Q.56 If
3 ≤ X ≤ 5 and 8 ≤ Y ≤ 11,
then which of the following options is TRUE?
Inequality of Ratios: Finding the Correct Range of X/Y
In questions involving inequalities, finding the correct range of a ratio requires
careful consideration of minimum and maximum values of the numerator and denominator.
Concept Used
The minimum value of X/Y is obtained by dividing the minimum value of X by the maximum
value of Y. The maximum value of X/Y is obtained by dividing the maximum value of X by
the minimum value of Y.
Step-by-Step Solution
Minimum Value of X/Y
Minimum X = 3 and Maximum Y = 11
Minimum X/Y = 3/11
Maximum Value of X/Y
Maximum X = 5 and Minimum Y = 8
Maximum X/Y = 5/8
Final Range of X/Y
3/11 ≤ X/Y ≤ 5/8
Correct Answer
Option (B): 3/11 ≤ X/Y ≤ 5/8
Explanation of All Options
Option (A): Uses incorrect bounds and gives a value greater than 1,
which is not possible since X < Y.
Option (B): Correctly uses the minimum X with maximum Y and maximum X
with minimum Y.
Option (C): Upper bound is invalid as it exceeds the possible value
of X/Y.
Option (D): Both bounds are incorrectly calculated.
Conclusion
The correct range of X/Y is obtained by using extreme values appropriately.
Hence, the correct answer is Option (B).
