GMAT Practice Question: If x, y, and k are positive and x is less than y, then \frac{x+k}{y+k} is
Question
If x, y, and k are positive and x is less than y, then \frac{x+k}{y+k} is
- 1
- greater than \frac{x}{y}
- equal to \frac{x}{y}
- less than \frac{x}{y}
- less than \frac{x}{y} or greater than \frac{x}{y}, depending on the value of k
Topics: inequalities, fractions
Solution
Step 1
We know that x is less than y and both are positive, so the ratio of the smaller to the larger is below one.
x<y \frac{x}{y}<1
Step 2
We then notice that adding the same positive amount to the numerator and denominator of a fraction below one makes the fraction larger.
\frac{x+k}{y+k}>\frac{x}{y}
Answer
greater than \frac{x}{y}
