Area, Members of Club, Candy Manufacturer

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PS 1:

A certain candy manufacturer reduced the weight of candy bar M by 20 percent but left the price unchanged. what was the resulting percent increase in the price per ounce of the candy bar M?

Say, initially the weight of each candy was W pounce and price of each candy was P.
Hence, initial price per ounce of each candy = P/W

After reducing the weight, weight of each candy bar = (W - 20% of W) = 0.8*W
After reducing the weight, price per ounce of each candy bar = P/0.8*W = 5P/4W

Hence, increase in price per ounce of each candy bar = (5P/4W - P/W) = P/4W
Hence, percentage increase in price per ounce of each candy bar = 100*(P/4W)/(P/W) = 100/4 = 25%

The correct answer is E.

PS 2:

Two members of a club are to be selected to represent the club at a national meeting. if there are 190 different possible selections of the 2 members, how many members does the club have?

Say, there are n members.
Then number of different possible selections of the 2 members out of n = nC2

So, nC2 = 190
--> n!/[(n - 2)!*2!] = 190
--> n(n - 1)/2 = 190
--> n(n - 1) = 380

Now we can solve this quadratic for n or we can look for a two-factor factorization of 380 so that the factors are consecutive integer.

As 380 can be expressed as 19*20, n = 20

The correct answer is A.

PS 3:

In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S =

As the triangles are similar, the ratio of their area will be equal to the ratio of the square of their corresponding sides.

So, s²/S² = 1/2
--> S² = 2s²
--> S = √2s

The correct answer is C.