Directions: Study the following questions carefully and answer the questions given below:
1
The average of a non-zero number and its square is 7 times the number. The number is:
» Explain it
A
Let the number be x. then, 

x +  x2  = 7x
2

x2 + x = 14x,     x2 – 13 x = 0,   x [ x – 13] = 0,   x = 0, 13.

So the number is 13 .      
2
The average of 5 consecutive numbers is 30. The largest of these numbers is:
» Explain it
C
Let the number be x, (x+1), (x+2), (x+3) & (x+4).

then,  ( x + (x+1) + (x+2) + (x+3) + (x+4) )  = 30.
5

5x + 10 = 150,   x = 140/5,   x = 28.  

So, the largest number is: x + 4 then,

put the value of x in the largest number:  x + 4 =  28 + 4  32. 

3
The average of seven consecutive odd numbers is 36. What is the difference between the highest and lowest numbers ?
» Explain it
C
Let the smallest odd number be x

so acc. to the que. the consecutive num are

x,  x + 2,  x + 4,  x + 6,  x + 8,  x + 10,  x +12.

So the diffrence is x + 12 - x = 12.

Hence, option C is correct.

4
The sum of four consecutive odd numbers is 30 more than the average of these numbers. What is the first of these numbers?
» Explain it
A
Let the numbers be xx + 2 , x + 4 & x + 6.

then,  (x + x + 2 + x + 4 + x + 6) –  x + x + 2 + x + 4 + x + 6  =  30
4

  4x + 12  – ( 4x + 12 )  = 30
4

Or, ( 4x + 12 – x – 3) = 30,   So, 3x = 21,  x = 7

So first number  x = 7.

Hence, option A is correct.

5
The mean of 13, 23, 33 , 43 , 53  is :
» Explain it
C
To solve this question, we can apply a short trick approach

13 + 23 + 33 +........n3  =   n2(n + 1)2
4

By the short trick approach, we get 

  1+ 2+ 3+......+ 53  =   52(5 + 1)2  =  52 × 62
4 4 4

⇒    ( 25 x 36 )  = (25 x 9 )  ⇒ 225.
4

So,  Required average =  ( 225 )   = 45.
5
 

Hence, option C is correct.