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# Is 2(a+b-c) an odd integer? 1. a, b and c are consecutive

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Is 2(a+b-c) an odd integer? 1. a, b and c are consecutive [#permalink]  07 May 2010, 09:32
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Question Stats:

91% (02:11) correct 9% (01:49) wrong based on 40 sessions
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  07 May 2010, 10:21
ykaiim wrote:
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?

You forgot to multiply the -1 by 2

2(a+b-c)
2(0+1-2)
2(-1) = -2

or 2a + 2b - 2c
2(0) + 2(1) - 2(2)
2-4 = -2

Is the question correct? Multiplying anything by 2 will never give an odd so the question states the answer. In which case you wouldn't need to test 1 or 2
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  07 May 2010, 16:07
lagomez wrote:
ykaiim wrote:
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?

You forgot to multiply the -1 by 2

2(a+b-c)
2(0+1-2)
2(-1) = -2

or 2a + 2b - 2c
2(0) + 2(1) - 2(2)
2-4 = -2

Is the question correct? Multiplying anything by 2 will never give an odd so the question states the answer. In which case you wouldn't need to test 1 or 2

I agree with lagomez. any number x 2 = Even
Something must be wrong
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  07 May 2010, 17:11
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Expert's post
ykaiim wrote:
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?

$$2(a+b-c)$$ can be:
odd, in case $$a+b-c=\frac{odd}{2}$$;
even, in case $$a+b-c=integer$$
not an integer at all, in case $$a+b-c$$ does not equal to any above. For example: $$a+b-c=\sqrt{2}$$ or $$a+b-c=0.3$$.

Guess statement (1) is saying: "a, b and c are consecutive integers". The word "consecutive" is redundant here. Just knowing that "a, b and c are integers" is enough to say that this statement is sufficient to answer the question. And the answer would be NO: a, b and c are integers --> $$a+b-c=integer$$ --> $$2(a+b-c)=even$$.

Statement (2) is clearly not sufficient.
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  07 May 2010, 17:31
Bunuel wrote:
ykaiim wrote:
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?

$$2(a+b-c)$$ can be:
odd, in case $$a+b-c=\frac{odd}{2}$$;
even, in case $$a+b-c=integer$$
not an integer at all, in case $$a+b-c$$ does not equal to any above. For example: $$a+b-c=\sqrt{2}$$ or $$a+b-c=0.3$$.

Guess statement (1) is saying: "a, b and c are consecutive integers". The word "consecutive" is redundant here. Just knowing that "a, b and c are integers" is enough to say that this statement is sufficient to answer the question. And the answer would be NO: a, b and c are integers --> $$a+b-c=integer$$ --> $$2(a+b-c)=even$$.

Statement (2) is clearly not sufficient.

What numbers can be substituted for A, B, and C and when multiplied by 2 gives you an odd integer?
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  07 May 2010, 17:49
1
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Expert's post
lagomez wrote:
Bunuel wrote:
ykaiim wrote:
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?

$$2(a+b-c)$$ can be:
odd, in case $$a+b-c=\frac{odd}{2}$$;
even, in case $$a+b-c=integer$$
not an integer at all, in case $$a+b-c$$ does not equal to any above. For example: $$a+b-c=\sqrt{2}$$ or $$a+b-c=0.3$$.

Guess statement (1) is saying: "a, b and c are consecutive integers". The word "consecutive" is redundant here. Just knowing that "a, b and c are integers" is enough to say that this statement is sufficient to answer the question. And the answer would be NO: a, b and c are integers --> $$a+b-c=integer$$ --> $$2(a+b-c)=even$$.

Statement (2) is clearly not sufficient.

What numbers can be substituted for A, B, and C and when multiplied by 2 gives you an odd integer?

Note that stem does not say that a, b and c are integers.

So for example: a=3/2, b=0, c=0 --> $$2(a+b-c)=3$$. As I said if $$a+b-c=\frac{odd}{2}$$, then $$2(a+b-c)=2*\frac{odd}{2}=odd$$. This option is ruled out by statement (1), which says that a, b and c are integers.

Hope it's clear.
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  07 May 2010, 21:13
Thanks Bunuel.

I think I need some revision also on Number Properties.
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  08 May 2010, 03:56
Bunuel wrote:
ykaiim wrote:
Is 2(a+b-c) an odd integer?

1. a, b and c are consecutive numbers
2. b=a+c

The OA is A. But, I think it is incorrect.
Case1: 0,1,2 the a+b-c = -1 (Yes)
Case2: 1,2,3 the a+b-c = 0 (No)

Can someone tell me where I am wrong?

$$2(a+b-c)$$ can be:
odd, in case $$a+b-c=\frac{odd}{2}$$;
even, in case $$a+b-c=integer$$
not an integer at all, in case $$a+b-c$$ does not equal to any above. For example: $$a+b-c=\sqrt{2}$$ or $$a+b-c=0.3$$.

Guess statement (1) is saying: "a, b and c are consecutive integers". The word "consecutive" is redundant here. Just knowing that "a, b and c are integers" is enough to say that this statement is sufficient to answer the question. And the answer would be NO: a, b and c are integers --> $$a+b-c=integer$$ --> $$2(a+b-c)=even$$.

Statement (2) is clearly not sufficient.

totally right
I assumed that a, b and c were integers
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Re: GmatClub Test: Number Properies - I (DS) [#permalink]  16 May 2010, 14:22
yup A must be the ans
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Re: Is 2(a+b-c) an odd integer? 1. a, b and c are consecutive [#permalink]  08 Nov 2013, 11:38
If we substitute b = a + c in 2(a+b-c), we get 4a. Now, whatever the value of a, the outcome will always be even. This statement should be sufficient too. In my opinion, the answer should be D.

I am not sure that whether what I have done is correct but, this is what came to my mind when I was attempting this question; I marked D.
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Re: Is 2(a+b-c) an odd integer? 1. a, b and c are consecutive [#permalink]  09 Nov 2013, 01:47
Expert's post
AasaanHai wrote:
If we substitute b = a + c in 2(a+b-c), we get 4a. Now, whatever the value of a, the outcome will always be even. This statement should be sufficient too. In my opinion, the answer should be D.

I am not sure that whether what I have done is correct but, this is what came to my mind when I was attempting this question; I marked D.

is-2-a-b-c-an-odd-integer-1-a-b-and-c-are-consecutive-93832.html#p722067
is-2-a-b-c-an-odd-integer-1-a-b-and-c-are-consecutive-93832.html#p722073

The correct answer is A, not D.
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Re: Is 2(a+b-c) an odd integer? 1. a, b and c are consecutive   [#permalink] 09 Nov 2013, 01:47
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