GRE /GMAT : Quantitative Comparison with solution

Directions:

In this section you will be given two quantities, one in column A and one in column B. You are to determine a relationship between the two quantities and mark.

1. If the quantity in column A is greater than the quantity in column B.
2. If the quantity in column B is greater than the quantity in column A.
3. If the quantities are equal.
4. If the comparison cannot be determined from the information that is given.

1. Quantity A: (-6)⁴ 
   Quantity B: (-6)⁵
1. if the quantity A is greater;
2. if the quantity B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : A

Soln:  ( -6)⁴  =(-1 * 6)⁴ = (-1)⁴  * 6⁴ =  (-1)² * (-1)²   * 6⁴ =6⁴

               (-6)⁵ = (-1)⁵ * 6⁵  = -1 * 6⁵ =-6⁵

So Ans is A

2. Quantity A: Time to travel 95 miles at 50 miles per hour 
   Quantity B: Time to travel 125 miles at 60 miles per hour
1. Quantity A is greater
2. Quantity A equals Quantity B
3. Quantity B is greater
4. Relationship Indeterminate

Ans : C

Soln : Time = Distance/Speed

          For Case A     Time= 95/ 50 = 1.

          For Case B      Time= 125/60=2.

          So B>A

3. Quantity A: (9/13)² 
   Quantity B: (9/13)^1/2
1. Quantity A equals Quantity B
2. Relationship Indeterminate
3. Quantity B is greater
4. Quantity A is greater

Ans : C

  Soln :  a^1/m  = ^m√a

For Case A it is (9/13)²

For Case B it is (9/13)^1/2 = √(9/13)  

So B>A

4. Quantity A: 4 / 100 
   Quantity B: 0.012 / 3
1. Quantity B is greater
2. Quantity A equals Quantity B
3. Quantity A is greater
4. Relationship Indeterminate

Ans : C

    For Case A  :  4/100=0.04

   For Case B : 0.012 / 3 = 0.04

So A=B

5. x = 2y + 3 
   y = -2

Quantity A: x 
Quantity B: -1

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given

Ans : C

x=2y+3 = 2(-2)+3 = -1

So both quantities are equal.

6. x + 2y > 8

Quantity A: 2x + 4y 
Quantity B: 20

1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : D

x+2y > 8 => 2(x+2y) > 2(8)

  2x+4y > 16

So the relationship cannot be determined from the information given

7. Quantity A: The number of months in 7 years 
   Quantity B: The number of days in 12 weeks
1. if the quantity in Column A is greater;
2. if the quantity in Column B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given

Ans : C

The no of months in 7 years = 7* 12 months = 84 months

The no of days in 12 weeks = 12* 7 days = 84 days

So two quantities are equal.

8. Quantity A: 1-1/27 
   Quantity B: 8/9 + 1/81
1. if the quantity in is greater;
2. if the quantity in is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : A

Case A 1-1/27 = 27-1/27 = 26/27=0.96

Case B 8/9 + 1/81

LCM of 9 and 81 is 81

So 8/9 + 1/81 = (8*9 +1)/81 = 73/81 =0.90

So A>B

9. r>s>0

Quantity A: rs/r 
Quantity B: rs/s

1. if the quantity A is greater;
2. if the quantity B is greater;
3. if the two quantities are equal;
4. if the relationship cannot be determined from the information given.

Ans : B

Case A rs/r and case B is rs/s

It is given that r>s

If you divide the same quantity by a smaller no the result will be greater.

10. Quantity A: 0.83 
    Quantity B: 0.81/3
1. Quantity B is greater
2. Relationship Indeterminate
3. Quantity A is greater
4. Quantity A equals Quantity B

Ans : C

Case A  0.83

Case B is 0.81/3 = 0.27

So A>B