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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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New post 15 Jul 2010, 13:11
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16
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A
B
C
D
E

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66% (01:34) correct 34% (01:42) wrong based on 409 sessions

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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
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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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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
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\(\sqrt{256} = 16\), 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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New post 23 Sep 2017, 10:15
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Top Contributor
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:

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Brent
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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 18 Oct 2018, 18:27
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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


Since √x > 16, then x > 16^2, or x > 256. So, x/16 > 256/16 or x/16 > 16. The only value in the answer choices that satisfies this condition is 17. In other words, x = 16 * 17 = 272, so x/16 = 17.

Answer: E
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Re: The positive integer x has a factor of 16. If the square roo   [#permalink] 18 Oct 2018, 18:27
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