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Q #11
⏰ :
Unlike in India, the pizzas in Italy are wafer thin and are square shaped. There is a square pizza that has to be cut into pieces to serve 115 guests. What is the minimum number of straight cuts required to divide the pizza into exactly 115 pieces. If it does not matter whether the pieces are equal sized or not.

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Q #12
⏰ :
In table tennis the first player to score 21 points wins. Service alternates between the two players every 5 points. A player can score points both during his service and his opponent’s service. Ali beat Badshah 21 – 16 in a game, 24 of the 37 points played were won by the player serving. Who served first?

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Q #13
⏰ :
In a nuclear plant there are warning lights placed at locations numbered 1 to 13 : The management wishes to set up the smallest possible number of fixed monitoring stations, so as to continuously monitor all the lights. A monitoring station set up at a given location, can of course monitor the light at that location. Further, from location 1, it is possible to see the lights at locations 2, 3, 4, 5, 6 and 7. From location 2, it is possible to see the lights at locations 1, 3, 5, 6, 7 and 8. From location 3, it is possible to see the lights at locations 1, 4, 5, 6 and 7. From location 4, it is possible to see the lights at locations 1, 7 and 9. From location 5, it is possible to see the lights at locations 4, and 10. From location 6, it is possible to see the lights at locations 3, and 11. From location 7, it is possible to see the lights at locations 2, 12 and 13. From location 8, it is possible to see the lights at locations 2 and 13. The minimum number of monitoring stations which must be set up is.

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Let the result of the multiplication and the addition be x.

    x = 1 + (1 x 2) + ( 1 x 2 x 3) + ……..+ ( 1 x 2 x 3 x 4 x ……..x 100)

    x = 1! + 2! + 3! + 5! +……..100!

    5!, 6!, 7!,…….all the numbers will end with zero.

    ∴The unit digit of x = unit digit of (1! + 2! + 3! + 4!)

    ∴ The unit digit of x = 3


Q #14
⏰ :
The figure below shows the network connecting cities, A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F?

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ABCF, ABF, ABEF, ABDCF, ABDEF, ADCF, ADCEF, ADEF, ADEF.

Q #15
⏰ :
Ashish is given Rs 158 in one rupee denomination. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

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The coins should be put as follows: 1, 2, 4, 8, 16, 32, 64, 1, 2, 4, 8, 16, and hence he can meet all denominations. Hence 12 bags.