Directions(1-5): What should come in place of question mark(?) in the given number series:
1. 4, 8, 24, 96, ?
A. 360
B. 180
C. 480
D. 260
E. None of these
2. 3, 5, 1, 9, -7, ?
A. 18
B. 21
C. 24
D. 25
E. None of these
3. 5, 8, 27, 104, 525, ?
A. 3244
B. 1241
C. 3144
D. 2344
E. None of these
4. 226, 222, 206, 170, 106, ?
A. 25
B. 12
C. 6
D. 18
E. None of these
5. 1, 5, 11, 49, 239, ?
A. 1200
B. 1336
C. 1441
D. 1527
E. None of these
Directions(6-10): In the following questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
1) if x > y
2) if x < y
3) if x> = y
4) if x <= y
5) if x = y or relation cannot be established between 'x' and 'y'.
6. 1) 3x^2 + 7x = 6
2) 6(2y^2 + 1) = 17y
7. 1) 20x^2 - 17x + 3 = 0
2) 20y^2 - 9y + 1 = 0
8. 1) x^2 - 5x + 6 = 0
2) y^2 + y - 6 = 0
9. 1) x^2 + 4x - 60 = 0
2) y^2 + y - 90 = 0
10.1) x^2 + 2x - 3 = 0
2) 2y^2 - 7y + 6 = 0
1. 4*1 + 4 = 8
8*2 + 8 = 24
24*3 + 24 = 96
96*4 + 96 = 480
2. 3 + 2 = 5
5 - 4 = 1
1 + 8 = 9
9 - 16 = -7
-7 + 32 = 25
3. 5*2 - 2 = 8
8*3 + 3 = 27
27*4 - 4 = 104
104*5 + 5 = 525
525*6 - 6 = 3144
4. 226 - 2*2 = 222
222 - 4*4 = 206
206 - 6*6 = 170
170 - 8*8 = 106
106 - 10*10 = 6
5. 1*2 + 3 = 5
5*3 - 4 = 11
11*4 + 5 = 49
49*5 - 6 = 239
239*6 + 7 = 1441
6.1) 3x^2 + 7x - 6 = 0
3x^2 + 9x - 2x - 6 = 0
3x(x+3)-2(x-3) = 0
(3x-2)(x-3) = 0
Thus, x = 2/3, 3
2) 12y^2 - 17y + 6 = 0
12y^2 - 9y - 8y + 6 = 0
3y(4y-3)-2(4y-3) = 0
(3y-2)(4y-3) = 0
Thus, y = 2/3, 3/4
Answer: x >= y
7.1) 20x^2 - 17x + 3 = 0
20x^2 - 5x - 12x + 3 = 0
5x(4x-1) -3(4x-1) = 0
(5x-3)(4x-1) = 0
Thus, x = 3/5, 1/4
2) 20y^2 - 9y + 1 = 0
20y^2 - 5y - 4y + 1 = 0
5y(4y-1) -1(4y-1) = 0
(5y-1)(4y-1) = 0
Thus, y = 1/5, 1/4
Answer: x >= y
8.1) x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x-3) -2(x-3) = 0
(x-2)(x-3) = 0
Thus, x = 2, 3
2) y^2 + y - 6 = 0
y^2 + 3y - 2y - 6 = 0
y(y+3) -2(y+3) = 0
(y-2)(y+3) = 0
Thus, y = 2, -3
Answer: x >= y
9.1) x^2 + 4x - 60 = 0
x^2 + 10x - 6x - 60 = 0
x(x+10) -6(x+10) = 0
(x-6)(x+10) = 0
Thus, x = 6, -10
2) y^2 + y - 90 = 0
y^2 + 10y - 9y - 90 = 0
y(y+10) -9(y+10) = 0
(y-9)(y+10) = 0
Thus, y = 9, -10
Answer: No relation can be established.
10.1) x^2 + 2x - 3 = 0
x^2 + 3x - x - 3 = 0
x(x+3) -1(x+3) = 0
(x-1)(x+3) = 0
Thus, x = 1, -3
2) 2y^2 - 7y + 6 = 0
2y^2 - 4y - 3y + 6 = 0
2y(y-2) -3(y-2) = 0
(2y-3)(y-2) = 0
Thus, y = 2, 3/2
Answer: x < y
8*2 + 8 = 24
24*3 + 24 = 96
96*4 + 96 = 480
2. 3 + 2 = 5
5 - 4 = 1
1 + 8 = 9
9 - 16 = -7
-7 + 32 = 25
3. 5*2 - 2 = 8
8*3 + 3 = 27
27*4 - 4 = 104
104*5 + 5 = 525
525*6 - 6 = 3144
4. 226 - 2*2 = 222
222 - 4*4 = 206
206 - 6*6 = 170
170 - 8*8 = 106
106 - 10*10 = 6
5. 1*2 + 3 = 5
5*3 - 4 = 11
11*4 + 5 = 49
49*5 - 6 = 239
239*6 + 7 = 1441
6.1) 3x^2 + 7x - 6 = 0
3x^2 + 9x - 2x - 6 = 0
3x(x+3)-2(x-3) = 0
(3x-2)(x-3) = 0
Thus, x = 2/3, 3
2) 12y^2 - 17y + 6 = 0
12y^2 - 9y - 8y + 6 = 0
3y(4y-3)-2(4y-3) = 0
(3y-2)(4y-3) = 0
Thus, y = 2/3, 3/4
Answer: x >= y
7.1) 20x^2 - 17x + 3 = 0
20x^2 - 5x - 12x + 3 = 0
5x(4x-1) -3(4x-1) = 0
(5x-3)(4x-1) = 0
Thus, x = 3/5, 1/4
2) 20y^2 - 9y + 1 = 0
20y^2 - 5y - 4y + 1 = 0
5y(4y-1) -1(4y-1) = 0
(5y-1)(4y-1) = 0
Thus, y = 1/5, 1/4
Answer: x >= y
8.1) x^2 - 5x + 6 = 0
x^2 - 3x - 2x + 6 = 0
x(x-3) -2(x-3) = 0
(x-2)(x-3) = 0
Thus, x = 2, 3
2) y^2 + y - 6 = 0
y^2 + 3y - 2y - 6 = 0
y(y+3) -2(y+3) = 0
(y-2)(y+3) = 0
Thus, y = 2, -3
Answer: x >= y
9.1) x^2 + 4x - 60 = 0
x^2 + 10x - 6x - 60 = 0
x(x+10) -6(x+10) = 0
(x-6)(x+10) = 0
Thus, x = 6, -10
2) y^2 + y - 90 = 0
y^2 + 10y - 9y - 90 = 0
y(y+10) -9(y+10) = 0
(y-9)(y+10) = 0
Thus, y = 9, -10
Answer: No relation can be established.
10.1) x^2 + 2x - 3 = 0
x^2 + 3x - x - 3 = 0
x(x+3) -1(x+3) = 0
(x-1)(x+3) = 0
Thus, x = 1, -3
2) 2y^2 - 7y + 6 = 0
2y^2 - 4y - 3y + 6 = 0
2y(y-2) -3(y-2) = 0
(2y-3)(y-2) = 0
Thus, y = 2, 3/2
Answer: x < y
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