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22 Jun 2023, 01:30
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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:
45%
(medium)
Question Stats:
66% (01:58) correct
34%
(01:46)
wrong
based on 41
sessions
History
Date
Time
Result
Not Attempted Yet
If A and B are integers, is A∗B^4 even?
(1) (2A + B)^3 is even.
(2) A + 3B is odd.
(1) (2A + B)^3 is even.
(2) A + 3B is odd.
22 Jun 2023, 01:40
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Pre-Think: If either A is even, or B is even, then A*B^4 is even.
If both A and B are odd, then A*B^4 is odd.
(1) Only
2A+B is even.
Because 2A has to be even, B is even.
A*B^4 is even.
Sufficient.
(2) Only
For A+3B to be odd,
Either A is even and B is odd
OR A is odd and B is even.
Either way, A*B^4 is even.
Sufficient.
Answer is thus (D).
If both A and B are odd, then A*B^4 is odd.
(1) Only
2A+B is even.
Because 2A has to be even, B is even.
A*B^4 is even.
Sufficient.
(2) Only
For A+3B to be odd,
Either A is even and B is odd
OR A is odd and B is even.
Either way, A*B^4 is even.
Sufficient.
Answer is thus (D).
22 Jun 2023, 01:45
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Asked: If A and B are integers, is A∗B^4 even?
(1) (2A + B)^3 is even.
2A + B is even
B is even
Bˆ4 is even
A. Bˆ4 is even
SUFFICIENT
(2) A + 3B is odd.
Either A is odd & 3B is even ; B is even; Bˆ4 is even; A. Bˆ4 is even
or
A is even; 3B is odd; B is odd; Bˆ4 is odd; A. Bˆ4 is even
A. Bˆ4 is even in both cases.
SUFFICIENT
IMO D
(1) (2A + B)^3 is even.
2A + B is even
B is even
Bˆ4 is even
A. Bˆ4 is even
SUFFICIENT
(2) A + 3B is odd.
Either A is odd & 3B is even ; B is even; Bˆ4 is even; A. Bˆ4 is even
or
A is even; 3B is odd; B is odd; Bˆ4 is odd; A. Bˆ4 is even
A. Bˆ4 is even in both cases.
SUFFICIENT
IMO D
