# Y is a subset of A such that the geometric mean of no two elements of Y is 350.

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Given  A = { 1, 3, 9, 27, 81,................................3100 }

Y is a subset of A such that the geometric mean of no two elements of Y is 350. N is the maximum possible number of elements in set Y.

A. What is the value of N?

1. 50
2. 51
3. 49
4. 52

B. In how many ways can the set Y be formed such that it has exactly N elements?

1. 250
2. 251
3. 350
4. 351

Geometric mean of two numbers is 350 if their multiple is 3100. This happens for 3x and 3y, where x + y = 100. So, out of 101 elements in A, we can have 101 possible values for (x, y) which means 50 pair of values. For these 50 pairs, we can only pick 1 value to be in Y. So, maximum number of elements in Y is 51.

Out of 51 elements we have a choice out of 2 for 50 elements. So, no. of ways in which set Y can be formed = 250.

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