flowstar86 wrote:If a and b are positive integers, is the product ab odd?

(1) b = 3
(2) a and b are consecutive integers

Yes, this is an example of those DS problems, in which you have to answer the question in YES or NO.

Statement 1: b = 3
If a = odd, then ab = odd
If a = even, then ab = even

Not sufficient

Statement 2: As a and b are consecutive integers, one of them must be always even and other is odd. The product of an odd and an even integer is always even. Hence, we can definitely answer the question in NO.

Sufficient

The correct answer is B.

flowstar86 wrote:If a and b are positive integers, is the product ab odd?

(1) b=3

(2) a and b are consecutive integers



My first idea was (E) but according to my book its (B). when i think about it (2) is sufficient to say that ab = even so its just asked if (1) and/or (2) is enough to say yes/no to the question right? --> we know with (2) that ab is even and so we can say that ab is not odd and therefore (B) is the right answer?

sry i dont really got the problem type

Hi Flowstar86!

You definitely are NOT alone by feeling confused with Data Sufficiency Yes/No questions; they can be tough to wrap your head around! It might take a little mulling over, but we want to remember that Data Sufficiency is all about getting A SINGLE answer but not about what that specific answer might be.

For the standard Value question ("how old is Issac?"), we are looking for a single number to spit out of the problem ("Issac is 28 years old"). But when the question is looking for a Yes/No type answer ("Is ab odd?"), we need to determine what it means to get ONE answer. So, if we answer YES and only yes - then that is a single answer (sufficient). But when we answer NO and only no - then that is also a single answer (sufficient). The only insufficient answer would be "Maybe!"

Humans have a real "Yes" bias in that we always want Yes to mean Correct, Right or Good ("Can I have a raise?", "will you marry me?"...we love our Yes answers don't we!!). But in the world of Data Sufficiency we are indifferent to the Yes or No, just that we can only answer in one way.

So just as you noted, Statement (1) tells us that b=3. If a were to equal something like 5, then our answer to the stem would be Yes. But if a were to equal 2, then the answer to the stem would be No. So Statement (1) tells us that MAYBE ab is odd or MAYBE ab is even...we cannot be sure if the answer is Yes or No...INSUFFICIENT.

But Statement (2) says that a and b are consecutive, meaning that one is even and one is odd. So this means that the product will always be an even number. Therefore Statement (2) tells us that we KNOW that ab is NOT odd, so we have sufficient information to give a single answer to the question (it just happens that the answer is NO). SUFFICIENT

**A final note to consider while studying - try to use terminology in the way I did above (saying insufficient and sufficient as opposed to "Statement (1) is wrong" or simply saying "No" after testing a statement). It might help you keep a clear distinction between Sufficient/Insufficient and Yes/No/Correct/Incorrect.**

Hope this helps clear up the confusion a bit!

Whit