If S is a sequence of 2 or more consecutive positive integers and if

As there is 2 or more consecutive num, There will be an even number among this sequence. Hence the product of the nos in the sequence will always be even.


There is an odd number of terms in S (Not necessary to be true) S {3,4}

The sum of the first and last terms in S is equal to the average (arithmetic mean) of the terms in S
Not true.

IMO A

Since we have alternate odd and even numbers, product of any two or more consecutive positive integers will always be even (since one of them will be even e.g. 2 and 3 or 5 and 6 etc)
Hence statement 1 holds.

S may have an odd number of terms or it may have an even number of terms e.g. 2 + 3 = 5 (Even number of terms but sum is odd)
Hence statement 2 is not necessary.

Whenever we have 2 or more consecutive positive integers, the AVERAGE of the first and the last terms is the average of the terms in S. It is also the middle term if we have odd number of terms Or average of middle two terms if we have even number of terms.
Hence statement 3 is not correct.

Answer (A)

The math on each of the options is really easy, so it doesn't matter much on this question, but this question type often gives you an opportunity to be strategic and save time. You do NOT always need to test all of the sentences and then go look for the correct answer. You do NOT need to test them in order. You SHOULD test whichever one is either easiest or will provide the most information. I generally like starting with one that appears in two or three answer choices but not in the other two or three answer choices.

Step 1: Look at the answer choices. 1 appears four times, 2 and 3 each appear three times. Start with either 2 or 3.
Step 2: There is an odd number of terms in S? Not necessarily, as we could have two terms. Eliminate B, D, and E.
Step 3. Look at the answer choices again. 1 is in both remaining answer choices, so testing it will tell us nothing. Test 3.
Step 4. The sum of a smaller number and a larger number will be equal to something smaller than the larger one? Nope. Eliminate C.

Answer choice A.