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)

GRE Math Problem 28

Because her test turned out to be more difficult than she intended it to be, a teacher decided to adjust the grades by deducting only half the number of points a student missed. For example, if a student missed 10 points, she received a 95 instead of a 90. Before the grades were adjusted the class average was A. What was the average after the adjustment?
(A)
(B)
(C)
(D)
(E)A+25

Solution for GRE Math Problem 27:
The sum of all vertical segments in the path P-R-T equals to the vertical distance between P and T. The sum of all horizontal segments in the path P-R-T equals to the horizontal distance between P and T. The same for the path P-Q-T. So, these paths are equal.
Answer:C

GRE Math Problem 27

All angles are right angles

Compare two values:

Column A	Column B
Distance from P to T via Q	Distance from P to T via R

Solution for GRE Math Problem 26:
The sum of four consecutive odd positive integers can be evaluated as (2n+1)+(2n+3)+(2n+5)+(2n+7)=8n+16=8(n+2). So, it is always divisible by 4
Answer:B

GRE Math Problem 26

The sum of four consecutive odd positive integers is always
(A) an odd number
(B) divisible by 4
(C) a prime number
(D) a multiple of 3
(E) greater than 24

Solution for GRE Math Problem 25:

And again we have the right triangle with legs of 180 and 240. And again we don't have to get square root from 180²+240². We can notice, that 180=3x60 and 240=4x60. So, it is an Egyptian triangle with hypotenuse of 5x60=300 yards.
Answer:(B) 300 yards

GRE Math Problem 25

Paul is standing 180 yards due north of point P. Franny is standing 240 yards due west of point P. What is the shortest distance between Franny and Paul?
(A) 60 yards
(B) 300 yards
(C) 420 yards
(D) 900 yards
(E) 9,000 yards

Solution for GRE Math Problem 24:

According to the Pythagorean theorem, a²+b²=d², where a and b are the sides of the rectangular closet, and d is its diagonal. Also, there is a famous Egyptian triangle with sides 3, 4 and 5: 3²+4²=5² For the given triangle, hypotenuse is and the shorter side is . So, the other side will be feet. So, the area of the closet is square feet.
Answer: (B)27

GRE Math Problem 24

The diagonal of the floor of a rectangular closet is feet. The shorter side of the closet is feet. What is the area of the closet in square feet?
(A)37
(B)27
(C)
(D)
(E)5

Solution for GRE Math Problem 23:

Since and , the product of these two fractions is bigger than 0.333x0.666
Answer:A

GRE Math Problem 23

Compare two values:

Column A	Column B
	(.333)(.666)

Solution for GRE Math Problem 22:

The units digit of a number in the power is influenced by the units digit of the initial number. the units digit of 14 is 4. Then, 4²=16, and the units digit of 14² will be 6. The units digit of 14³ and be found as 6x4=24, it will be 4 again. So, in the odd powers, the units digit of 14 will be 4, and in the vene powers it will be 6.
As for 16, all the powers of the number, which ends with 6, will end wilh 6. Therefore, the columns are equal.
Answer:C