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02 Feb 2024, 02:30
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B
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Difficulty:
45%
(medium)
Question Stats:
70% (01:55) correct
30%
(01:53)
wrong
based on 163
sessions
History
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Not Attempted Yet
If a and b are positive integers, is ab an even number?
(1) (a + 1)b is an even number
(2) (a + 1)^b is and odd number
(1) (a + 1)b is an even number
(2) (a + 1)^b is and odd number
02 Feb 2024, 03:47
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IMO B
Q: ab-even i.e either a or b even?
1. (a+1)b = even
so if a= even; E+O=O so b = even. YES
but if a=odd, b= odd/even NS
2. (a+1)^b = odd
so this is only possible if a= even
Therefore B
Q: ab-even i.e either a or b even?
1. (a+1)b = even
so if a= even; E+O=O so b = even. YES
but if a=odd, b= odd/even NS
2. (a+1)^b = odd
so this is only possible if a= even
Therefore B
02 Feb 2024, 12:25
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Correct option should be B.
Statement 1:
(a+1)b = even
There can be a case when (a+1) is even and b is odd. That gives us a as an odd number and b as an even number - which makes ab odd.
On the other hand, (a+1) can be odd b can be odd, which makes a an even number and ab an odd number.
So there are multiple possibilities from this statement. Not sufficient.
Statement 2:
\((a+1)^b\) is odd.
This can only be possible when (a+1) is odd. So, a is even - which makes ab an even number.
Sufficient
Hence, statement 2 alone is sufficient but statement 1 is not.
Hence, option B
Statement 1:
(a+1)b = even
There can be a case when (a+1) is even and b is odd. That gives us a as an odd number and b as an even number - which makes ab odd.
On the other hand, (a+1) can be odd b can be odd, which makes a an even number and ab an odd number.
So there are multiple possibilities from this statement. Not sufficient.
Statement 2:
\((a+1)^b\) is odd.
This can only be possible when (a+1) is odd. So, a is even - which makes ab an even number.
Sufficient
Hence, statement 2 alone is sufficient but statement 1 is not.
Hence, option B
