Question 1

What should come in place of question mark (?) in the following question? 52000 ÷ 40 ÷ 65 × 30 = ? - √400

Accepted Answer

52000 ÷ 40 ÷ 65 × 30 = ? - √400 (52000 ÷ 40) ÷ 65 × 30 = ? - 20 (1300 ÷ 65) × 30 = ? - 20 20 × 30 = ? - 20 600 = ? - 20 ? = 620

Question 2

What should come in place of question mark (?) in the following question? 12.5 × 3.2 × 8.8 = ?

Accepted Answer

12.5 × 3.2 × 8.8 = 352

Question 3

What should come in place of question mark (?) in the following question? 41% of 600 - 250 = ? - 77% of 900

Accepted Answer

41% of 600 - 250 = ? - 77% of 900 ⇒ 246 - 250 = ? - 693 ⇒ 246 -250 + 693 = ? ⇒ ? = 689

Question 4

What should come in place of question mark (?) in the following question? 65% × 700 + √196 – 9 × 3 = ?

Accepted Answer

As per the BODMAS rule, Addition and subtraction can be treated on same priority (from left to right) when they are in consecutive order. 65% × 700 + 14 - 9 × 3 65 × (700/100) + 14 - 27 455 + 14 - 27 = 442

Question 5

In the question given below, two equations are provided. Solve the equations and establish the relationship between x and y I. 2x2-13x-189=0 II. 2y2-3y-189=0

Accepted Answer

I. 2x2 - 13x - 189 = 0 2x2 - 27x + 14x - 189 = 0 x(2x - 27) + 7(2x - 27) = 0 x = -7, 27/2 II. 2y2 - 3y - 189 = 0 2y2 - 21y + 18y - 189 = 0 y(2y - 21) + 9(2y - 21) = 0 y = -9, 21/2 When x, as well as y, have both positive and negative values then no relationship can be established between them because if we consider x to be positive then the negative value of y will be lesser than x. If we consider x to be negative then positive value of y will be greater than x.

Question 6

In each of the following questions two equations I and II are given. Solve both the equations and give answer: I. x2+2x-195=0II. y2+30y+225=0

Accepted Answer

I. x2 + 2x - 195 = 0 = (x+15) (x-13) => x = -15, 13 II. y2 + 30y + 225 = 0 = (y+15) (y+15) => y = -15, -15 So x ≥ y

Question 7

In each of these questions, two equations (I) and (II) are given. I. 2x2+19x+42 = 0II. 4y2+43y+30 = 0

Accepted Answer

I. 2x2 + 19x + 42 = 0 2x2 + 12x + 7x + 42 = 0 2x (x+6) + 7(x +6) = 0 (2x+7) (x+6) = 0 x = -7/2, -6 I I. 4y2 + 43y + 30 = 0 4y2 +40y + 3y + 30 = 0 4y(y + 10) + 3(y + 10) (4y + 3)(y + 10) = 0 y = -3/4, -10 So answer is no relation.

Question 8

3x2-14x+16=05y2-16y+12=0

Accepted Answer

3x2 – 14x + 16=0 3x2 –6x – 8x + 16=0 3x (x-2) – 8 (x-2) (3x-8) (x-2)=0 x=8/3 or 2 5y2 – 16y + 12=0 5y2 – 10y – 6y + 12=0 5y (y-2) – 6 (y-2)=0 (5y-6) (y-2)=0 y=6/5 or 2 Can't be determined.

Question 9

In the question, two equations I and II are given. You have to solve both the equations and give answer x2-11x+28=0y2-18y+81=0

Accepted Answer

x2 – 11x + 28=0 x2 – 7x – 4x + 28=0 x (x-7) – 4 (x-7)=0 (x-4) (x-7)=0 x=4, 7 y2 – 18y + 81=0 y2 –9y – 9y + 81=0 y (y-9) – 9 (y-9)=0 (y-9) (y-9)=0 y=9, 9 So, x<y.

Simplification Questions