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Q #36
:

Directions: Select the correct alternative from the given choice.

Shonika and Smaraki are playing a game where they pick up coins alternately from the coins kept on a table. The rules of the game say that

  1. Each person has to pick up at least one coin in her turn
  2. No person can pick up more than 6 coins in each turn

The person who picks up the last coin from the table is the loser and the other person is the winner.

Some time during the game when it was Shonika's turn, there were 38 coins on the table. Without Shonika'srealinsing it, Smaraki wanted to surreptitiously remove some coins from the table. How many coins should she remove to ensure her own win irrespective of what moves Shonika makes later?

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Number of coins = 38 Winning strategy = 7k + 2 coin is to be picked. 7k + 2 coin in this case is 37. Hence Smaraki should surreptitious remove 2 coins (38th and 37th).

Q #37
:

Directions: Select the correct alternative from the given choice.

Shonika and Smaraki are playing a game where they pick up coins alternately from the coins kept on a table. The rules of the game say that

  1. Each person has to pick up at least one coin in her turn
  2. No person can pick up more than 6 coins in each turn

The person who picks up the last coin from the table is the loser and the other person is the winner.

What is the least number of coins greater than 20 at the beginning of the game to ensure a win for Shonika if Smaraki makes the first move?

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Number of coins on the table should be grater than 20. Winning strategy is 7k + 2 coin, which has to be picked. The number greater than 20 satisfying this is 23. If Smaraki makes the first move (with the number of coins on the table being 23 or greater) then Smaraki can ensure that she picks the 23rd coin to win. However if there are 22 coins on the table Smaraki will not win irrespective of the strategy she uses.

Q #38
:

Directions: Select the correct alternative from the given choice.

Shonika and Smaraki are playing a game where they pick up coins alternately from the coins kept on a table. The rules of the game say that

  1. Each person has to pick up at least one coin in her turn
  2. No person can pick up more than 6 coins in each turn

The person who picks up the last coin from the table is the loser and the other person is the winner.

If the rules of the game are changed such that the person clearing the table wins the game, the other rules remaining the same, how many coins should Shonika pick up when it is her turn to ensure a win for herself given that there are 18 coins on the table?

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The winning strategy in case the person picking the last coin wins is that the person should pick is controlling number + 1 number the coins. • Winning Strategy = (7k + 1)th coin is to be picked • 7k + 1st coin closest to 18 is 15 • 4 coins have to be picked (i.e., 18th , 17th, 16th,15th)

Q #39
:

Directions: Select the correct alternative from the given choice.

Mr. Ghosh took his students on a picnic to the local Zoo. In the first enclosure they saw four monkeys A, B, C and D each eating a different fruit seated at four different places. It is known that

  • A does not eat Guavas and is near the grassy lawn.
  • The monkey near the rocks is eating the apples.
  • The monkey eating the peach is not on the tree.
  • C is not on the tree and D does not eat oranges.
  • B is near the stream and does not eat the peach.

Which of the following is the true statement?

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D eats the Guava and C is near the rocks is the true statement.

Q #40
:

Directions: Select the correct alternative from the given choice.

Mr. Ghosh took his students on a picnic to the local Zoo. In the first enclosure they saw four monkeys A, B, C and D each eating a different fruit seated at four different places. It is known that

  • A does not eat Guavas and is near the grassy lawn.
  • The monkey near the rocks is eating the apples.
  • The monkey eating the peach is not on the tree.
  • C is not on the tree and D does not eat oranges.
  • B is near the stream and does not eat the peach.

Which of the following is eating a peach and is on the grassy lawn?

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A is eating a peach and is on the grassy lawn