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

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Question Stats: 65% (01:35) correct 35% (01:42) wrong based on 421 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
Math Expert V
Joined: 02 Sep 2009
Posts: 61189

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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, ...

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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

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

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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.

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

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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.

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