Question 1

The number whose square is equal to the difference of the squares of 37 and 23 is:-

Accepted Answer

37 2 – 23 2 = 840 Required number = 840 = 28 . 98

Question 2

If a--b = 4 and ab = 45, find the value of a3 - b3

Accepted Answer

( a – b ) 2 = a 2 + b 2 - 2 ab ⇒ 16 = a 2 + b 2 – 90 ⇒ a 2 + b 2 = 106 a 3 – b 3 = ( a – b ) ( a 2 + b 2 + ab ) ⇒ a 3 – b 3 = 4 X ( 106 + 45 ) ⇒ a 3 – b 3 = 4 X 151 ⇒ a 3 – b 3 = 604

Question 3

If a/(a+b) = 15/21, what is (a+b)/(a-b) is equal to?

Accepted Answer

a/(a + b) = 15/21 → a = 15, a + b = 21 → b = 21– 15 = 6 ⇒ a – b =15 – 6 = 9 ⇒ (a + b)/(a – b) = 21/9

Question 4

(798+579)2- (798-579)2798 x 579 =

Accepted Answer

⇒ 4(798 X 579) / (798 X 579) ⇒ 4

Question 5

If x varies as y and x = 8 when y = 15 then the value of x when y = 10 is:

Accepted Answer

x : y = 8 : 15 If y = 10, x = 8/15 X 10 y = 16/3

Simplification Questions