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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] New post 02 Jun 2010, 08:48
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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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Re: DS - Inequality [#permalink] New post 02 Jun 2010, 10:41
Expert's post
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.

Answer: A.

Hope it's clear.
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Re: DS - Inequality [#permalink] New post 02 Jun 2010, 10:59
i: The only perfect square in this range is 16, so sqrt x = 4; sufficient
ii: sqrt x can be 3 or 4. insufficient.

Answer is A.
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Re: DS - Inequality [#permalink] New post 02 Jun 2010, 17:28
(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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Re: DS - Inequality [#permalink] New post 02 Jun 2010, 17:43
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Expert's post
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 can not 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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: DS - Inequality [#permalink] New post 02 Jun 2010, 18:02
Thanks for the explanation. I will embed it in my head.

I've given you a +1 Kudos.
Re: DS - Inequality   [#permalink] 02 Jun 2010, 18:02
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