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Math Expert V
Joined: 02 Sep 2009
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Question Stats: 51% (01:29) correct 49% (01:56) wrong based on 83 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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Math Expert V
Joined: 02 Sep 2009
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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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Wont 2(a+b-c) result into an even integer irrespective of the statements below? Thus, making either statement sufficient.
Math Expert V
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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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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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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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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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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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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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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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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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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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Quote which i can relate to.
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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").

Bunuel Please correct me if I am wrong but in the first case when we take a+b-c as 0 then the expression is 0 and the answe is 'no' then how come the answer is A??. take the case of 1,2,and 3 where a+b-c is coming as 0.
Math Expert V
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Midhila 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").

Bunuel Please correct me if I am wrong but in the first case when we take a+b-c as 0 then the expression is 0 and the answe is 'no' then how come the answer is A??. take the case of 1,2,and 3 where a+b-c is coming as 0.

ZERO.

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.
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Midhila 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").

Bunuel Please correct me if I am wrong but in the first case when we take a+b-c as 0 then the expression is 0 and the answe is 'no' then how come the answer is A??. take the case of 1,2,and 3 where a+b-c is coming as 0.

A lot of folks are making this mistake here — if we consistently get an answer of "no", the statement is sufficient.

Data Sufficiency asks us if we can answer a question. It doesn't matter what the answer is, so long as that answer is definitive. In yes/no questions (like this one), getting a "no" in all cases for a statement means that we can definitively answer the question: the answer is no! This means that the statement is sufficient. For a statement to be insufficient, we need to get both a "yes" and a "no".

Given Statement 1, no matter which numbers we select, we will get that $$2(a + b - c)$$ is an even integer — anything multiplied by 2 (an even number) will be even, zero or otherwise. This gives us an answer of "no". There is no case in which we can get a "yes". Thus, there is one definitive answer (no), and the statement is sufficient.

This is the most classic Data Sufficiency mistake in the book, but it's a fundamental misunderstanding of the Data Sufficiency question type, and fixing it should be your highest priority. Half of all Quant questions are Data Sufficiency, so you have to understand this question structure inside and out. I recommend creating a consistent routine for Data Sufficiency questions (mantras, scratch paper organization, etc.) and sticking to it: I personally don't rule a statement insufficient on a yes/no Data Sufficiency question unless I have both a "Y" and an "N" written next to the statement on my scratch paper. Re: M14-36   [#permalink] 11 Jul 2019, 08:20
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