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10 Dec 2017, 08:25
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
59% (01:38) correct
41%
(01:14)
wrong
based on 143
sessions
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If x is an integer and \(x\neq{31}\), is \(\frac{31-x}{x}\) an integer?
(1) x > 1.
(2) x is an even number.
self made -
(1) x > 1.
(2) x is an even number.
self made -
chetan2u
\(\frac{31-x}{x}=\frac{31}{x}-\frac{x}{x}=\frac{31}{x}-1\)
as \(x\neq{31}\) and \(31\) is a prime number, so the only way the above equation can be an integer is if \(x=1\), \(-1\) or \(-31\)
Statement 1: as \(x>1\) so the equation is not integer. Sufficient
Statement 2: Again as \(x\neq31, 1, -1\) or \(-31\), so the equation will not be an integer. Sufficient
Option D
11 Dec 2017, 06:14
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chetan2u
(31-x)/x can be written as 31/x - 1. Here -1 is already an integer, so 31/x - 1 will be an integer only when 31/x is an integer. This will be true only if x takes the following values: 1, 31, -1, -31 (its easy to see which values will satisfy because 31 is a prime number and thus has only 2 factors - 1 and 31. But the negative values of these will also result in integer). But we are already given that x is NOT equal to 31. So the only possible integer values of x which will result in 31/x being an integer are: 1, -1, -31.
(1) x > 1
This means there is simply no value x can take which will make 31/x an integer (because 1, -1, -31 are not possible here given that x > 1). So this can never be an integer. This gives us an answer as NO to the question. Sufficient.
(2) x is an even number.
Since 31 is odd, it can never be divisible by any even number. So 31/x cannot be an integer. This gives us an answer as NO to the question. Sufficient.
Hence D answer
