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GRE Practice Test

GRE Practice: Problem Solving GRE Practice Test 5


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Question: 1

A cylinder's diameter is reduced to one-third. The volume remains the same. How many times will the length become? Indicate the correct option.

  1. 3
  2. 6
  3. 5
  4. 12
  5. 9

Correct Answer: E

Explanation:

Let the initial length be l and new length be l'.

Let the original diameter be 6r and radius be 6r/2=3r.

The new diameter will be 6r/3=2r and radius will be 2r/2=r

Volume=π*(3r)2*l = pi*r2*l'

9r2*l=r2*l'

9l=l'

The length becomes 9 times itself.

Option E is true.

[π=22/7]

Question: 2

If x+1/x=4, then which of the following is the value of x2+1/x2? Indicate the correct option.

  1. 16
  2. 4
  3. 18
  4. 12
  5. 14

Correct Answer: E

Explanation:

x+1/x=4

(x+1/x)2=x2+1/x2+2*x*1/x

x2+1/x2=(x+1/x)2-2

=42-2=16-2=14

Option E is correct.

Question: 3

Triangle ABC is right angled at A. AL is drawn perpendicular to BC. Which of the following is true? Indicate the correct option.

  1. Angle ABC = Angle ACB
  2. Angle BAL = Angle ALC
  3. Angle ACL = Angle ABL
  4. Angle BAL = Angle ACB
  5. Angle ALB = Angle ACB

Correct Answer: D

Explanation:

Options A and C need not be true and hence they are incorrect.

Option B is false as angle ALC is a right angle while angle BAL is an acute angle.

Similarly option E is false.

We check option D now.

In triangle ABL,

angle BAL+angle ALB+angle B=180

angle BAL+90+angle B=180

angle BAL+angle B=90

angle BAL=90-angle B ...(1)

In triangle ABC,

angle A + angle B + angle C = 180

90 + angle B +angle C = 180

angle B + angle C = 180-90=90

angle ACB=90-angle B ...(2)

From (1) and (2), we conclude that option D is true.

Question: 4

Pam has a field in the shape of a polygon with 10 sides. Into how many triangular fields can she cut her field so that she can access each field from the same vertex? Indicate the correct option.

  1. 3
  2. 5
  3. 7
  4. 8
  5. 9

Correct Answer: D

Explanation:

A polygon with n sides can be cut into (n-2) triangles with a common vertex.

The bigger field with 10 sides can be cut into (10-2)=8 triangular fields with a common vertex.

Option D is true.

Question: 5

What is the area enclosed by the points (1,4), (4,-2) and (9,-12)? Indicate the correct option.

  1. 0
  2. 24
  3. 38
  4. 26
  5. 36

Correct Answer: A

Explanation:

(1,4), (4,-2), (9,-12) are the three points.

Area = 1/2[1*(-2)-4*4+4*(-12)-(-2)*9+9*4-1*(-12)]

=1/2[-2-16-48+18+36+12]

=1/2(0)=0

Option A is true.

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