M14-36

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.

Answer: A

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.

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.

I don't agree with the explanation. what if a, b and C are consecutive negative integers. We might get 2(a+b-c) as a negative integer? Then we do not know whether it will be even/odd. Please explain.

Even integer is an integer which is divisible by 2 without a remainder, so ..., -4, -2, 0, 2, 4, 6, ... are all even numbers.
Odd integer is an integer which is NOT divisible by 2, so ..., -5, -3, -1, 1, 2, 5, ... are all odd numbers.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

We are asked whether \(2(a+b-c)\) is odd int or not?
S1: a,b,c are consecutive integers, which means any addition, subtraction, multiplication done with a,b,c will result in integer. Thus (a+b-c) will be int, and any 2*int = always even integer.
Thus this expression will never be odd int.
S1 sufficient.

S2: \(b=a+c\)
Here 2 cases will be there.
1) a,b,c are int. Then it again is the same case as S1, and expression will always be even, and again the answer will No.
2) a,b,c are not int.
Let us simplify the expression first. i.e (a+b-c) will be 2a [given information in S2].
Let a=1/3 , then \(2(a+b-c)\) will give a fraction value i.e neither odd nor even.
but if a=1/2, then \(2(a+b-c)\) will give answer as 1 i.e odd. Thus we get different values in different cases. Thus S2 not sufficient.
Answer is A.