MISSION CGL MAINS 2015 : Quant Quiz

1.If the difference of the squares of two natural numbers is 37, then the sum of the squares of the numbers will be

(1) 690

(2) 687

(3) 685

(4) 672

2.The smallest number to be subtracted from 4750 so as to get a perfect square number is 

(1) 126

(2) 162

(3) 216

(4) 612

3.A cricket player has an average score of 30 runs for 42 innings played by him. In an innings, his highest score exceeds his lowest score exceeds his lowest score by 100 runs. If these two innings are excluded, his average of the remaining 40 innings is 28 runs. His highest score in an innings is

(1) 125

(2) 120

(3) 110

(4) 100

4.The average of four consecutive even numbers is 27. The largest of these number is

(1) 28

(2) 26

(3) 32

(4) 30

5.The average monthly salary of the workers in a workshop is Rs. 8,500. If the average monthly  salary  of 7 technicians is Rs.10,000 and average monthly salary of the rest is Rs. 7,800, the total number of workers in the workshop is

(1) 18

(2) 20

(3) 22

(4) 24

6.In a class, the number of girls is 20% more than that of the boys. The strength of the class is 66. If 4 more girls are admitted to the class, the ratio of the number of boys to that of the girls is 

(1) 1 : 2

(2) 3 : 4

(3) 1 : 4

(4) 3 : 5

7.If A’s salary is 25% more than B’s salary, then B’s salary is how much lower than A’s salary?

(1) 33 1/3%

(2) 25%

(3) 20%

(4) 16 2/3%

8.Rs. 366 are to be divided amongst A, B and C so that A may get 1/2 as much as B and C together and B may get 2/3 as much as A and C together. A’s share will be

(1) Rs. 120

(2) Rs. 122

(3) Rs. 124

(4) Rs. 128

9.Ram and Gopal have money in the ratio 7 : 17 and Gopal and Krishna also have money in the same ratio 7 : 17. If Ram has Rs. 490, Krishna has

(1) Rs. 2,330

(2) Rs. 2,680

(3) Rs. 2,890

(4) Rs. 3,000

10.The ratio of the principal and its yearly amount is 8 : 9. What is the rate of simple interest per annum?

(1) 12%

(2) 12 1/2%

(3) 10%

(4) 10 1/2%

Answers and Solution:

1.(3) Let the number be x and y
x > y ∴ x^2-y^2 = 37
= (x+y) (x-y) = 37×1
= x+y = 37 and x-y = 1
∴ x^2+y^2 = ((x+y)^2+(x-y)^2  )/2
=((37)^2+(1)^2)/2
= 685

2.√4750 = 68.9
68×68 = 4624
∴ Required Number = 4750 – 4624
= 126
3.(4)
4.(4) Second Number = Average – 1
= 26
∴ Fourth number = 26+4 = 30

5.(3)Let the total number of worker in the workshop be X.
∴ 8500* x = 10000*7+(x-7)*7800
= 8500x-7800x = 70000-54600
= 700x = 15400
∴ x = 22

6.(2) Boys : Girls = 6 : 5
∴ Girls = 6/11×66=36
Boys = 30
New ratio = 30 : (36+4)
= 30 : 40
= 3 : 4
7.(3)
8.(2)
9.(3) Ram : Gopal = 7 : 17
Gopal : Krishna = 7 : 17
∴ Ram Krishna = 7/17 × 7/17 = 49/289
∴ Amount with Krishna = 289/49 × 490
= 2890
10.(2)