How many positive rational numbers less than 1 are there such that the sum of the numerator and the denominator doesn’t exceed 10.

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answer is B.

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Detailed Solution

Concept: Assume a rational number to be pq , such that both p and q are integers and q 0. Keeping in mind the conditions given in the question one can easily find the rational no. required. As given, the rational number must be less than 1.
The denominator of the number must be greater than the numerator.
∴ q >p
→ Also given, the sum of p and q must not exceed the value 10.
∴ p +q < 10
The possible rational numbers under the constraints are:
12, 13, 14, 15, 16, 17, 18, 19, 23, 25, 27, 28, 34, 35, 45
Thus, there are a total of 15 rational numbers.
Hence, the correct answer is option 2.

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