Data Sufficiency

Hey guys. I was wondering if anyone could explain the answers to problems 20 and 23 on Section 2 Practice Test. I knew number 20 could be solved algebraically, but I couldn't come up with the equations. Number 23 just has me completely stumped. Any help would be greatly appreciated!

Here's number 20:

20. The table above gives the number of calories and grams of protein per kilogram of foods S and T. If a total of 7 kilograms of S and T are combined to make a certain food mixture, how many kilograms of food S are in the mixture?
(1) The mixture has a total of 12,000 calories.
(2) The mixture has a total of 810 grams of protein.

Here's number 23:

23. S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?
(1) 1 is in S.
(2) 2 is in S.

Hi Pray,

Cant solve the 1st qn as u havent provided the table.

Regarding the 2nd question,
the questions is whether -4 is in the set.

1) 1 is in th set. Which means -1 is also in the set. We cant proceed any further. INSUFF

2) 2 is in the set. Which means -2 is also in the set. And -4 will also be in the set as 2 x -2 = -4 (Given as the 2nd condition) SUFF

Answer is B

I'd guess that the answer to the 1st question would be D (assuming that S and T have different caloric and protein densities).