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Q #21
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Directions : These questions are based on the data given below.

This game is played by two people. Put 18 dots on a black board or on paper. Each player is to erase 1, 2 or 3 dots in his playing turn. Turns alternate between the two players, i.e. player 1 takes turn 1, then player 2 takes turn 2, then player 1 takes turn 3, and so on. You need not chose a number and stay with it. For instance, you might erase 1 dot on your firs turn, 2 dots on your second, 1 dot on your third and 3 dots on your fourth turn. The player who erases the last dot loses. You make the first move, and both players play intelligently, and you win. What is the number of dots that were erased in turns 1, 2 and 3 together?

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Always 1 less in the last move. And for each successive move, less is (maximum that can be drawn + 1) Hence 19, 15, 11 and 7. (Note that it is because every move made by 1 can be squared off to 4. i.e. 1 + maximum draw).

Q #22
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Directions : These questions are based on the data given below.

A number of children played at marbles. Each child won a different number of games and the total number of games won by the boys equaled the total number of games won by the two girls. As a memento of the occasion, they each received a present of marbles, equal to the square of the number of games he or she had won. In total, the boys recieived as many marbles as the girls, and the total number of marbles received by all of them together was less than 100. How many marbles were given as present?

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82 marbles were given as presents. [3 boys (1, 2, 6) and 2 girls (4, 5)] 1 x 1 + 2 x 2 + 6x 6 = 4 x 4 + 5 x 5 = 41

Q #23
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Directions : These questions are based on the data given below.

A Math Club devices the following method for encoding positive integers. First the integer is expressed in base 5, second a one to one correspondence is established between the digits that appear in the expression in base 5 and the elements of the set {A, E, I, O, U}. Using this correspondence, the members find that three consecutive integers in increasing order are coded as AOU, AOI, AAE respectively. What is the base – 10 expression for the integer coded AEIOU?

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AAE follows AOI establishes E ↔ 0 and 1 ↔ 4. Since AOI follows AOU, I immediately follows U and thus U ↔ 3. AAE follows AOI also establishes
A follows O and so O ↔ 1 and A ↔ 2.

    Hence, AEIOU ↔ 20413s = 2(625) + 4(25) + 1(5) + 3 = 1358.


Q #24
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Directions : These questions are based on the data given below.

What is the digit at the ten’s place in the number 2^99?

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Q #25
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Directions : These questions are based on the data given below.

Each letter represents a different digit, and the division represents a common fraction that can be written as a repeating decimal. What is the fraction?

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