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# M14-36

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:54
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Difficulty:

75% (hard)

Question Stats:

43% (01:06) correct 57% (01:09) wrong based on 115 sessions

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

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

(2) $$b = a + c$$

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Joined: 02 Sep 2009
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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
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
1
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
1
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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SandySilva

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12 May 2018, 21:57
Hello,

The explanation given by Bunuel, is very short and need more background.

We all know that any number multiplied by 2 is an Even Number, so it might seem like the question stem has the answer in itself, but do note that the question says, Even Integer , so if any of the variable in the given expression is a fraction, then the answer is No and variable is an Integer than Yes.

Statement 1 :- This statement clarifies that the variable in the expression are Integers, so sufficient

Statement 2: The expression: b = a+c, means a= b-c, replacing this in the question stem: therefore 2(a+a), but we dont know whether "a" is an integer or not, so not sufficient.
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03 Feb 2019, 11:03
Guys, what if consecutive integers in S1 are 1, 2 and 3? Then we have 2*(1+2-3)=0 and thus option A is insufficient?
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03 Feb 2019, 11:14
Bunuel wrote:
Is $$2(a + b - c)$$ an odd integer?

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

(2) $$b = a + c$$

1) a , b and c are consecutive integers, This will give value as a No for all the test cases

1,2,3
3,2,1

2) b = a+c

2 (2a)

4a, now a can be 1/4 which will answer the question as a Yes

or a = 1, which will answer the question as a No

A
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Director
Joined: 09 Mar 2018
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03 Feb 2019, 11:15
lenakuz wrote:
Guys, what if consecutive integers in S1 are 1, 2 and 3? Then we have 2*(1+2-3)=0 and thus option A is insufficient?

Hi lenakuz

It wont be insufficient, it will answer the question as a No

is 0 an odd integer, No it is an even integer.
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Re: M14-36   [#permalink] 03 Feb 2019, 11:15
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# M14-36

Moderators: chetan2u, Bunuel

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