DS1000 S2 Q16,22,23 - need explaination

[joyseychow]

16. What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly 1/2 red.
(2) Each of 3 faces of C is entirely white.

OA:C

22. Each person on a committee with 40 members voted for exactly one of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast?
(1) Candidate F received 11 of the votes.
(2) Candidate H received 14 of the votes.

OA:A

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

OA:B

[gaggleofgirls]

16. What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly 1/2 red.
(2) Each of 3 faces of C is entirely white.

So we need to be able to know what fraction of the surface area of each face is red and then we can combined that to find the fraction of the surface area is red.

1) only tells us about 3 faces but not about the other 3 INSUFFICIENT

2) only tells us about 3 faces but not about the other 3 INSUFFICIENT

1+2 combined) tells us about all 6 faces (since if 3 are part red and 3 are completely white, they can't be the same three faces or overlap in any way). Therefore we have the data we need to determine the fraction.

Answer = C

22. Each person on a committee with 40 members voted for exactly one of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast?
(1) Candidate F received 11 of the votes.
(2) Candidate H received 14 of the votes.

40=F+G+H
We need to know if F>G and F>H

A quick glance 1 and 2 makes you think that you have one equation with 3 variables, so you need two more equations before you can get the answer so you would need both F=11 and H=14 before you could solve (that would give you answer C), but look deeper.

1) If F=11, then 40=11 = G=H
29 = G+H
there is no way to split 29 between two numbers so that neither number is greater than 11 (1+28, 2+27...14+15). F, G and H have to be integers since they represent votes and you can't cast a fraction of a vote.

Since either G or H has to be > F, then we know that F did not win - SUFFICIENT

2) H=14
40-14 = F + G
26 = F + G
26 CAN be split between two numbers in ways that give F the biggest total or not. If split evenly, F=13 and G=13 and H has won. But if split so F=15 and G = 11, the F wins. - INSUFFICIENT

Answer = A

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

The stem tells us that if a then -a
and if a and b then ab

You also have to realize that -a can be b (since it is just another number that is not a),
So, if a then -a and therefore a(-a)

1) 1 is in S
so -1 is in S
so 1(-1) = 1 is in S
We don't know what else is in S, so we still don't know if -4 is in S - INSUFFICIENT

2) 2 is in S
so -2 is in S
so 2(-2) is in S
-4 is in S and that gives us what we want to know - SUFFICIENT

Answer = B

-Carrie

[joyseychow]

16. What fractional part of the total surface area of cube C is red?
(1) Each of 3 faces of C is exactly 1/2 red.
(2) Each of 3 faces of C is entirely white.

So we need to be able to know what fraction of the surface area of each face is red and then we can combined that to find the fraction of the surface area is red.

1) only tells us about 3 faces but not about the other 3 INSUFFICIENT

2) only tells us about 3 faces but not about the other 3 INSUFFICIENT

1+2 combined) tells us about all 6 faces (since if 3 are part red and 3 are completely white, they can't be the same three faces or overlap in any way). Therefore we have the data we need to determine the fraction.

Answer = C

For Statement 1, do we really need to know the other 3 since cube has 6 sides? We know how many sides is red and the total is 6. So, why can't statement 1 be sufficient?