GRE Math Problem 77

Compare two values:

Column A	Column B
x	y

Solution for GRE Math Problem 76:

The value of this angle can be found as the sum of the angles a and b. As 20 minutes is 1 third of an hour, angle a is one third of 360 degrees, and equals to 120 degrees.
Then, angle b is two thirds of and angle between "11" and "12", then, it is two thirds of 30 degrees, which equals to 20 degrees.
Total 120+20=140 degrees
Answer: C

GRE Math Problem 71

Peter's grade was higher than that of Victor.and Victor's grade was less than that of Georgette.

Column A	Column B
Georgette's grade	Peter's grade

Solution for GRE Math Problem 70:



Area=length x width

New Area=length x (1.25 width) = 1.25 (length x width) = 1.25 Area

Area will increase by 25%.


Answer:(A) 25%

GRE Math Problem 65

a < b

Column A	Column B
ab	a+b

Solution for GRE Math Problem 64:

As we can see, the circle whose diameter is a is located within the square whose side is a for any value of a. So, the square’s area is greater.


Answer: A

GRE Math Problem 63

c and d are positive

Column A	Column B
c	d

Solution for GRE Math Problem 62:
Point (a,b) lays in the quarter where x<0 and y>0. So, a<0 and b>0 and b>a
Answer:B

GRE Math Problem 62

Column A	Column B
a	b

Solution for GRE Math Problem 61:
326(31)-326(19) =326(31-19)=326(12) – here we need not make any calculations, because there is only one answer which is more than 10 times greater than 326

Answer:(A)3,912

GRE Math Problem 53

Column A	Column B
a + b	c + d

Solution for GRE Math Problem 52:
In order to solve this, we should know about similarity of geometry figures. If the dimensions of the rug are in the same ratio as those of the floor, they are called similar rectangles. And the areas of similar figures are in the same ratio as the squares of their linear measures. => The linear measures of similar figures are in the same ratio as the square roots of theis areas. Here we have, that the area of the rug is twice smaller, that the floor, then, its length will be √2 times smaller, than the length of the floor. This gives us

 Answer:(D)

GRE Math Problem 51

Two researchers spent a total of 35 hours on a certain project. One of the researchers spent 25 percent fewer hours on the project than the other.

Column A	Column B
The difference between the number of house spent by each	7

Solution for GRE Math Problem 50:

The sandwich with, let's say, lattuce on onion and the the sandwich with onion on lattuce are different sanwiches. So, to calculate the total number of sandwiches, we should use arrangements, not combinations. number of arrangement of m items out of n ones is A(n,m)=n!/(m-n)!=n*(n-1)*(n-2)*...*(n-m+1) A(4,1)=4 A(4,2)=4*3=12 A(4,3)=4*3*2=24 A(4,4)=4*3*2*1=24 Total 24+24+12+4=64>32. Answer:A

GRE Math Problem 50

A vegetarian sandwich shop has a choice of 4 different sandwich toppings.

Column A	Column B
The number of different types of sandwiches that can be made if at least one topping has to be used and each topping cannot be used more than once.	32

Solution for GRE Math Problem 49:
There is the possibility for m=5 ,n=5, thus m=n. But there also can be m=1, n=25 and m
In general, the relation is unknown.
Answer:D

GRE Math Problem 49

m and n are positive integers mn = 25

Column A	Column B
m	n

Solution for GRE Math Problem 48:
Putting r=0, t=0 we have 0=0. Putting r=1, t=1 we have 10 > 6
Answer: D, unable to determine

GRE Math Problem 48

Compare:

Column A	Column B
5(r +t)	5r + t

Solution for GRE Math Problem 47:
x(x + y) + y(x + y) = (x+y)(x+y) = (x + y)²
Answer:C, they are equal

GRE Math Problem 47

Compare:

Column A	Column B
(x + y)2	x(x + y) + y(x + y)

Solution for GRE Math Problem 46:
(a + 2)(b + 3)=ab+3a+2b+6
(a + 3)(b + 2)=ab+2a+3b+6

Let's find the difference:
(a + 2)(b + 3)–(a + 3)(b + 2) = ab+3a+2b+6 – (ab+2a+3b+6) = a–b

 Since there are no restrictions for a and b, their difference can have any sign, then, answer is D, unable to determine
Answer:D

GRE Math Problem 46

Compare:

Column A	Column B
(a + 2)(b + 3)	(a + 3)(b + 2)

Solution for GRE Math Problem 45:
Just make calculations: 2*3+3*2=12
Answer: (C) 12

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 11

Given: x<y
Compare two values:

Column A	Column B
The average (arithmetic mean) of x and y	The average (arithmetic mean) of x, y, and y

Solution for GRE Math Problem 10:

In 1990 for twice less money we could buy twice more potatoes. So, the cost became 2x2=4 times less than in 1980. So, the price in 1990 was a quarter or 25% of the price in 1980. But the question is “By what percent did the price of potatoes decrease from 1980 to 1990?” Assuming price in 1980 as 100%, we get 100%–25%=75%
Answer:C

Math Problem 4

n is an odd positive integer

Compare two values:

Column A	Column B
The number of prime factors of n	The number of prime factors of 2n

Solution for GRE Math Problem 3:

Lets consider three possibilities: numbers x and y can be bot positive, negative and positive and 0 and 1. (They both can't be negative, because their sum is x+y=1>0).

In the first case, as x>0, y>0, x+y=1, we can say that x<1 and y<1, so their product will be less than 1.

In the second case, the product of positive and negative values is negative, so, less than one.

And for the pair (1;0), xy=0<1. That's why column B is always bigger.

Answer: B

Math Problem 2

Compare two values:

Column A	Column B
65% of a

Solution for GRE Math Problem 1:

Number 19 has only two positive divisors. They are numbers 1 and 19. So, their sum is 1+19=20, and their product is 1x19=19. Column A is bigger.

Answer: A

Math Problem 1

Compare two quantities.

Column A	Column B
The sum of the positive divisors of 19	The product of the positive divisors of 19

For the questions like this the correct answer is
A if the quantity in Column A is greater

B if the quantity in Column B is greater

C if the two quantities are equal

D if it is impossible to determine which quantity is greater