Directions(1-5): Find the missing numbers in the given series:
1. 4, 16, 26, 34, 40, _
A. 44
B. 42
C. 40
D. 46
E. None of these
Sol. 4 + 12 = 16
16 + 10 = 26
26 + 8 = 34
34 + 6 = 40
40 + 4 = 44
2. 825, 582, 501, 474, 465, _
A. 475
B. 465
C. 462
D. 483
E. None of these
Sol. 825 - 582 = 243
582 - 501 = 81
501 - 474 = 27
474 - 465 = 9
465 - 462 = 3
243/3 = 81
81/3 = 27
27/3 = 9
9/3 = 3
3. 8, 12, 24, 60, 180, _
A. 620
B. 600
C. 610
D. 630
E. None of these
Sol. 8 + 8*0.5 = 12
12 + 12*1 = 24
24 + 24*1.5= 60
60 + 60*2 = 180
180 + 180*2.5=630
4. 3, 4, 10, 33, 136, _
A. 675
B. 665
C. 685
D. 655
E. None of these
Sol. 3*1 + 1 = 4
4*2 + 2 = 10
10*3 + 3 = 33
33*4 + 4 = 136
136*5 + 5 = 685
5. 16, 17, 13, 22, 6, _
A. 25
B. 15
C. 31
D. 17
E. None of these
Sol. 17 - 16 = 1
13 - 17 = -4
22 - 13 = 9
6 - 22 = -16
31 - 6 = 25
6. The front and rear wheels of an off-track vehicle have radii of 2 feet and 5 feet respectively. What is the distance travelled, if the front wheel completes 15 revolutions more than the rear wheel ?
A. 50Ï€ feet
B. 64Ï€ feet
C. 72Ï€ feet
D. 100Ï€ feet
E. None of these
Sol. Suppose the front wheel completes n revolutions
Then, the rear wheel completes (n – 15) revolutions.
The distance travelled by the front wheel = 4nπ
And by rear wheel (n – 15) × 10Ï€ = 10nÏ€ – 150Ï€.
Since these distances are equal, we get 4nÏ€ = 10nÏ€ – 150Ï€, which on solving yields n = 25.
Thus the distance travelled is 4nπ = 100π feet.
7. The 5000 litres tank of a two-storied apartment complex is 1/5th full. The apartment on the 1st floor consumes 120 litres of water every hour while the apartment on the 2nd floor consumes 180 litres of water every hour. The caretaker turns on the pump that lets in 45 litres of water every minute into the tank. How long will it take to fill the tank ?
A. 115 min
B. 100 min
C. 84 min
D. 68 min
E. None of these
Sol. Suppose the tank is filled in h hours.
In these h hours, the apartment on the 1st floor would have consumed 120h litres of water.
And the apartment on the 2nd floor would have consumed 180h litres of water.
The pump can pour in 45 litres of water every minute, i.e., 2700 litres of water every hour.
So, the total amount of water that has to be let into the tank is 4000 + 120h + 180h = 4000 + 300h litres.
Equating this to 2700h, we get,
4000 + 300h = 2700h, which yields h = 5/3 hours or 100 minutes.
8. Population of a town increases by 15.9% every decade. The urban population increases by 18%, whereas the rural population increases by 4%. What is the ratio of the urban population to the rural population ?
A. 17:3
B. 11:25
C. 17:11
D. 7:11
E. None of these
Sol. Suppose the urban population is U and the rural population is R.
Then, 18U + 4R = 15.9(U + R).
So, (18 – 15.9)U = (15.9 – 4)R, which yields,
U : R = 11.9 : 2.1 = 17 : 3.
9. A Math question paper has 10 questions, each with sub-questions (a) and (b). If a student can solve any sub-question from any five questions, in how many ways can she do so ?
A. 8064
B. 1024
C. 15,504
D. 59,049
E. None of these
Sol. The student can choose 5 out of the 10 questions in 10C5 = 252 ways.
Each of these 5 questions can be answered in 2 ways.
Thus the total number of ways is 10C5 × 2^5 = 252 × 32 = 8064 ways.
10. The height of a right circular cone is decreased by 20%. By what percent should the diameter of the base be decreased so that the volume of the right circular cone is decreased by 35.2%?
A. 6.66%
B. 9%
C. 10%
D. 11.11%
E. None of these
Sol. Suppose the original radius and height are 10 each.
Since (1/3)Ï€ is a constant, we can simple work with (r^2)*h and say that the original volume is 1000.
The new height is 8 and the new volume is 648.
If the new radius is R, then R^2 = 648/8 = 81 ⇒ R = 9.
Thus the radius and therefore the diameter is reduced by 10%.
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