Quant : Simplification

1. ? % of 824 + 244 = 1480
1) 140
2) 150
3) 100
4) 180
5) 120


2. 24.5 × 8.4 × 16 = ?
1) 3292.8
2) 3492.8
3) 3294.8
4) 3192.8
5) 3094.8

Directions: In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y. Give answer:
1) if x > y
2) if x >= y
3) if x < y
4) if x <= y
5) if x = y or relationship between x and y cannot be determined.

3.
I. 2x^2 + 13x + 20 = 0
II. 2y^2 – 3y – 35 = 0

4.
I. 12x^2 – 41x + 35 = 0
II. 4y^2 – 17y +15 = 0

5.
I. 4x^2 – 4 = 60
II. 3y^2 + 3 = 51

6.
I. 28x^2 – 9x – 9 = 0
II. 7y^2 + 24y + 9 = 0

Answers:
1. 2
2. 1
3. 5
I. 2x^2 + 8x + 5x + 20 = 0
(2x + 5) (x + 4) = 0  x = -5/2,– 4

II. 2y^2 – 10y + 7y – 35 = 0
(2y + 7) (y – 5) = 0  y = -7/2, 5

Relationship between x and y does not exist.

4. 5;
I. 12x^2 – 20x – 21x + 35 = 0
(4x –7) (3x – 5) = 0
x = 7/4, 5/3
II. 4y^2 – 12y – 5y + 15 = 0  (4y – 5) (y – 3) = 0
y = 5/4, 3
Relationship between x and y does not exist

5.5;
I. 4(x^2 – 1) = 60
x^2 – 1 = 15
x = +/- 4

II. 3(y^2 + 1) = 51
y^2 + 1 = 17
y = +/- 4
Hence x = y

6. 2;
I. 28x^2 – 21x + 12x – 9 = 0
(7x + 3) (4x – 3) = 0
x = -3/7, 3/4

II. 7y^2 + 21y + 3y + 9 = 0
(7y + 3) (y + 3) = 0
y = -3/7,–3