, 21:04
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? (3) [#permalink]

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17 May 2011, 13:12
IEsailor wrote:
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5
________________________________________________________________
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

$$\sqrt{x}$$ is an integer means x is also an integer.
(1)
11<x<17
x can be 12,13,14,15,16.
But, only 16 will incur an integral root.
Thus; x=16 and $$\sqrt{x}=4$$
Sufficient.

(2)
2<$$\sqrt{x}$$<5
$$\sqrt{x}$$ can be either 3 or 4.
Not Sufficient.

Ans: "A"
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Re: If x is an integer, what is the value of x? (3) [#permalink]

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17 May 2011, 13:29
From 1
what if sqrt x = -4, even then x is 16
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Re: If x is an integer, what is the value of x? (3) [#permalink]

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17 May 2011, 13:49
IEsailor wrote:
From 1
what if sqrt x = -4, even then x is 16

Here's the rule:
Square root or any positive even root of a positive number will ALWAYS be positive.

$$\sqrt{16}=+4$$
$$\sqrt{36}=+6$$
$$\sqrt[4]{16}=+2$$

But, if $$x^2=16$$
x can be +4 or -4.
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Re: If x is an integer, what is the value of x? (3) [#permalink]

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17 May 2011, 21:51
a. 16^(1/2) = 4 here.
b 3 or 4 are possible values.

As, (x^2)^1/2 = |x| meaning 4^(1/2) = 2 so, its always a positive value.
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Re: If x is an integer, what is the value of x? (3) [#permalink]

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18 May 2011, 05:30
(1)

x = 16

Sufficient

(2)
x = 9 or 16

Insufficient

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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, 13:00
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, 12:51
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, 14:35
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? [#permalink]

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11 Aug 2016, 09:06
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Hi Bunuel

In statement 2 3 is not a perfect square and ques says sqrt x is an integer. Please clarify
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Re: If x is an integer, what is the value of x? [#permalink]

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11 Aug 2016, 10:20
rahulgupta99 wrote:
Hi Bunuel

In statement 2 3 is not a perfect square and ques says sqrt x is an integer. Please clarify

Solution says: $$\sqrt{x}$$ can be 3 or 4, so x is 3^2 or 4^2.
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Re: If x is an integer, what is the value of x? [#permalink]

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26 Apr 2017, 08:56
If √x is an integer, what is the value of √x?
(1) 11<x<17
(2) 2<√x<5

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Re: If x is an integer, what is the value of x?   [#permalink] 26 Apr 2017, 08:56
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