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12 Jan 2024, 02:30
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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:
55%
(hard)
Question Stats:
55% (01:29) correct
45%
(01:15)
wrong
based on 88
sessions
History
Date
Time
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Not Attempted Yet
If a and b are positive integers, is \(a^2 + 3ab\) an even number ?
(1) a is an even number.
(2) b is an odd number.
(1) a is an even number.
(2) b is an odd number.
12 Jan 2024, 02:46
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If an and b are positive integers, is \(a^2 + 3ab\) an even number ?
\(a^2+3ab=a(a+3b)\)
(1) a is an even number.
a is even, so a(a+3b) becomes even(even+3b), and will be even irrespective of b.
Sufficient
(2) b is an odd number.
Let b=2n+1
a(a+3b)=a(a+3(2n+1))=a(a+6n+3)=a(a+3)+a(6n)
Now, a(6n) is even. Also, a(a+3) will be even as ‘a’ and ‘a+3’ will have opposite odd/even property.
Thus entire expression is again even.
Sufficient
D
\(a^2+3ab=a(a+3b)\)
(1) a is an even number.
a is even, so a(a+3b) becomes even(even+3b), and will be even irrespective of b.
Sufficient
(2) b is an odd number.
Let b=2n+1
a(a+3b)=a(a+3(2n+1))=a(a+6n+3)=a(a+3)+a(6n)
Now, a(6n) is even. Also, a(a+3) will be even as ‘a’ and ‘a+3’ will have opposite odd/even property.
Thus entire expression is again even.
Sufficient
D
12 Jan 2024, 12:58
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Bunuel
OA is D
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