Free GRE Test Practice Test (Page 3 ) & Exam Questions

QUESTION: 6

r > s

Quantity A
r + s

Quantity B

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

Answer(s): C

Explanation:

The expression in Quantity B can be simplified:

Since r > s, we can cancel out r - s in the numerator and denominator, leaving us with:
r + s

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QUESTION: 7

The two circles have centers at B and C, respectively, and are mutually tangent. Each circle has radius r.

Quantity A
The perimeter of quadrilateral ABCD

Quantity B
8r

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

Answer(s): A

Explanation:

The two circles are mutually tangent, meaning they touch at exactly one point.

Each circle has a radius r.

The quadrilateral ABCD consists of two segments (AB and CD) that are straight lines connecting the points where the circles touch the perimeter.
The total length of the perimeter of quadrilateral ABCD can be broken down as:
1. The sum of the lengths of the straight segments AB and CD (each equal to 2r because they are the sum of the radii of the two circles).
2. The length of the arc from the circumference of each circle: since each circle has a radius r, the circumference of each circle is 2r. Half of the circumference will be r, which is the arc length from B to C and from A to D.
Thus, the perimeter of quadrilateral ABCD is:
2r + 2r + r + r = 4r + 2r
Now, compare the two quantities: 4r + 2r (Quantity A) and 8r (Quantity B) Since 2 6.28, we know that 4r + 2r 4r + 6.28r = 10.28r, which is greater than 8r.

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QUESTION: 8

The product of the positive numbers x and y is less than the sum of x and y.

Quantity A
The sum of the reciprocal of x and the reciprocal of y

Quantity B
1

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

Answer(s): A

Explanation:

We are given the inequality:
xy < x + y
We need to compare:
Quantity A: The sum of the reciprocals of x and y, which is:

Quantity B: 1
From the given inequality xy < x + y, dividing both sides by xy (which is positive since x, y > 0) gives:

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QUESTION: 9

In the xy-plane, line segment, RS is one of the sides of square RSTU (not shown).

Quantity A
The area of square RSTU

Quantity B
13

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.

Answer(s): C

Explanation:

The given points are:
· R (0, 2)
· S (3, 0)
Since RS is one side of square RSTU, the side length of the square is d (the result of the distance formula):

Area = side length2