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Q #46
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Quants Question

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

A set of natural numbers, P, is formed using some of the first 1000 natural numbers. The set contains the maximum number of elements such that each element satisfies the following two conditions. I.. No numbers of the set P is prime. II. Any two numbers of the set P are prime to each other. What could be the greatest possible natural number in the set P?

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Consider the square root of 1000. The largest prime less than this is 31. So the set of all prime numbers less than or equal to 31 i.e., { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31} must be represented in set A. The above set itself cannot be set A, as the members of set A are non-prime. Therefore, each member of set A must represent exactly one of these prime numbers as, set A is such that maximum number of elements. If, any member of the set is a combination of 2 or more primes from the above set, then the number of elements in set A will get reduced as the members of this set should be co-prime to each other. Set A could be {22, 32, 52, 112, 132, 172, 192, 232, 292, 312,} It can be noted that there are more possibilities for set A. A number of set A could t, a product of exactly one prime number from the original set and another prime number which is not from the original set. If none of the prime numbers is used on more than one occasion then the set of numbers will be co-primes and hence satisfy the coordination for set A. Consider 999 999 – 99 x 11 = 27 x 37 = 33 x 37 The prime number 3 from the original set is represented only once even though it is multiplied three times. Therefore 999 can be a member of the set and it is obviously the larges.

Q #47
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Quants Question

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

If x is a positive quantity such that 2 x ? 3log 5 2 , then x is equal to

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Q #48
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Quants Question

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

The values of the numbers 2^2004 and 5^2004 are written one after another. How many digits in all are there?

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Q #49
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Quants Question

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 #50
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Quants Question

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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