71. It is dark in my bedroom and I want to get two socks of the same colour from my drawer, which contains 26 red and 24 blue and 34 brown socks. How many socks do I have to take from the drawer to get at least two socks of the each colour?
Answer:
Explanation:Maximum of (red, blue, brown) + 2nd maximum of (red, blue, brown) + 2
36 + 24 + 2 = 62.
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72. There are two boxes, one containing 21 red balls and the other containing 25 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red is maximized. This maximum probability is
Answer:
Explanation:From the given data, 1/2*(1+20/45) = 65/90=.72
The maximum probability=.72
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73. A family consists of father, mother, two sons and the youngest daughter. The age of first son and daughter are in the ratio 3:1. The mother is 3.5 times as old as the second son. The age of the second son is 2/3 of the age of the first son. The age of the youngest daughter is 5 years. What is the age of the mother?
Answer:
Explanation:Let us take the ages of Father, Mother, First son, Second son and daughter as F, M, S1, S2 and D respectively.
Given,
S1: D = 3: 1 M = 3.5 (S2) S2 = 2/3 (S1) D = 5
Now, S1: D = 3: 1 => S1 = 3D => S1 = 3(5) => 15 So, S1 = 15
S2 = 2/3 (S1) => S2 = 2/3(15) => 10 S2 = 10
M = 3.5 (10) => 35
Mother's age is 35
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74. Rahul buys an article at Rs.15850 from the retailer who sells it at a profit of 15 %. The retailer bought it from a wholesaler who sold it at a profit of 20 %. The manufacture sold it at a profit of 30 % to the wholesaler. Find the cost price of manufacturing the article (approximately)?
Answer:
Explanation:Going from options Option 8835
If manufacturing cost is 8835,
Manufacturer to Wholesaler = 30/100 * 8835 = 2650.5 Total = 8835 + 2650.5 = 11485.5
Wholesaler to Retailer = 20/100 * 11485.5 = 2297.1 Total = 11485.5 + 2297.1 = 13782.6
Retailer to Rahul = 15/100 * 13782.6 = 2067.34 Total = 13782.6 + 2067.34 ~ 15850
Hence option 8835 will be the answer.
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75. 66 people {a1, a2,..., a66} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ...,{a65, a66}, {a66, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Answer:
Explanation:For minimum people in a set we can consider handshakes as {a1, a2, a3}, {a4, a5, a6},
{a7, a8, a9},…….{ an-2,an-1,an}
For minimum people, we can consider the set {a2, a5, a8… an-1}.
So, MINIMUM people in a set = n / 3 so n/3=66/3=22
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76. There will be 20 3s in between 1 to 100
Similarly, 20 3s in between 200 to 300 but (100+20) in between 300 to 400 (because at unit place 19 3s and 10's place 1 and 100 3s at 100's place ) and 20 3s in between 400 to 500
20 3s in between 500 to 600
20 3s in between 600 to 700
20 3s in between 700 to 800
20 3s in between 800 to 900
20 3s in between 900 to 1000
So total number of 3s will be 180+19+1+100 = 300 This count is in decimal but in question base value is 8 so we need to convert (300)8 = 192
Answer:
Explanation:t=24
D = 4*sqrt(24 - 8) D = 4*sqrt(16)
D = 4*4 D = 16
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77. If there are 30 cans out of them one is poisoned. If a person tastes very little of this he will die within 14 hours so they decided to test it with mice. Given that a mouse dies in 24 hours and you have 24 hours in all to find out the poisoned can, how many mice are required to find the poisoned can?
Answer:
Explanation:The mice will die within 24 hours not exactly on the 24th hour.
For example, if there are 7 cans,
1st Can's solution is given to mice A. 2nd Can's solution is given to mice B. 3rd Can's solution is given to mice C. 4th Can's solution is given to A and B. 5th Can's solution is given to B and C. 6th Can's solution is given to C and A. 7th Can's solution is given to A, B and C.
Then within 24 hours if A alone dies, Can 1 is poisoned. If B alone dies, Can 2 is poisoned.
If C alone dies, Can 3 is poisoned.
A and B dies if Can 4 is poisoned, B and C dies if Can 5 is poisoned, C and A dies if Can 6 is poisoned & if all A, B, C dies then Can 7 is poisoned.
From this we can tell that to check 23-1 = 7 Cans we need 3 mouse.
Therefore we can tell that in order to check 30 Cans (25-1 = 31 maximum) we need 5 mouse.
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78. The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 6) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
Answer:
Explanation:In decimal system total no. of 3's from 1 to 1000 are 100*3 = 300 In base 6, value of 300 = 3*(6^2) + 0*(6^1) + 0*(6^0) = 108.
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79. Mr.Govind was a building contractor. He was doing reasonably well in his business but was always on an expansion mode. Mr.Govind won a contract with the Corporation and his business began to boom, so he decided to deploy more people in his projects. If he were to increase his labour force by 33.33%, what will be percentage reduction in the work load of each employee?
Answer:
Explanation:As we know if men increase the workload of each employee will decrease
i.e., men are inversely proportional to work load of an employee.
As we see in percentage concept, if there is 1/n increase, there will be 1/n+1 decrease
Here 33.33% increase which equals=1/3 There will be 1/4 decrease=25%
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80. If Valentine's day of 2005 was celebrated on a Monday. What day is Feb 14th, 2010?
Answer:
Explanation:In leap year 2 odd days Ordinary year 1 odd days.
From 2005 to 2010, there is one leap year and 4 ordinary year. So totally 6 odd days.
So answer is Sunday.
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