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11 Dec 2019, 00:14
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If A, B and C are integers, is A + B + C even?
(1) A - C - B is even
(2) (A - C)/B is odd
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11 Dec 2019, 03:17
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If A, B and C are integers, is A + B + C even?
A + B + C = e. Cases are:
e + e + e = e
e + o + o = e
o + e + o = e
o + o + e = e
(1) A - C - B is even
Cases for A - B - C = e
e - e - e = e
e - o - o = e
o - e - o = e
o - o - e = e
All cases suffice the requirement.
SUFFICIENT.
(2) (A - C)/B is odd
(A - C) / B = Odd
A - C = (Odd) * B. Cases are:
e - e = (o)e
o - o = (o)e
o - e = (o)o
e - o = (o)o
Again all cases satisfy the requirement.
SUFFICIENT.
Answer D.
A + B + C = e. Cases are:
e + e + e = e
e + o + o = e
o + e + o = e
o + o + e = e
(1) A - C - B is even
Cases for A - B - C = e
e - e - e = e
e - o - o = e
o - e - o = e
o - o - e = e
All cases suffice the requirement.
SUFFICIENT.
(2) (A - C)/B is odd
(A - C) / B = Odd
A - C = (Odd) * B. Cases are:
e - e = (o)e
o - o = (o)e
o - e = (o)o
e - o = (o)o
Again all cases satisfy the requirement.
SUFFICIENT.
Answer D.
11 Dec 2019, 03:55
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(1) A - (B+C) is even
If both A and (B+C) are odd, then both A-(B+C) and A+(B+C) are even.
If both A and (B+C) are even, then both A-(B+C) and A+(B+C) are even.
SUFFICIENT
(2) (A - C)/B is odd
If both B and (A-C) are odd, then (A-C)/B is odd and A+B+C is even.
If both B and (A-C) are even, then (A-C)/B is odd and A+B+C is even.
SUFFICIENT
FINAL ANSWER IS (D)
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If both A and (B+C) are odd, then both A-(B+C) and A+(B+C) are even.
If both A and (B+C) are even, then both A-(B+C) and A+(B+C) are even.
SUFFICIENT
(2) (A - C)/B is odd
If both B and (A-C) are odd, then (A-C)/B is odd and A+B+C is even.
If both B and (A-C) are even, then (A-C)/B is odd and A+B+C is even.
SUFFICIENT
FINAL ANSWER IS (D)
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