Quant Quiz

Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer:

1) if x > y 

2) if x >= y 

3) if x < y

4) if x <= y 

5) if x = y or relationship between x and y cannot be determined.

1. 

I. 20x^2 + 73x + 63 = 0 

II. 16y^2 + 16y + 3 = 0

2. 

I. x^2 – 26x + 165 = 0 

II. y^2 – 36y + 315 = 0

3. 

I. 3x^2 – 32 x + 77 = 0 

II. 2y^2 + 23y + 56 = 0

4. 

I. 63x^2 + 71x + 20 = 0 

II. 45y^2 + 52y + 15 = 0

5. 

I. x^2 + 16x + 63 = 0 

II. 6y^2 – 37y + 52 = 0

6. A fruit seller had some pineapples. He sells 30% of pineapples and still has 350 pineapples. Originally he had how many pineapples?

1) 480 

2) 500 

3) 400 

4) 460 

5) 450

7. P, Q and R hire a penthouse for Rs. 2250. If they used it for 8 hr, 10 hr and 12 hr respectively, the rent paid by R will be:

1) Rs. 800 

2) Rs. 950 

3) Rs. 900 

4) Rs. 850 

5) Rs. 1000

8. Two pipes can fill a tank in 20 hrs and 24 hrs respectively. A third pipe can empty the tank in 40 hours. If all the three pipes are opened and function simultaneously. Then, in how much time the tank will be full?

1) 10 hrs 

2) 15 hrs 

3) 16 hrs 

4) 12 hrs 

5) 18hrs

9. 15 times A is equal to 10 times B. If 10 is subtracted from B it is 22 less than 3 times of A. What is the sum of A and B?

1) 10 

2) 20 

3) 24 

4) 18 

5) 28

10. A train covers 450 km in 6 hours. The speed of bike is half of the speed of train. How much time will the bike take to cover the distance of 300km?

1) 6 hr 

2) 7.5 hr 

3) 7 hr 

4) 10 hr 

5) 8 hr

1. 3;

I. 20x^2 + 45x + 28x + 63 = 0

(5x + 7) (4x + 9) = 0

x = -7/5, 9/4

II. 16y^2 + 12y + 4y + 3 = 0

(4y +1) (4y +3) = 0

y = -1/4, -3/4

x < y

2. 4;

I. x^2 – 15x – 11x + 165 = 0

or, (x – 11) (x – 15) = 0

or, x = 11, 15

II. y2 – 21y – 15y + 315 = 0

or, (y – 15) (y – 21) = 0

or, y = 15, 21

x <= y

3. 1;

I. 3x^2 – 21x – 11x + 77 = 0

or, (3x – 11) (x – 7) = 0

x = 11/3, 7

II. 2y^2 + 16y + 7y + 56 = 0

or, (2y + 7) ( y + 8) = 0

y = -7/2,–8

x > y

4. 5;

I. 63x^2 + 35x + 36x + 20 = 0

(7x +4) (9x + 5) = 0

x = -4/7, -5/9

II. 45y^2 + 27y + 25y + 15 = 0

(9y + 5) (5y + 3) = 0

y = -5/9, -3/5

No relationship between x and y exists

5. 3;

I. x^2 + 9x + 7x + 63 = 0

(x + 7) (x + 9) = 0

x = –7, –9

II. 6y^2 – 24y – 13y + 52 = 0

(6y – 13) ( y – 4 ) = 0

y = 13/6, 4

x < y

6. 2;

Let the total number of pineapple be x

70/100 x = 350

x = 350 * 100/70 = 500

7. 3;

Ratio of their uses = 8 : 10 : 12 = 4 : 5 : 6

Rent paid by R = 6/15 * 2250 = Rs. 900

8. 2;

Part of tank filled in 1 hour

1/20 + 1/24 - 1/40 = 15

Thus, required time for the tank to be filled = 15 hrs.

9. 2;

15 A = 10 B

3A = 2B

Now, B – 10 = 3A – 22

or, B – 10 = 2B – 22 or, (Put 3A = 2B)

or, B = 12

A = 2*12/3 = 8

Required sum = 20

10. 5;

Speed of train = 450/6 = 75 km/hr

Speed of bike = 75/2 = 37.5 km/hr

Time taken by bike = 300/37.5 = 8 hour