Data Sufficiency

Question 1: This one takes a ridiculous amount of time to solve. Don't try to solve on the test; take a guess and move on.

The two pieces of info given are very similar, so it's not likely to be the case that one works and the other doesn't. So A and B aren't going to be right. C, D, and E should all stay in as possibilities - and just guess. The problem looks like it can't be done, so I wouldn't guess E. (Reverse psychology ) And it just really doesn't seem like one piece of info can get me there, so I'd guess C.

This is a weighted average problem. IF you REALLY understand weighted averages, you'll be able to follow my math explanation below. But don't feel badly if you don't - this is a tough topic and the question is just designed to slow you down - the full math would take way too long to do. So if you don't thoroughly comprehend this topic, just guess and keep going.

The average manager's salary (AM) is 5,000 below the overall average (AE). The average director's salary (AD) is 150,000 above the overall average. If we think of these three numbers on a number line, we can say that they are separated by a certain number of evenly spaced "units."

--AM-AE------------------------------AD--

The distance between AM and AE is 5,000. The distance between AE and AD is 150,000. 150,000/5,000 = 30. So every one tick mark equals 5000 and notice there's one tick between AM and AE and 30 ticks between AE and AD.

This means that, for every 30 managers, there is one director. The % of directors, then, is 1/31. Correct answer is C.

Question 3
The median of 3 positive integers equals the value of the middle term. So the question is whether z is the middle term of the three.

(1) who knows? We could have x = 1, z = 2, y = 3, which makes z the median. Or we could have x = 1, y = 2, z = 3, which makes y the median. Cross off answers A, D.

(2) Yes! This means y and z take up either spots 1 and 2 or spots 2 and 3 in the list of 3 terms. Further, y and z are equal - so the value of z will always be equal to the middle term, even if the middle term happens to be y. (Note that the question didn't ask you if Z is the median itself, but if z is equal to the median.) Answer is B.

Question 4:

Rev = 500,000. Costs = labor + materials. Profit = Rev - costs.
is 500,000 - labor - materials > 150,000 ?
rephrase: is 350,000 > labor + materials ?

(1) (assume this is supposed to say total cost was 3 times cost for materials). This tells us that materials = 1/3 total costs, so labor must be 2/3 total costs. But we don't know what the numbers are. Cross off A, D.

(2) profit was greater than labor cost. Don't know. 500,000 - L - M > L or 500,000 - M > 2L. Labor could be $1, and materials could be 400,000 so profit would be 99,998. Labor could be $1, and materials could be $4, so profit would be 499,995.

(1) AND (2) M = 1/3C, L = 2/3C, and 500,000 - M > 2L.
500,000 - 1/3C > 2(2/3C)
500,000 > 4/3C + 1/3C
500,000 > 5/3C
300,000 > C

So the costs are at least 300,000. So profit is at most 200,000, but they could be below or above 150,000. Can't tell. Answer is E.