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GRE Practice: Problem Solving Select Many GRE Practice Test 2


Good you are taking our practice tests. But please make sure you complete all the practice problems from Official GRE Guide. Official GRE Guide is from the test makers(Yes You read it right they conduct the GRE exam worldwide.) ETS.:- The Official Guide to the GRE General Test, Third Edition
Powered by GreGuide Version 2.2.1 Copyrights 2007, GreGuide.com

Question 1

Which of the following is a quadratic equation? Indicate all correct options.

  1. (z+1)(z+2)(z+3)(z+4)=9
  2. x2+4x+5=0
  3. y(y+2)+y(y+3)+y(y+4)=y(y+5)
  4. z(2z+3)=0
  5. z(1/2)+5z=32

Correct Answer: B, C and D

Explanation:

(z+1)(z+2)(z+3)(z+4)=9 is a polynomial equation of degree 4.
x2+4x+5=0 is a quadratic equation
y(y+2)+y(y+3)+y(y+4)=y(y+5) is a quadratic equation
z(2z+3)=0 is a quadratic equation
z(1/2)+5z=32 is not a quadratic equation since it contains a term with an irrational power.
B, C and D are quadratic equations.

Question 2

A, B and C can together complete a work in 30 days working 5 hours daily. Which of the following statements is true? Indicate all correct statements.

  1. A completes the work in 10 days working alone for 5 hours daily
  2. B can complete the work in 40 days working alone for 3 hours daily
  3. We cannot determine how many days A and B will take to complete the work, working together for 7 hours daily
  4. We cannot determine how many days A will take to complete the work working alone for 5 hours daily
  5. C will take more than 30 days to complete the work working alone for less than 5 hours daily

Correct Answer: C, D and E

Explanation:

We are given that A, B and C complete the work in 30 days working for 5 hours daily.
We need more information to determine how many days each will take to complete the work working alone.
Options A and B are false and C and D are true.
Option E is true since even if A and B do not contribute towards the work, C shall take at least 30 days to complete it working 5 hours daily. Since he works for less than 5 hours daily, he shall take more than 30 days.

Question 3

Two trains of equal lengths are running on parallel tracks in the same direction. If their speeds differ by 4 km/hr, then which of the following statements is true? Indicate all such statements

  1. They cross each other in 10 minutes if they are 1/3 km long
  2. They cross each other in an hour if each train is a km in length
  3. The time taken by the trains to cross each other is independent of their lengths
  4. The time taken by the trains to cross each other is inversely proportional to their relative speed
  5. The time taken by the trains to cross each other is more than the time they would take if they run in opposite directions

Correct Answer: A, D and E

Explanation:

Time taken by the trains to cross each other = Sum of their lengths/difference of their speeds Option C is false and D is true.

Let the length of each train be x km
Time = 2x/4 = x/2
If x = 1/3 km then time = 1/3/2 = 1/6 = 60/6 minutes = 10 minutes
Option A is true.

If x = 1 km then time = 1/2 hour
Option B is false.

If the trains would run in opposite directions, their speeds would get added.
Hence, they would take lesser time to cross each other than they do when they run in the same direction.
Option E is true.

Question 4

1, 5 and 9 are in AP. Which of the following are in AP? Indicate all correct options.

  1. 5+9, 9+1, 1+5
  2. 1/(5*9), 1/(9*1), 1/(1*5)
  3. 12, 52, 92
  4. 1(1/5+1/9), 5(1/9+1/1), 9(1/1+1/5)
  5. 1/(5+9), 1/(9+1), 1/(1+5)

Correct Answer: A, B and D

Explanation:

A: 5+9, 9+1, 1+5 can be rewritten as 14, 10, 6
6-10=-4 and 10-14 =-4
Option A is true.

B: 1/(5*9), 1/(9*1), 1/(1*5) can be rewritten as 1/45, 1/9, 1/5
1/5-1/9=(9-5)/(5*9)
=4/45
1/9-1/45=(5-1)/45=4/45
Option B is true

C: 12, 52, 92 can be written as 1, 25, 81
81-25=56 and 25-1=24
Option C is not true.

D: 1(1/5+1/9), 5(1/9+1/1), 9(1/1+1/5) can be written as 14/45, 50/9, 54/5
54/5-50/9 = (486-250)/45 = 236/45
50/9-14/45 = (250-14)/45 = 236/45
Option D is true

E: 1/(5+9), 1/(9+1), 1/(1+5) can be written as 1/14, 1/10, 1/6
1/6-1/10 = (10-6)/60 = 4/60
1/10-1/14 = (14-10)/140 = 4/140
Option E is not true.

Question 5

The cost of one orange is equal to the cost of four bananas and the cost of three bananas is equal to the cost of 5 eggs. Which of the following is true? Indicate all correct statements.

  1. 3 oranges and 20 eggs can be purchased for the same price
  2. 3 oranges and 4 bananas cost equal
  3. The ratio of the price of one orange to that of one banana to that of one egg is 15:5:3
  4. Bananas are the costliest
  5. Oranges are the costliest

Correct Answer: A and E

Explanation:

Let the cost of one orange, one banana and one egg be O, B and E respectively.
O = 4B, 3B = 5E
O = 4(5E/3) = 20E/3
Hence, 3O=20E
O:B:E = 4B:B:3B/5
= 4:1:3/5
= 20:5:3
Option C is false, D is false and E is true.

O:E = 20:3
The price of one orange is equal to 20/3 times the price of one egg
3 oranges cost equal to 20 eggs
Option A is true.
O:B=4:1 Option B is false.

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