Question
A pack has 100 cards. Each card was marked with a
different number from 100 to 199. A card was selected at random. Find the probability that the number on it is not a perfect square.Solution
The numbers range from 100 to 199 (inclusive). The perfect squares in this range are: 100 (10²), 121 (11²), 144 (12²), 169 (13²), 196 (14²). So, there are 5 perfect squares. Total cards = 100. Number of non-perfect square cards = 100 - 5 = 95. Required probability = Favorable outcomes / Total outcomes = 95/100 = 19/20.
Two numbers P and Q are in the respective ratio 7: 9 and their sum is 80. Then, P is equal to:
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