41. Which of the following numbers are completely divisible by 11?
A. 3245682
B. 283712
C. 438416
D. 36894
Answer: All are divisible
Explanation:Note: If the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.
[(Sum of digits at odd places) - (Sum of digits at even places)]/11
=> [(3+4+6+2) - (2+5+8)]/11 => (15 - 15)/11 = 0/11 = 0
similarly others number are divisible by 11
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42. If a number cube is rolled once and coin is tossed once. What is the probability that the coin will show tails and composite number on the cube?
Answer: 1/6
Explanation:Numbers on cube (1,2,3,4,5,6)
Composite number on dice are 4 and 6.
So, Probability that the coin will show tails and composite number on the cube = (1/2) *(2/6) = 1/6
Note: Composite number is a positive integer that can be formed by multiplying together two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself
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43. The time a passenger train takes to cross another freight train is twice when the passenger train crosses the freight train running in opposite directions. What is the ratio of their speeds?
Answer: 3:1
Explanation:Lets assume speed of freight train = X Km/hr
speed of passenger train = Y Km/hr.
and sum of their length = D Km.
When trains are running in same direction:
so Time = D/(X-Y) ---------- (1)
When trains are running in opposite direction:
So, Time = D/(X+Y) --------- (2)
By eq. (1) & (2)
[D/(X-Y)] = 2 * [D/(X+Y)]
=> 2X-2Y = X+Y
=> X = 3Y
=> X:Y = 3:1
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44. The banker's gain on a bill due 2 year hence at 10% per annum is Rs. 8. The true discount is:
Answer: Rs. 40
Explanation:True Discount = (B.G*100)/(Rate*Time)
T.D = (8*100)/(10*2)
= 8*5 = Rs. 40
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45. If x(a) = a^2+2a-1, then x(8)-x(5) =
Answer: 45
Explanation:x(8) = 64 + 16 - 1 = 79
x(5) = 25 + 10 - 1 = 34
So, x(8)-x(5) = 79 - 34 = 45
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46. If a certain computer is capable of printing 4900 monthly credit card bills per hour, while a new model is capable of printing at a rate of 6600 per hour, the old model will take approximately how much longer than the new model to print 10000 bills?
Answer: 31 min.
Explanation:Old model is capable of printing at a rate of 4900 per hour
New model is capable of printing at a rate of 6600 per hour
Old model time taken to print 10000 cards = 10000/4900 = 100/49
New model time taken to print 10000 cards = 10000/6600 = 100/66
Old model - new model: 100/49 - 100/66 = 1700 /(49*66) = 850/(49 * 33) = 0.525 hrs => 31 mins
Therefore, the old model will take approximately 31 mins longer than the new model to print 10000 bills
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47. To finish a piece of work, P takes Five times as Q and six times as R. Working together, they can finish the work in 4 days. Q can do the work alone in:
Answer: 48/5 days
Explanation:Lets assume Q take x days to finish the work
so P take time = 5x, and R take time R=5x/6
Given, They took 4 day to finish the work.
1/5x+1/x+6/5x= 1/4 => 12/5x = 1/4
x=48/5
So, Q can do work alone in 48/5 days.
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48. If 3/p = 6 and 3/q = 15 then p - q = ?
Answer: 3/10
Explanation:Given, p=1/2,q=1/5
So, p-q = (3/6 - 3/15) = (1/2 - 1/5) = 3/10
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49. Total of the ages of A, B ahd C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present
Answer: 30 years.
Explanation:Let their ages 10 years ago is x, 2x and 3x years.
(x + 10) + (2x + 10) + (3x + 10) = 90 hence x= 10
B's present age = (2x + 10) =30 years.
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50. The sum of a number and its square is 1406. What is the number?
Answer: 37
Explanation:Lets assume the no. = x
so x+x^2=1406
by putting values from options
37+37^2
=37(37+1)
=37*38 =1406
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