   Directions: Study the following questions carefully and answer the questions given below:
Important for :
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

 13 + 23 + 33 +......+ 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.