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Is ABC an odd integer?

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Is ABC an odd integer? [#permalink]

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New post 17 Sep 2017, 12:48
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

36% (00:36) correct 64% (00:40) wrong based on 48 sessions

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Is ABC an odd integer?

1. AB is an even integer
2. BC is an even integer
[Reveal] Spoiler: OA

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we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
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Last edited by bkpolymers1617 on 19 Sep 2017, 11:00, edited 1 time in total.

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Re: Is ABC an odd integer? [#permalink]

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New post 17 Sep 2017, 12:52
Bunuel : Can you help? I don't have the official explanation, but believe that the answer is C. Please let me know if that is correct. I can prove it, but it would be great if it comes from an expert. Thanks
_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

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Re: Is ABC an odd integer? [#permalink]

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New post 17 Sep 2017, 14:59
IMO, Answer should be D.

1. St. 1 - AB is even - A term of the form (even no. * X ) will always be even. Hence , its even. Suff.
2. St 2- BC is even - same - Suff.

Kudos, if it helps.

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Re: Is ABC an odd integer? [#permalink]

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New post 17 Sep 2017, 20:23
D can not be tge answer. You are assuming that A, B and C are integers which is not true. Can be fractions as well, in which case, we will get scenarios in which they are not integers. So choice d is 100% incorrect
_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

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Re: Is ABC an odd integer? [#permalink]

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New post 19 Sep 2017, 10:12
Hey Everyone, so here is the explanation:

1. AB is even- Insufficient. Say AB=2, and C =3/2, then ABC is what ? An odd number. Now take another scenario, take AB=4, C=6. ABC is what? An even number. Hence insufficient. Those who assumed that C is an integer must have believed that A is sufficient.

2. BC is even- Insufficient. Say BC=2, and A = 3/2, then ABC is what ? An odd number. Now take another scenario, take BC=4, A=6. ABC is what? An even number. Hence insufficient. Those who assumed that A is an integer must have believed that B is sufficient.

Now combined, we are sure that one of the 3 numbers is surely an integer. If you multiply ABC in any way, you will have only 2 situations-
1. either ABC is not an integer itself
2. Or ABC is an even integer.

But in no case, would ABC be an odd integer. Hence C is the answer
_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

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Re: Is ABC an odd integer? [#permalink]

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New post 19 Sep 2017, 10:56
bkpolymers1617 wrote:
Is ABC an odd integer?

1. AB is an even integer
2. BC is an even integer



C cant be the answer. The answer should be E

Let us take 2 cases
Case 1. a=1/2,b=4, c=1/2
Case 2 a=1/2, b=8., c=1/2

Now use both the statements,

One of the cases will be even integer and other will give odd.

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Re: Is ABC an odd integer? [#permalink]

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New post 19 Sep 2017, 10:59
KS15 wrote:
bkpolymers1617 wrote:
Is ABC an odd integer?

1. AB is an even integer
2. BC is an even integer



C cant be the answer. The answer should be E

Let us take 2 cases
Case 1. a=1/2,b=4, c=1/2
Case 2 a=1/2, b=8., c=1/2

Now use both the statements,

One of the cases will be even integer and other will give odd.



Thanks for posting this. I ll correct this. I had asked the experts, but since there was no revert, I gave my thoughts. I ll change the OA. Thanks
_________________

we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender!

Kudos [?]: 184 [0], given: 33

Re: Is ABC an odd integer?   [#permalink] 19 Sep 2017, 10:59
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