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# M14-36

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

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15 Sep 2014, 23:54
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Difficulty:

75% (hard)

Question Stats:

45% (01:07) correct 55% (01:10) wrong based on 100 sessions

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Is $$2(a + b - c)$$ an odd integer?

(1) $$a$$, $$b$$, and $$c$$ are consecutive integers

(2) $$b = a + c$$
[Reveal] Spoiler: OA

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15 Sep 2014, 23:54
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$a + b - c$$ is an integer. Thus, $$2(a + b - c)$$ is an even integer.

Statement (2) by itself is insufficient. Consider $$a = b = c = 0$$ (the answer is "no") and $$a = 1.25$$, $$c = -1.25$$, $$b = 0$$ (the answer is "yes").

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30 Jan 2015, 07:01
Wont 2(a+b-c) result into an even integer irrespective of the statements below? Thus, making either statement sufficient.

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30 Jan 2015, 07:37
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Wont 2(a+b-c) result into an even integer irrespective of the statements below? Thus, making either statement sufficient.

No. For example, if a+b-c=1/2, then 2(a+b-c)=1, or if a+b-c=1/3, then 2(a+b-c)=2/3, not an integer at all.
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02 Feb 2015, 05:31
Fantastic question!

Just shows how questions that look so easy are actually so deceptive

Yeah .... even I marked D - Wrong Ans

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12 Apr 2015, 10:29
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$a + b - c$$ is an integer. Thus, $$2(a + b - c)$$ is an even integer.

Statement (2) by itself is insufficient. Consider $$a = b = c = 0$$ (the answer is "no") and $$a = 1.25$$, $$c = -1.25$$, $$b = 0$$ (the answer is "yes").

I understand why answer is D but can't understand why in explanation used such example: $$a = 1.25$$, $$c = -1.25$$, $$b = 0$$ is (the answer is "yes")
We have question "Is $$2(a+b−c)$$ an odd?"
let's put this numbers in the question and we receive: $$2(1.25+0-1.25) = 0 = even$$

I think correct example will be $$a = \frac{1}{4}$$ $$b = \frac{1}{4}$$ and $$c =0$$
$$b = a - c$$ :
$$\frac{1}{4} = \frac{1}{4} - 0$$

and $$2(a+b−c)$$:
$$2(\frac{1}{4}+\frac{1}{4}-0) = 1 = odd$$

Am I miss something or this is misprint in explanation?
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14 Apr 2015, 04:40
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Expert's post
Harley1980 wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. From S1 it follows that $$a + b - c$$ is an integer. Thus, $$2(a + b - c)$$ is an even integer.

Statement (2) by itself is insufficient. Consider $$a = b = c = 0$$ (the answer is "no") and $$a = 1.25$$, $$c = -1.25$$, $$b = 0$$ (the answer is "yes").

I understand why answer is D but can't understand why in explanation used such example: $$a = 1.25$$, $$c = -1.25$$, $$b = 0$$ is (the answer is "yes")
We have question "Is $$2(a+b−c)$$ an odd?"
let's put this numbers in the question and we receive: $$2(1.25+0-1.25) = 0 = even$$

I think correct example will be $$a = \frac{1}{4}$$ $$b = \frac{1}{4}$$ and $$c =0$$
$$b = a - c$$ :
$$\frac{1}{4} = \frac{1}{4} - 0$$

and $$2(a+b−c)$$:
$$2(\frac{1}{4}+\frac{1}{4}-0) = 1 = odd$$

Am I miss something or this is misprint in explanation?

If $$a = 1.25$$, $$c = -1.25$$, $$b = 0$$, then $$2(a + b - c) = 2(1.25+0 -(-1.25)) = 2*2.5=5$$, not 0.
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02 Jan 2018, 02:52
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Another way to solve statement 2.

Is 2(a+b−c) an odd integer?

(2) b=a+c

Put b=a+c in original equation.
2(a+a+c-c)--> 2*2a.
If a= 1/4 then 2*2*1/4 is odd. And if a= any odd or even integer 2*2a will be even. Insufficient.

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Re: M14-36   [#permalink] 02 Jan 2018, 02:52
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# M14-36

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