EXERCISE 6.A (OBJECTIVE TYPE QUESTIONS) (IN 16 20 SOLUTION)

16.       The average of a non – zero number and its square is 5 times the number. The number is:

a)      9

b)      17

c)       29

d)      295

17.       The average of 7 consecutive numbers is 20. The largest of these numbers is:

a)      20

b)      22

c)       23

d)      24

18.       The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers?

a)      2

b)      5

c)       8

19.       The sum of three consecutive odd numbers is 38 more than the average of these numbers. What is the first of these numbers?

a)      13

b)      17

c)       19

d)      Data inadequate

e)      None of these

20.       The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is:

a)      15 years

b)      15.5 years

c)       16 years

d)      Cannot be computed with the given information.

ANSWERS

 16.A

17.C

18.C

19.B

20.D

SOLUTION 

 16.       Let the number be X. then,

X + X² / 2 = 5X   X² - 9X = 0    x (X – 9) =0   X = 0  X= 9.

So, the number is 9.

17.       Let the numbers be X, X + 1, X  2, X +3, X +4, X+5 and X+6.

Then, X + (X + 1) +(X + 2) + (X + 3) + (X + 4) + (X + 5) + (X + 6) / 7 = 20

 Or 7x + 21 = 140 or 7X =119 or X = 17.

Largest number =X + 6 = 23.

18.       Let the numbers be X, X + 2, X + 4, X + 6 and X + 8.

Then, X + ((X + 2)  + (X + 4)  + (X + 6) + (X + 8) / 5 = 1 or 5X + 20 = 305 or X = 5

So, required difference =(5 + 8) – 57 = 8.

19.       Let the numbers be x, X + 2 and X +4.

Then, (X + X + 2 + X + 4) – (X + x + 2 + X + 4) / 3 = 38

Or (3X + 6) – ( 3X + 6) / 3 =38 or 2 (3X + 6) / 3 = 38 or 2 (3X + 6) = 114 or 6X = 102 or X= 17.

So, first number =X = 17.

20.       Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given.

       So, the data provided is inadequate.