OGQR 2020: Question No. 80
If x, y, and k are positive and x is less than y, then (x + k) / (y + k) is
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Algebra |
| Sub-Topic | Ratio / Inequality |
| Difficulty | Medium |
Solution
Given
In this question, we are given
- The numbers x, y, and k are positive.
- Also, x is less than y.
To Find
We need to determine
- The possible range of (x+ k) / (y+ k).
Approach & Working
We know that
- x < y
Or, xk < yk [Since k is a positive number, multiplication does not change the sign of inequality.]
Or, xk + xy < yk + xy [Adding xy on both sides]
Or, x (y + k) < y (x + k) [Taking x and y common on each side]
Or, x /y< (x+ k) / (y+ k). [Since y and (y + k) are positive numbers, division does not change the sign of inequality.]
Hence, the correct answer is option B.
Takeaways:
- Multiplying/dividing both sides of an inequality by a positive number does not change the sign of the inequality.
- Example: If x < y, then 2x < 2y.
- Multiplying/dividing both sides of an inequality by a negative number reverses the sign of the inequality.
- Example: If x < y, then -2x > -2y.
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