Q.1 If 3 ≤ x ≤ 5 and 8 ≤ y ≤ 11 then which of the following options is TRUE?
- (A) 3/5 ≤ x/y ≤ 8/5
- (B) 3/11 ≤ x/y ≤ 5/8
- (C) 3/11 ≤ x/y ≤ 8/5
- (D) 3/5 ≤ x/y ≤ 8/11
Introduction
Questions based on finding the range of an algebraic expression are very common in school exams,
Olympiads, and competitive tests. Such problems test conceptual clarity of inequalities,
fractions, and interval analysis.
In this article, we will solve the given inequality problem step by step, determine the minimum
and maximum values of X/Y, and analyze each option to find the correct answer confidently.
Key Concept Used
Since X and Y are both positive, the range of the ratio
X⁄Y is found as:
- Minimum value = (minimum of X) ÷ (maximum of Y)
- Maximum value = (maximum of X) ÷ (minimum of Y)
Step-by-Step Solution
Step 1: Minimum Value of X⁄Y
Minimum X = 3, Maximum Y = 11
(X⁄Y)min =3⁄11
Step 2: Maximum Value of X⁄Y
Maximum X = 5, Minimum Y = 8
(X⁄Y)max =5⁄8
Final Range
3⁄11≤X⁄Y≤5⁄8
Correct Answer
Option (B)
Quick Exam Tip
For positive variables:
Minimum of X⁄Y = minimum X ÷ maximum Y
Maximum of X⁄Y = maximum X ÷ minimum Y
Conclusion
This problem is a classic example of range determination using inequalities.
By carefully identifying the extreme values of the numerator and denominator,
the correct interval can be found quickly and accurately.
Such questions are easy-scoring when approached systematically.
