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The positive integer x has a factor of 16. If the square roo

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The positive integer x has a factor of 16. If the square roo [#permalink]

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The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16?

A. 13
B. 14
C. 15
D. 16
E. 17
[Reveal] Spoiler: OA

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Re: Problem solving [#permalink]

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New post 15 Jul 2010, 14:20
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aimingformba wrote:
The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16?
a. A – 13
b. B – 14
c. C – 15
d. D – 16
e. E – 17


Given: \(x=16k\) (where \(k\) is a positive integer) and \(\sqrt{x}=\sqrt{16k}>16\) --> \(x=16k>16^2\) --> divide by 16 --> \(\frac{x}{16}=k>16\). So as \(\frac{x}{16}=k=integer>16\), then \(\frac{x}{16}\) can be 17, 18, ...

Answer: E.
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Re: The positive integer x has a factor of 16. If the square roo [#permalink]

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Re: The positive integer x has a factor of 16. If the square roo [#permalink]

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New post 09 Oct 2014, 21:45
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The positive integer x has a factor of 16. If the square roo [#permalink]

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New post 21 Oct 2014, 23:42
\(\sqrt{256} = 16\), so we can directly ignore option A, B, C & D as they will not give \(\sqrt{x} > 16\)

Options remains = 17

Answer = E
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Re: The positive integer x has a factor of 16. If the square roo [#permalink]

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Re: The positive integer x has a factor of 16. If the square roo [#permalink]

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New post 23 Sep 2017, 08:20
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Re: The positive integer x has a factor of 16. If the square roo [#permalink]

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New post 23 Sep 2017, 10:15
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aimingformba wrote:
The positive integer x has a factor of 16. If the square root of x is > 16, which of the following could equal x/16?

A. 13
B. 14
C. 15
D. 16
E. 17


Bunuel's solution is perfect.
However, we can also test the answer choices....

A) 13
This means x/16 = 13, which means x = (16)(13)
We're told that √x > 16
Notice that √(16²) = 16
Since (16)(13) is LESS THAN 16², we can be certain that √(16)(13) is LESS THAN 16
Since this answer choice does not satisfy the condition that √x > 16, we can ELIMINATE A

B) 14
This means x/16 = 14, which means x = (16)(14)
Since (16)(14) is LESS THAN 16², we can be certain that √(16)(14) is LESS THAN 16
Since this answer choice does not satisfy the condition that √x > 16, we can ELIMINATE B

.
.
.
E) 17
This means x/16 = 17, which means x = (16)(17)
Since (16)(17) is GREATER THAN 16², we can be certain that √(16)(17) is GREATER THAN 16
Since this answer choice satisfies the condition that √x > 16, this must be the correct answer.

Answer:
[Reveal] Spoiler:
E


Cheers,
Brent
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Re: The positive integer x has a factor of 16. If the square roo   [#permalink] 23 Sep 2017, 10:15
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