Quant Quiz

1. The sum of four consecutive even numbers is 260. What would be the smallest number?

(1) 60           

(2) 64           

(3) 62           

(4) 66           

(5) 70

2. The marked price of an article is Rs. 680. After two successive discounts it is sold for Rs. 408 if the first discount is 25 % then the rate of second discount is

(1) 15%          

(2) 20 %         

(3) 30 %

(4) 25 %         

(5) None of thes

3. If 5 litres of water are evaporated on boiling from 20 litres of salt solution containing 20 percent salt. The percentage of salt in the remaining solution is

(1) 26.67        

(2) 22.5         

(3) 24.33

(4) 13           

(5) None of these

4. A cistern is half full of water. Pipe A can fill the remaining part in 3 minutes and pipe B in 5 minutes. Once the cistern is emptied, how much time will they take to fill it together completely?

(1) 3 minutes    

(2) 3 min, 30 sec 

(3) 3 min, 45 sec

(4) 4 min        

(5) None of these

5. Volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. The ratio of their height is

(1) 1: 5         

(2) 5: 4         

(3) 5: 16  

(4) 25 :64       

(5) None of these

Directions—(Q. 6–10) In the following questions two equations numbered I and II are given. You have to solve both the equations and answer accordingly -

Give answer If

(1) x > y  

(2) x ≥ y        

(3) x < y

(4) x ≤ y        

(5) x = y or the relationship can’t be established

6.

I. x^2 – 4 = 0               

II. y^2 + 5y + 6 = 0

7.   

I. x^2 – 9x + 18 = 0         

II. y^2 – 13y + 42 = 0

8.   

I. x^3 – 62 = 63       

II. y^3 – 123 = 93

9.   

I. 7x + y = 22         

II. 5x - 2y = 13

10.  

I. 2x^2 + 11x + 12 = 0       

II. 5y^2 + 27y + 10 = 0




ANSWERS

1. (3)
Let the numbers be x, x+2, x+4 and x+6. Now
x + (x+2) + (x+4) + (x+6) = 260
x = 62

2. (2)
Original Price = 680
Price after first discount = 0.75 * 680 = 510
Second discount = (510 - 408)/510 = 20%

3. (1)
Amount of salt in original solution = 20% of 20 = 4
Percentage of salt in new solution = 4/15 * 100 = 26.67%

4. (3)
Pipe A and B can fill half the tank in 3 minutes and 5 minutes, So they can fill the empty tank in 6 min and 10 min respectively.
Time taken by them to fill the empty tank together = (6 * 10)/ 6 + 10 = 3 min 45 sec

5. (4) Ratio of heights = (V1/V2) * (r1/r2)^2 = 1/4 * 25/16 = 25 : 64

Solutions (6-10)
6. (2)
x = 2, -2  and   y = -3, -2

7. (4)
x = 3, 6   and   y = 6, 7

8. (3)
x = 5   and   y = 6

9. (1)
x = 3  and   y = 1

10. (5)
x = -4, -3/2   and   y = -5, -2/5