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18 Jun 2020, 02:49
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E
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Difficulty:
45%
(medium)
Question Stats:
58% (01:24) correct
42%
(01:11)
wrong
based on 131
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If x = a/b and x is an integer, is x an even integer?
(1) a is even.
(2) b is even.
Are You Up For the Challenge: 700 Level Questions
(1) a is even.
(2) b is even.
Are You Up For the Challenge: 700 Level Questions
18 Jun 2020, 03:02
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Bunuel
Question: is x = evem?
x = a/b
STatement 1: a = even
If b = odd then x = even
If b = even then x = even/odd hence
NOT SUFFICIENT
STatement 2: b = even
i.e. a must be even for x to be integer but
a/b = even/even = even or odd hence
NOT SUFFICIENT
Combining the stateemnts
b = even then x = even/odd hence
NOT SUFFICIENT
Answer: Option E
18 Jun 2020, 03:02
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x = a/b
and x -> integer
St. 1:
'a' is even
=> let 'a' = 10
Since, x -> integer
=> 'b' can take the following values {1,2,5,10}
Now, if b = 2, => x = 5 i.e; odd - integer
if b = 5, => x = 2 i.e; even - integer
=> St. 1 is insufficient
St. 2:
'b' is even
=> let 'b' = 4
=> for x to be an inetger, 'a' has to be a multiple of 'b'
=> a = {4,8,12....... infinity}
=> x can either be even integer or odd integer
=> St. 2 is insufficient
St. 1 and St. 2:
=> a - > even, b -> even
=> Let 'a' = 20
=> for x to be an integer, 'b' can take values = {2,4,10,20} (Since, b is now only even)
=> When a = 20, b = 2, => x = 10 (even integer)
But, when a = 20, b = 4, => x = 5 (odd integer)
=> St. 1 and St. 2 together are also insufficient.
=> Answer: E
and x -> integer
St. 1:
'a' is even
=> let 'a' = 10
Since, x -> integer
=> 'b' can take the following values {1,2,5,10}
Now, if b = 2, => x = 5 i.e; odd - integer
if b = 5, => x = 2 i.e; even - integer
=> St. 1 is insufficient
St. 2:
'b' is even
=> let 'b' = 4
=> for x to be an inetger, 'a' has to be a multiple of 'b'
=> a = {4,8,12....... infinity}
=> x can either be even integer or odd integer
=> St. 2 is insufficient
St. 1 and St. 2:
=> a - > even, b -> even
=> Let 'a' = 20
=> for x to be an integer, 'b' can take values = {2,4,10,20} (Since, b is now only even)
=> When a = 20, b = 2, => x = 10 (even integer)
But, when a = 20, b = 4, => x = 5 (odd integer)
=> St. 1 and St. 2 together are also insufficient.
=> Answer: E
