Exams › IBPS PO › Quantitative Aptitude

There are 63 cards in a box numbered from 1 to 63. Each card has only one number. Quantity I: Probability of picking a card whose digits, if interchanged, result in a number which is 36 more than the number picked. Quantity II: Probability of picking a card whose number is a multiple of 8 but not of 16.

1. Quantity I > Quantity II
2. Quantity I < Quantity II
3. Quantity I ≥ Quantity II
4. Quantity I ≤ Quantity II

Correct answer: Quantity I > Quantity II

Solution

For Quantity I, the only number satisfying the condition is 18, since reversing 18 gives 81 and 81 - 18 = 63, not 36; checking all valid two-digit numbers in 1 to 63 gives no such number, so the probability is 0. For Quantity II, numbers that are multiples of 8 but not 16 are 8, 24, 40, 56, giving probability 4/63. Therefore Quantity I < Quantity II.

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