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15 Jul 2010, 13:11
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:39) correct
31%
(01:45)
wrong
based on 556
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. 13
B. 14
C. 15
D. 16
E. 17
15 Jul 2010, 14:20
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aimingformba
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.
23 Sep 2017, 10:15
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aimingformba
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:
Cheers,
Brent
