GRE Math Problem 78

In the preceding figure, if l₁||l₂, what is the value of x?

(A) 36 (B)54 (C)90 (D)144 (E) 154

Solution for GRE Math Problem 77:
As the angle between the base of the triangle and the vertical line is not marked, the relation between x and y could be of any value. Answer:D

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 68

 If the area of the triangle BCE is 8, what is the area of the square ABCD?
(A) 4
(B) 8
(C) 16
(D) 22
(E) 82


Solution for GRE Math Problem 67:
As and , then PQRS is a parallelogram. And as PQ=QR, it is a rhomb. Its obtuse angle equals 120 degrees, and the acute angle is 60 degrees. Then, triangle PQR is equilateral and PQ=QR=QP=3
Answer: (C) 3

GRE Math Problem 66

If A is the point (-4, 1) and B is the point (2, 1), what is the area of the circle which has AB as a diameter?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 36


Solution for GRE Math Problem 65:


1 < ab < 2
2 < a+b < 4

So, ab < 2 < a+b


Answer:B

GRE Math Problem 64

a<1

Column A	Column B
The area of a square whose side is a	The area of a circle whose diameter is a

Solution for GRE Math Problem 63:
As

then



Let’s find the difference

Then c

Answer:B

GRE Math Problem 59

The length of each side of a square is
What is the perimeter of the square?
(A) x + 1
(B) 3x + 1
(C) 3x + 4
(D)
(E) It cannot be determined from the information given.

Solution for GRE Math Problem 58:

How much, in dollars, will receive the second one?
240-180 = 60

What is the difference between the amounts received by the two persons?
180-60=120

Answer: (C)$120

GRE Math Problem 55

Column A	Column B
The average (arithmetic mean) of a, b, c, d, e,f, and g	50

Solution for GRE Math Problem 54:
In a right triangle with the catheti of  3 and 4, the hypotenuse is 5. But there is no sign indicating that the triangle shown is the right one. So, c can be both greater than 5 (if the angle between the sides of 3 and 4 is obtuse) and less that 5 (if the angle is accute)
Answer: D

GRE Math Problem 54

Compare:

Column A	Column B
c	5

Solution for GRE Math Problem 53:

As the point (a,b) lays on the positive direction of X axis, a>0, b=0.

As the point (c,d) lays on the negative direction of Y axis, c=0, d<0

Then a + b=a>0 and c + d=d<0 and a + b> c + d

Answer:A

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 40

Column A	Column B
The sum of the areas of two equilateral triangles whose sides are 10	The area of one equilateral triangle whose sides are 20

Solution for GRE Math Problem 39:
If x was 90, AB would be a hypotenuse in the right isosceles triangle and its value would be .
And for x > 90, AB will be even longer.
Answer: A

GRE Math Problem 39

x>90

Column A	Column B
The length of AB	7

Solution for GRE Math Problem 38:
How many three-digit numbers are?
The first digit can be any of 9, the second - any of 10, so does the third. Total 9x10x10=900 combinations.

How many three-digit palindromes are?
The first digit can be any of 9, the second - any of 10, and the third one must be exactly the same as the first, thus, leaving only 1 possibility. Total 9x10x1=90.

The probability that a three-digit number chosen at random is a palindrome is 90x900=0.1
Answer: C

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 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 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 18

If the lengths of two of the sides of a triangle are 9 and 10, which of the following could be the length of the third side?

I. 1 II. 11 III. 21

(A) None

(B) I only

(C) II only

(D) I and II only

(E) I, II, and III

Solution for GRE Math Problem 17:

The amount of money, which employee earned per week is M=40x. As it left the same after the reduction of hours, the new amount of money earned per hour is
Answer:D

Math Problem 6

From the time 6:15 p.m. to the time 7:45 p.m. of the same day, the minute hand of a standard clock describes an arc of
(A) 30°
(B) 90°
(C) 180°
(D) 540°
(E) 910°

Solution for GRE Math Problem 5:

Value in column A is 5x3=15. Value in column B is 2+4x4=18. therefore, column B is greater.

Answer:B