Is 49 in the set S?

First there is no mention of how many numbers are there in the setS.

However, if you combine the two

You get that the if there is only one number in the set it will have to be 49 OR (49*49)

S1. Multiple of 7 S2. Squares of numbers

IMO E

IMO E
clearly
(1) does not give any range or any info : hence 49 may or may not be present => innsufficient
(2) does not mention the range => insufficient

(1) and (2) => multiple of 7 and square number => can be 7*7,7*(7*7*7) ...etc hence again range is important to be known => no unique answer => insufficient
(E) is the valid choice

The trick in the question is its wording.

(1) All numbers in set S are multiples of 7.

Here, some will read the statement and interpret it in the following way 'All multiples of 7 are in set S.' which is definitely not what is given. What is given is that every element of the set S is a multiple of 7 so as an example, S could be {7, 0, -14, 28}... every element is a multiple of 7 but the set does not have all multiples of 7.

(2) All numbers in set S are square numbers.

Exact pitfall in this statement too. Some will read the statement and interpret it in the following way 'All perfect squares are in set S.' which is definitely not what is given. What is given is that every element of the set S is a perfect square but the set does not have all perfect squares.

So people would be replying with 2 most common answers to this question - (D) the most popular incorrect answer
(E) the correct answer

(1) All numbers in set S are multiple of 7.
S={21,35} or {7,14,21,28,35,42,49,56} ==> Insufficient

(2) All numbers in set S are square numbers.
S={4,16,64,100} or {1,9,25,49,81,121} ===> Insufficient

Merging both
Our set should have (multiple of 7)\(^2\)
S={\(7^2(49),14^2,21^2\)} or {\(77^2,700^2,35^2\) }==>Still Insufficient

Answer is E

could zero be in the set?

Yes, because 0 is both a multiple of 7 (0/7 = integer) and square of an integer (0 = 0^2).