A bit elaborate approach
From statement 1,the product of small and large number is positive.
The possible scenarios are like below,
S1={-1,-2,-3}, +ve
S2={1,2,3},+ve
If it contain both positive and negative integers,statement 1 will not be valid.
Ex:S={-1,2,3},the product is -ve
So Set should contain either all positive or all negative integers.
If the set of integers is as S2,it it sufficient. But for S1 since the number of integers are unknown,statement 1 is insufficient.
From statement 2,there are even number of integers in a set.So the possible scenarios,
S1={-1,2,3,4}=-ve
S2={1,2,3,4}=+ve
Since both scenarios are there statement 2 is insufficient.
Combining both,the conditions are,
1.The sets should contain either all positive integers or all negative integers.
2.There should be even number of intergers.
.So the possible scenarios are,.
S1={-1,-2,-3,-4}
S2={1,2,3,4}
since there are even number of integers,the product of all integers will be positive for both S1 and S2 and sufficient.
Hence answer is C
