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Joined: 12 Aug 2015
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Schools: Boston U '20 (M)
GRE 1: Q169 V154 If A,B,C are three integers and AB+C is even ; which of the following  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (01:50) correct 34% (01:39) wrong based on 181 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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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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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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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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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

Since AB + C is even, we can have:

Case 1: A, B, and C are all odd,

or

Case 2: A, B, and C are all even,

or

Case 3: A is odd and B and C are even,

or

Case 4: B is odd and A and C are even.

Now let’s analyze the three given statements.

If it’s case 3, A + C is odd and thus it’s not even.

If it’s case 4, B + C is odd and thus it’s not even.

If it’s case 1, ABC is odd and thus it’s not even.

Thus, none of the scenarios have to be true.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If A,B,C are three integers and AB+C is even ; which of the following   [#permalink] 11 Aug 2019, 19:47
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If A,B,C are three integers and AB+C is even ; which of the following

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