Directions (1-4): 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:
a) if x > y
b) if x >= y
c) if x < y
d) if x <= y
e) if x = y or relationship between x and y cannot be determined.
Directions (5-6): Find the value of ‘?’ in the number series given below.
5. 9, 27, 31, 155, 161, 1127, ?
(a) 135
(b) 1288
(c) 1135
(d) 2254
(e) 1168
6. 9, 22, 24, 37, ?, 52
(a) 39
(b) 42
(c) 45
(d) 50
(e) 29
Directions (7-10): In the following number series one number is wrong. Find out the wrong number.
7. 16, 40, 100, 250, 630
(a) 630
(b) 100
(c) 250
(d) 40
(e) 16
8. 21, 48, 162, 969, 7748
(a) 7748
(b) 21
(c) 969
(d) 48
(e) 162
9. 118, 239, 96, 264, 68, 293
(a) 293
(b) 264
(c) 96
(d) 68
(e) 239
10. 128, 320, 1120, 5040, 27720, 180190
(a) 27720
(b) 5040
(c) 320
(d) 1120
(e) 180190
Answers:
1. (e)
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.
2. (e)
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
3. (e)
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
4. (b)
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
Hence x >= y
Directions (5-6): Find the value of ‘?’ in the number series given below.
5. 9, 27, 31, 155, 161, 1127, ?
(a) 135
(b) 1288
(c) 1135
(d) 2254
(e) 1168
5. (c)
Given pattern is,
2nd term → 9*3 = 27
3rd term → 27+4 = 31
4th term → 31*5 = 155
5th term → 155+6 = 161.
6th term → 161*7 = 1127
Missing term → 1127+8 = 1135.
6. 9, 22, 24, 37, ?, 52
(a) 39
(b) 42
(c) 45
(d) 50
(e) 29
Directions (7-10): In the following number series one number is wrong. Find out the wrong number.
7. 16, 40, 100, 250, 630
(a) 630
(b) 100
(c) 250
(d) 40
(e) 16
7. (a)
16 * 5/2 = 40
40 * 5/2 = 250
250 * 5/2 = 625 not equal to 630
Hence there should be 625 in place of 630
8. 21, 48, 162, 969, 7748
(a) 7748
(b) 21
(c) 969
(d) 48
(e) 162
8. (d)
The series is:
21 × 2 – 1 = 41 not equal to 48
41 × 4 – 2 = 162
162 × 6 – 3 = 969
969 × 8 – 4 = 7748
Hence, there should 41 in place of 48.
9. 118, 239, 96, 264, 68, 293
(a) 293
(b) 264
(c) 96
(d) 68
(e) 239
9. (c)
The series is:
118 + (11)2 = 239
239 – (12)2 = 95 not equal to 96
95 + (13)2 = 264
264 – (14)2 = 68
68 + (15)2 = 293
Hence there should be 95 in place of 96.
10. 128, 320, 1120, 5040, 27720, 180190
(a) 27720
(b) 5040
(c) 320
(d) 1120
(e) 180190
10. (e)
The series is
128 * 5/2 = 320
320 * 7/2 = 1120
1120 * 9/2 = 5040
5040 * 11/2 = 27720
27720 * 13/2 = 180180 not equal to 180190
