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.

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.

1.
I. 12x^2 – 59x + 72 = 0
II. 8y^2 – 58y + 99 = 0

2.
I. x^2 + x – 20 = 0
II. y^2 + 13y + 40 = 0

3.
I. x^2 + 12x + 36 = 0
II. 5y^2 – 2 15y + 3 = 0

4.
I. 10x^2 – 29x – 21 = 0
II. y^2 + 13y – 68 = 0

5.
I. 72x^2 – 163x + 88 = 0
II. 56y^2 – 187y + 156 = 0

Directions: What value should come in the place of question mark (?) in the following number series?

6. 291, 272, ?, 276, 287, 280
1) 281
2) 298
3) 287
4) 289
5) 279

7. 449, 890, 361, 986, ?, 1098,
1) 257
2) 275
3) 267
4) 252
5) 277

8. 18, ?, 172, 524, 1588, 4796
1) 62
2) 66
3) 54
4) 72
5) 56

9. 342, 463, 613, 792, 1000, ?
1) 1089
2) 1273
3) 1256
4) 1149
5) 1237

10. 24, 48, ?, 36, 4, 16, 1
1) 24
2) 10
3) 16
4) 12
5) 8

1. 3
I. 12x^2 – 32x – 27x + 72 = 0
(3x – 8) (4x – 9) = 0
x = 8/3 , 9/4

II. 8y^2 – 22y – 36y + 99 = 0
(2y – 9) (4y – 11) = 0
y = 9/2 , 11/4
x < y

2. 2
I. x^2 + 5x – 4x – 20 = 0
(x – 4) (x + 5) = 0
x = 4, –5

II. y^2 + 5y + 8y + 40 = 0
(y + 8) (y + 5) = 0
y = –8, – 5
x >= y

3. 3
I. (x + 6)^2 = 0
x = –6

II. 2
(√ 5y – √ 3)^2 = 0
y = √ 3/ √ 5
x < y

4. 5
I. 10x^2 – 35x + 6x – 21 = 0
(5x + 3) (2x – 7) = 0
x = –3/5 , 7/2

II. y^2 + 17y – 4y – 68 = 0
(y – 4) (y + 17) = 0
y = 4, – 17
No relationship between x and y exists.

5. 3
I. 72x^2 – 64x – 99x + 88 = 0
(8x – 11) (9x – 8) = 0
x = 11/8, 8/9

II. 56y^2 – 91y – 96y + 156 = 0
(7y – 12) (8y – 13) = 0
y = 12/7 , 13/8
x < y

6. 4
7. 1

8. 5

9. 5

10. 4