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16 Sep 2014, 00:11
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If \(x\) is a positive number and \(a=\sqrt{x} * x - x\), which of the following must be true?
I. \(a\) is even
II. \(a\) is positive
III. \(a\) is an integer
A. I only
B. II only
C. III only
D. I and II
E. None of the above
I. \(a\) is even
II. \(a\) is positive
III. \(a\) is an integer
A. I only
B. II only
C. III only
D. I and II
E. None of the above
16 Sep 2014, 00:11
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Official Solution:
If \(x\) is a positive number and \(a=\sqrt{x} * x - x\), which of the following must be true?
I. \(a\) is even
II. \(a\) is positive
III. \(a\) is an integer
A. I only
B. II only
C. III only
D. I and II
E. None of the above
Note that we are asked "which of the following MUST be true", not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
If \(x=\frac{1}{4}\) then \(a=\sqrt{x} * x - x=\frac{1}{2}*\frac{1}{4}-\frac{1}{4}=-\frac{1}{8}\). Now, \(-\frac{1}{8}\) is not an integer at all (hence not even) and also not positive, so none of the options MUST be true.
Answer: E
If \(x\) is a positive number and \(a=\sqrt{x} * x - x\), which of the following must be true?
I. \(a\) is even
II. \(a\) is positive
III. \(a\) is an integer
A. I only
B. II only
C. III only
D. I and II
E. None of the above
Note that we are asked "which of the following MUST be true", not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
If \(x=\frac{1}{4}\) then \(a=\sqrt{x} * x - x=\frac{1}{2}*\frac{1}{4}-\frac{1}{4}=-\frac{1}{8}\). Now, \(-\frac{1}{8}\) is not an integer at all (hence not even) and also not positive, so none of the options MUST be true.
Answer: E
General Discussion
22 Nov 2014, 12:13
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Hi Bunnel,
A very basic question can fractions be classified as even / odd. Sry if it is very basic. Got a sudden doubt in the test.
A very basic question can fractions be classified as even / odd. Sry if it is very basic. Got a sudden doubt in the test.
