Data Sufficiency - 53

Answer: D

From statement (1): Square root of a number less than 1 is also less than 1 - sufficient
From statement (2): Reciprocal of any number less than 1 is greater than the number - sufficient

Data Sufficiency - 52

If x is not equal to zero, is 1/x > 1 ?

1) y/ x > y
2) x^3 > x^2

Answer: B

From statement (1): y/x > y
=> y > xy
=> y(1-x) > 0
y>0 when x is less than 1 or y<0 when x is greater than 1 ---- hence insufficient

From statement (2): x^3 > x^2
=> x^2(x-1) > 0
=> x^2 >0 and x>1
Since x>1, 1/x can not be greater than 1 ---- hence sufficient

Hence B

Data Sufficiency - 51

A store purchases 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price, what was the store's gross profit on the 20 coats?

1). If the selling price per coat had been twice as much, the store's gross profit on the 20 coats would have been 2400

2). If the store selling price per coat had been $2 more, the store's gross profit on the 20 coats would have been 440

Answer: B

Suppose the cost of each coat = x

Suppose sales price = y

=> Total cost = 20x and sales price = 20y

We are required to find the profit: 20(y-x).

From statement 1): It is given that 20(2y-x)=2400

Doesn't helps to find out 20(y-x) --- insufficient

From statement 2): It is given that 20(y+2-x) = 440,

=> 20(y-x) = 400 --- sufficient

Hence B

Problem Solving - 56

A certain stock exchange designates each stock with a one- , two-,or three-letter code ,where each letter is selected from the 26 letters of the alphabet. If the letter may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A) 2951

B) 8125

C) 15600

D) 15302

E) 18278

Answer: E

Total ways to pick a 3 letter code = 26*26*26 = 26^3
Total ways to pick a 2 letter code = 26*26 = 26^2
Total ways to pick a 1 letter code = 26

Thus total stocks: 26^3 + 26^2 + 26 = 26(26^2 + 26 + 1) = 18278