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B
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Difficulty:
35%
(medium)
Question Stats:
65% (01:15) correct
35%
(01:22)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
Is integer x odd?
(1) x is greater than 2
(2) The difference between any two factors of x is always even
(1) x is greater than 2
(2) The difference between any two factors of x is always even
15 Oct 2016, 18:13
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(1) x is greater than 2
X can be 3,4,5,6... not sufficient
(2) The difference between the two members of any pair of factors of x is even
Difference between two numbers is even ==> Two numbers are (Odd, Odd) or (Even, Even)
Consider X as even, 8: Factors are 1,2,4 & 8. We have odd and even factors, whose difference will come as Odd (8-1 = 7). We will have 1 as factor for every number.
Hence X cannot be an even number
Consider X as Odd, 15: Factors: 1,3,5,15 - All odd factors => Difference between any two numbers will be an even number.
X is an odd number
(2) is Sufficient.
X can be 3,4,5,6... not sufficient
(2) The difference between the two members of any pair of factors of x is even
Difference between two numbers is even ==> Two numbers are (Odd, Odd) or (Even, Even)
Consider X as even, 8: Factors are 1,2,4 & 8. We have odd and even factors, whose difference will come as Odd (8-1 = 7). We will have 1 as factor for every number.
Hence X cannot be an even number
Consider X as Odd, 15: Factors: 1,3,5,15 - All odd factors => Difference between any two numbers will be an even number.
X is an odd number
(2) is Sufficient.
15 Oct 2016, 21:00
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stonecold
1) Clearly insuff...
2) Let x=6(even) having factors 1,2,3,6 then any pair (1,2)(2,3)(3,6) have difference is odd
But if we take x=3,5,15 or any odd then the pair gives the difference even number
e.g- x=15 then factors 1,3,5,15 difference (3-1)(5-3)(5-15).....even
Thus x=odd---------suff.
Ans B
