GRE Math Problem 35

Given:
a²=b,
a>0

Compare two values:

Column A	Column B

Solution for GRE Math Problem 34:
To divide a number by a power of 10 we should remove as amany zeroes, as the respected power of ten has. So, the first fraction can be reduced by dividing the nominator and denominator by 10, and the second one - by 1000. The both will equal to
Answer: C, they are equal.

GRE Math Problem 34

Compare two values:

Column A	Column B

Solution for GRE Math Problem 33:

The number of men is 3x and the nuber of women is 2x employees. Total 5x = 240. Then, x = 48 and 3x = 144.

Answer: (D) 144

GRE Math Problem 33

 In a certain company, the ratio of the number of women employees to the number of men employees is 3 to 2. If the total number of employees is 240, then how many of the employees are men?
(A) 40
(B) 48
(C) 96
(D) 144
(E) 160


Solution for GRE Math Problem 32:
The surface area of the cube with edge of 3 is 6x3²=54 square inches. The surface area of the smaller cube with the edge of 1 will be 6x1²=6 square inches. From one cube 3x3x3 we'll get 3³=27 cubes 1x1x1, their total surface area will be 27x6=162 square inches. the unpainter area is 162-54=108<100
Answer:Column A is greater.

GRE Math Problem 32

A wooden cube whose edges are 3 inches is painted red.
The cube is then cut into 27 cubes whose edges are 1 inch.

Column A	Column B
The total surface area of all of the unpainted faces	100 square inches

Solution for GRE Math Problem 31:
10¹⁰⁰=2¹⁰⁰x5¹⁰⁰, therefore, it is divisible by 5⁷⁵, but not divisible by 75⁵=5⁵x3¹⁰. That's why the first remainder will be 0, and the second one will be greater than 0.
Answer: Columb B is greater

GRE Math Problem 31

Compare two values:

Column A	Column B
The remainder when 10100 is divided by 575	The remainder when 10100 is divided by 755

Solution for GRE Math Problem 30:
The average of three digits is 2 means, that their sum is 6. There are 7 tripples of digits with the sum of 6. they are: 6,0,0; 5,1,0; 4,2,0; 4,1,1; 3,3,0; 3,2,1; 2,2,2.
6,0,0 gives only one 3-digit number: 600.
For 5,1,0 we have 510, 501, 150, 105.
For 4,2,0: 420, 402, 240, 204.
For 4,1,1: 411, 141, 114.
For 3,3,0: 330, 303.
For 3,2,1: 321, 312, 231, 213, 123, 132.
For 2,2,2: 222.
Total 21 numbers.
Answer: Column A is greater.

GRE Math Problem 30

Compare two values:

Column A	Column B
The number of positive three-digit numbers for which the average (arithmetic mean) of the three digits is equal to 2	20

Solution for GRE Math Problem 29:

Answer:(E)

GRE Math Problem 29

What is the average (arithmetic mean) of 3³⁰, 3⁶⁰, and 3⁹⁰?
(A) 3⁶⁰
(B)3¹⁷⁷
(C)3¹⁰ + 3²⁰ + 3³⁰
(D) 3²⁷ + 3⁵⁷ + 3⁸⁷
(E)3²⁹+3⁵⁹+3⁸⁹

Solution for GRE Math Problem 28:

Is the class average before the adjustment was A, then the average of missed points was 100-A. After the adjustment, the average of missed points became . So, the average of points gained became
Answer:(A)