If a, b, and c are integers. Is a + b + c even?

Question

(1) a + b is even
(2) a + c is even

M36-50

Bunuel · Accepted Answer

Official Solution:

If  a ,  b , and  c  are integers. Is  a + b + c  even? 
 
(1)  a + b  is even
 
The above means that either both  a  and  b  are even or both are odd. No info about  c . Not sufficient.
 
(2)  a + c  is even
 
The above means that either both  a  and  c  are even or both are odd. No info about  b . Not sufficient.
 
(1)+(2) If all three unknowns are even, then  a + b + c  is even but if all three unknowns are odd, then  a + b + c  is odd. Not sufficient.

Answer: E

Chethan92 · Answer

From statement 1 :

a+b is even, 
Odd+Odd = Even
Even+Even = Even
If c is Odd then a+b+c is Odd
If c is Even then a+b+c is Even
 Insufficient .

From statement 2 :

a + c is even
Odd+Odd = Even
Even+Even = Even
If b is Odd then a+b+c is Odd
If b is Even then a+b+c is Even
 Insufficient .

Combining both :
a + b is even and a + c is even
Consider a =3, b = 5 and c = 7.
a+b = 8 = even.
a+c = 3+7 = 10 = even.
But a+b+c = 15 = odd.
Consider a =2, b = 4 and c = 6.
a+b = 6 = even.
a+c = 8 = even.
But a+b+c = 12 = even.
 Insufficient .

Hence  E  is the answer.

shashankism · Answer

Question : is a+b+c even

Statement 1: a+b is even
even + even or odd +odd
(a= E, b=E or a=O, b = O ; No idea about c)
 NOT SUFFICIENT

Statement 2 : a+c is even
even + even or odd +odd
(a= E, c=E or a=O, c = O ; No idea about b)
 NOT SUFFICIENT

Combined : 
From statement 1, if a=E, b = E.. also if a=E, from statement 2, c= E
So, a+b+c = E

From statement 1, if a=O, b = O.. also if a=E, from statement 2, c= O
So, a+b+c = O
 NOT SUFFICIENT

Answer E

Archit3110 · Answer

from 1:
a+b would be even ; if both a & b are even or both a,b are odd, value of c is not given if c is odd then a+b+c would be odd else if c is even then a+b+c would be even 
in sufficient

From 2:
a+c is even: again both a& c can be either odd or even, b is not sure whether its even or odd so a+b+c can be either even or odd
insufficient

From 1& 2:
value of a,b,c are not clear whether all are even or odd so IMO E would be correct.

Bunuel · Answer

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If a, b, and c are integers. Is a + b + c even?

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If a, b, and c are integers. Is a + b + c even?

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