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If A,B,C are three integers and AB+C is even ; which of the following

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If A,B,C are three integers and AB+C is even ; which of the following  [#permalink]

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New post 03 Aug 2016, 03:48
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (01:52) correct 33% (01:36) wrong based on 207 sessions

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If A,B,C are three integers and AB+C is even ; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even

1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them

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Re: If A,B,C are three integers and AB+C is even ; which of the following  [#permalink]

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New post 03 Aug 2016, 04:49
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stonecold wrote:
If A,B,C are three integers and AB+C is even ; which of the following must be true?
A) A+C is even
B) B+C is even
C) ABC is even

1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them


The question asks what MUST be true. So, we can ELIMINATE any answer choice where we can find an example that makes the statement false.

A) A+C is even
If A = 1, B = 2 and C = 2, then the given statement (AB+C is even) is true.
HOWEVER, statement A is FALSE since A + C = 1 + 2 = 3, and 3 is NOT even.
Since statement A is not necessarily true, we can ELIMINATE answer choices 2 and 4

IMPORTANT: Answer choices 1 and 3 both suggest that statement C is true. So, let's check C

C) ABC is even
If A = 1, B = 1 and C = 1, then the given statement (AB+C is even) is true.
HOWEVER, statement C is FALSE since ABC = (1)(1)(1) = 1, and 1 is NOT even.
Since statement C is not necessarily true, we can ELIMINATE answer choices 1 and 3

This leaves only one answer choice: 5 (aka E)

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Re: If A,B,C are three integers and AB+C is even ; which of the following  [#permalink]

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New post 03 Aug 2016, 06:18
stonecold wrote:
If A,B,C are three integers and AB+C is even ; which of the following must be true?
A)A+C is even
B)B+C is even
C)ABC is even

1) Only C
2) Both A and B
3) Both B and C
4) All of them
5) None of them


Case 1:-

AB+C= Even
E+E= E
O*E + E= E
E*O +E= E

Case 2:-
AB+C= Even
O+O= E
O*O +O= E

A)A+C is even- Only possible with Case 2
B)B+C is even- Only Possible with Case 2
C)ABC is even- Only Possible with case 1

No option is 'MUST BE TRUE'

E is the answer
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Re: If A,B,C are three integers and AB+C is even ; which of the following  [#permalink]

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New post 03 Aug 2016, 07:10
A=odd b=odd c= odd
A/b one of them even or boTh even and c=e
So none of them


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Re: If A,B,C are three integers and AB+C is even ; which of the following  [#permalink]

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New post 26 Feb 2018, 04:41
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Re: If A,B,C are three integers and AB+C is even ; which of the following &nbs [#permalink] 26 Feb 2018, 04:41
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