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02 Jun 2023, 01:30
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D
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Difficulty:
35%
(medium)
Question Stats:
67% (01:25) correct
33%
(01:41)
wrong
based on 75
sessions
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If a, b and c are positive integers, is a + b + c even?
(1) (a + b + c)/2 is an integer.
(2) a = b/2 = c/3
(1) (a + b + c)/2 is an integer.
(2) a = b/2 = c/3
02 Jun 2023, 01:41
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a+b+c even?
note that we know that a,b,c are integers greater than 0.
1)
Sufficient.
This statement implies that a+b+c=integer*2. Any integer*2 is automatically even.
2)
We know that b is even.
A can possibly be odd (consider the case of b=2) but in this specific case (a=1, b=2,c=3) the sum is even as (odd+odd+even=even)
For all b!=2, a is even.
If a is even, then so must c be even - as c divided by 3 is a*3 which is some even number times 3.
This makes the sum (even+even+even) which is even.
D.
note that we know that a,b,c are integers greater than 0.
1)
Sufficient.
This statement implies that a+b+c=integer*2. Any integer*2 is automatically even.
2)
We know that b is even.
A can possibly be odd (consider the case of b=2) but in this specific case (a=1, b=2,c=3) the sum is even as (odd+odd+even=even)
For all b!=2, a is even.
If a is even, then so must c be even - as c divided by 3 is a*3 which is some even number times 3.
This makes the sum (even+even+even) which is even.
D.
02 Jun 2023, 02:36
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(1) Only
a+b+c=2k (k is an integer)
So a+b+c is even
Sufficient
(2)Only
b=2a (a is an integer)
c=3a
So a+b+c=6a and must be even
Sufficient
The answer is thus (D).
a+b+c=2k (k is an integer)
So a+b+c is even
Sufficient
(2)Only
b=2a (a is an integer)
c=3a
So a+b+c=6a and must be even
Sufficient
The answer is thus (D).
