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Math Expert V
Joined: 02 Sep 2009
Posts: 64220
If a, b, and c are integers. Is a + b + c even?  [#permalink]

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1 00:00

Difficulty:   25% (medium)

Question Stats: 75% (01:12) correct 25% (01:00) wrong based on 139 sessions

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

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

_________________
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1120
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities)
If a, b, and c are integers. Is a + b + c even?  [#permalink]

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1
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.

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Re: If a, b, and c are integers. Is a + b + c even?  [#permalink]

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1
Bunuel wrote:
If a, b, and c are integers. Is a + b + c even?

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

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

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Re: If a, b, and c are integers. Is a + b + c even?  [#permalink]

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

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

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 64220
Re: If a, b, and c are integers. Is a + b + c even?  [#permalink]

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

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

_________________ Re: If a, b, and c are integers. Is a + b + c even?   [#permalink] 24 Dec 2018, 00:31

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