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What value should come in the place of (?) in the following number series?
895, 623, 487, 419, 385, ?
895 623 487 419 385 368
272 136 68 34 17
(÷2) (÷2) (÷2) (÷2) (÷2)
15, 25.5, 46.5, 78, 120, ?
15 + (1 * 10.5) = 25.5
25.5 + (2 * 10.5) = 46.5
46.5 + (3 * 10.5) = 78
78 + (4 * 10.5) = 120
120 + (5 * 10.5) = 172.5
3, 6, 15, 42, 123, ?
3 + 31 = 6
6 + 32 = 15
15 + 33 = 42
42 + 34 = 123
123 + 35 = 366
69, 86, 105, 126, ?
50, 56, 68, 86, 110, ?
50 + 6 = 56
56 + 12 = 68
68 + 18 = 86
86 + 24 = 110
110 + 30 = 140
In each of the following questions, two equations are given. You have to solve both the equations to find the relation between x and y.
I: 2x2 – 55x + 378 = 0
II: 2y2 + 37y + 171 = 0
From I
2x2 – 55x + 378 = 0
=>2x2 – 27x - 28x + 378 = 0
=> (x – 14) (2x – 27) = 0
=> x = 14, 27/2
From II
2y2 + 37y + 171 = 0
=>2y2 + 18y + 19y + 171 = 0
=> (2y + 19) (y + 9) = 0
=> y = -9, -19/2
Hence, x > y
I: x2 + 11x + 28 = 0
II: 9y2 + 32y + 15 = 0
x2 + 11x + 28 = 0
=>x2+ 7x + 4x + 28 = 0
=> (x + 4) (x + 7) = 0
=> x = -4, -7
9y2 + 32y + 15 = 0
=>9y2 + 27y + 5y + 15 = 0
=> (9y + 5) (y + 3) = 0
=> y = -3, -5/9
Hence, x < y
I: x2 - 6x - 7 = 0
II: y2 - 19y + 84 = 0
x2 - 6x - 7 = 0
=>x2 - 7x + x - 7 = 0
=> (x – 7) (x + 1) = 0
=> x = -1, 7
y2 - 19y + 84 = 0
=>y2 – 12y - 7y + 84 = 0
=> (y – 12) (y – 7) = 0
=> y = 12, 7
Hence, x ≤ y
I: x2 + 9x - 52 = 0
II: y2 + 4y - 32 = 0
x2 + 9x - 52 = 0
=>x2+ 13x – 4x - 52 = 0
=> (x – 4) (x + 13) = 0
=> x = 4, -13
y2 + 4y - 32 = 0
=> (y + 8) (y – 4) = 0
=> y = 4, -8
Hence relationship between x and y cannot be determined
I: x2 – 841 = 0
II: y3 – 29791 = 0
x2 – 841 = 0
=> x2 = 841
=> x = ± 29
y3 – 29791 = 0
=> y3 = 29791
=> y = 31
Correct (-)
Wrong (-)
Skipped (-)