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1. A and B can do work for \$600. A alone can do the work in 6 days and B alone can do the work in 8 days. With the help of C they complete the work in 3 days. What money each will get?
• Calculate the days C will take to complete the work
• 1/A + 1/B + 1/C = 1/3
• 1/C = 1/3 – (1/6 + 1/8)
• C = 24 days
• Distribution of money
• A:B:C = 1/6 : 1/8 : 1/24
• A:B:C = 4:3:1
• Hence, A will get \$300, B will get \$225 and C will get \$75

1. In how many ways can the ant reach the sugar? Following the paths in the diagram below.
• 8 ways
• 3 ways from A
• A – C – SUGAR
• A – C – G – SUGAR
• A – D – G – SUGAR
• 3 ways from B
• B – E – SUGAR
• B – E – H – SUGAR
• B – F – H – SUGAR
• 2 ways from E
• E – SUGAR
• E – H – SUGAR

1. Two pipes A and B can fill a tank in 24 mins and 32 mins respectively. After how many minutes B should be closed so that the tank is filled in 18 mins?
• B is closed after X mins
• Work done by A in 18 mins is 18/24
• Work done by B in x mins is X/32
• Finding x
• 18/24 + X/32 = 1
• X = 8 mins

1. In how many ways can the ant reach sugar? The ant can move either horizontally (in one direction) or vertically (in one direction) along the lines.
• Steps
• There are 6 vertical steps
• There are 6 horizontal steps
• Total ways = 12! / (6! * 6!)

1. An airplane files on the four sides of a square at 200 km/hr, 400 km/hr, 600 km/hr and 800 km/hr. What is the average speed of the airplane?
• Average speed = 1 / (1/200 + 1/400 + 1/600 + 1/800)
• 384 km/hr

1. In how many ways can you spell ABRACADABRA?
• The direct formula is (n-1) C ((n-1)/2)
• It works for only odd number of layers
• Here n = 11
• Number of ways = 10 C 5

1. There are 2 sections in the college. In section A there are 36 students and the average weight is 42 kg. in section B there are 44 students and the average weight is 35 kg. What is the average weight of all the students?
• Weighted average = (36*42 + 44*35) / (36 + 44)
• 38.15 kg

1. A boy and girl decided to meet at a café between 8 pm and 9 pm. They deicded that each person will wait for 20 mins and leave. What is the probability that they will meet?
• Starting point
• Boy goes to café x mins after 8 pm
• Girl goes to café y mins after 8 pm
• Diagram
• The boy and girl will meet in the shaded region
• Probability = (total area – un-shaded area) / total area
• Total area = 60 * 60 = 3600
• Un-shaded area = 2 * (1/2 * 40 * 40) = 1600
• Probability = 2000 / 3600 = 5 / 9

1. Divide \$672 in the ratio 5:3?
• A = 672 * (5/8) = 420
• B = 672 * (3/8) = 252

1. A drawer contains 100 black and 200 white socks. What is the minimum number of pulls that guarantee a pair of same color?
• 3 pulls
• B, B. B
• B, B, W
• B, W, B
• B, W, W
• W, W. W
• W, W, B
• W, B, W
• W, B, B

1. A person’s salary was reduced by 50% and subsequently increased by 50%. How much percent did the person lose?
• Original salary = 1
• Reduced by 50%, salary = 1*0.5 = 0.5
• Increased by 50%, salary = 0.5*1.5 = 0.75
• Loss = (1-0.75) / 1 = 25%

1. A customer buys goods worth 100 rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase. The customer gives the shopkeeper a 1000 rupee note. However, the shopkeeper has no change, so he goes next door to another shopkeeper to get change for the 1000 rupee note. He keeps 100 for himself and returns 900 to the customer. Later, the shopkeeper from next door comes back with the 1000 rupee note with a stamp on it saying “counterfeit” and takes his money back. How much loss does the shopkeeper make?
• Transaction from next door shopkeeper
• Cash inflow: Rs 1000
• Cash outflow: Rs1000
• Transaction from customer
• Cost of goods sold: Rs 100
• Cash outflow: Rs 900
• There is a total loss of Rs 1000

1. In what ratio water should be added to milk to gain 20% by selling the mixture at cost?
• Mixture
• Liters of milk = m
• Liters of water = w
• Cost price
• Cost price of milk = x
• Cost price of water = 0
• Cost price of mixture = mx
• Selling price and profit
• Selling price = (m+w) * x
• Profit = 20% of mx
• Calculations
• [(m+w) * x] – [mx] = [20/100 * mx]
• wx = 20/100 mx
• w/m = 1/5
• In 6 liters of mixture, 5 liters is milk and 1 liter is water

1. A, B, C and D are walking and come to an old wooden bridge. The bridge is weak and only able to carry the weight of two of them at a time. They must carry a torch on each crossing, they only have one torch and it can’t be thrown from one end to the other end. They can all cross the bridge at different speeds. A can cross in 1 minute, B in 2 minutes, C in 5 minutes and D in 10 minutes. What is the minimum time in which they can cross the bridge?
• A and B cross the bridge in 2 mins
• A returns with torch in 1 min
• C and D cross the bridge in 10 mins
• B returns with torch in 2 mins
• A and B cross the bridge in 2 mins
• Total 17 mins

1. In how many ways can the letter of DIRECTOR be arranged such that the vowels are always together?
• Observations
• There are 8 words
• There are 3 vowels (I, E, O)
• R is coming 2 times
• Arrangements
• There are 6! possible combinations for all letters such that the vowels come together
• There are 3! possible combinations for all vowels
• (6! * 3!) / 2!

1. How many squares are on the chess?
• (1^2) + (2^2) + (3^2) + (4^2) + (5^2) + (6^2) + (7^2) + (8^2)
• 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1
• 204

1. Two cards are drawn at random from a pack of 52 cards. What is the probability that both are black or both are queen?
• Options
• Prob that both are black = (26/52) * (25/51)
• Prob that both are queen = (4/52) * (3/51)
• Prob that both are black queen = (2/52) * (1/51)
• Probability
• [(26/52) * (25/51)] + [(4/52) * (3/51)] – [(2/52) * (1/51)]
• (650 + 12 – 2) / 2652
• 660 / 2526

1. There are 25 horses and among them you need to find out the fastest 3 horses. You can conduct race among at most 5 horses at a time to find out their relative speed. At no point you can find out the actual speed of the horse in a race. Find out the minimum number of races required to get the top 3 horses.
• First 5 races
• Make group of 5 horses and run 5 races.
• Group 1 – a1 > b1 > c1 > d1 > e1
• Group 2 – a2 > b2 > c2 > d2 > e2
• Group 3 – a3 > b3 > c3 > d3 > e3
• Group 4 – a4 > b4 > c4 > d4 > e4
• Group 5 – a5 > b5 > c5 > d5 > e5
• 6th race
• Top horses from each group – a1 > a2 > a3 > a4 > a5
• Fastest horse is a1
• We need to find the 2nd and 3rd fastest horse
• 7th race
• b1 and c1 can be faster than a2
• b2 can be baster than a3
• b1 > c1 > a2 > b2 > a3
• We are able to identify the 2nd and 3rd fastest horse
• Hence, 7 races

1. A bag contains 6 white balls and 4 black balls. What is the probability that they are of same color?
• 1st ball is white
• First draw = 1/2
• Second draw = 5/9
• 1st ball is black
• First draw = 1/2
• Second draw = 3/9
• Probability
• (1/2 * 5/9) + (1/2 * 3/9)
• 8/18 = 4/9

1. A cube having a side of 6 inches is painted red on all the faces and then cut into smaller cubes of 1 inch each. Find the total number of smaller cubes so obtained? How many cubes will have three faces painted? How many cubes will have only two faces painted? How many cubes will have only one face and no side painted?
• Total number of smaller cubes = 6*6*6 = 216
• Cubes at the corners of the original cube will have three faces painted = 8
• 4 cubes from each edge will have 2 faces painted = 4 * 12 = 48
• The 4*4 cubes from each face will have 1 face painted = 4 * 4 * 6 = 96
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