Q1:jipmat 2025QA › MiscellaneousMediumQA · MCQ

After adding 5 to both numerator and denominator of the following fractions, arrange them in ascending order of the magnitude of change in their values. A. $\frac{2}{3}$ B. $\frac{3}{4}$ C. $\frac{4}{5}$ D. $\frac{5}{6}$

• AD < C < A < B
• BD < A < B < C
• CD < C < B < A
• DA < B < C < D

Pick an option to attempt

Show solution

The Setup: We are giving these fractions a +5 glow-up on both the top and bottom. We need to measure how much their value *changed* (New - Old), and then rank those changes from smallest to largest. Step 1: Create a general formula for the change. Let the fraction be $\frac{n}{d}$. $$\text{Change}=\frac{n+5}{d+5}-\frac{n}{d}$$ $$\text{Change}=\frac{d(n+5)-n(d+5)}{d(d+5)}$$ $$\text{Change}=\frac{nd+5d-nd-5n}{d(d+5)}=\frac{5(d-n)}{d(d+5)}$$ Step 2: Notice the cheat code. For all our fractions (A, B, C, D), the difference between the denominator and numerator is exactly $1$ ($3-2=1$, $4-3=1$, etc.). So $d-n=1$ for all of them! The change formula simplifies to just $\frac{5}{d(d+5)}$. Step 3: Evaluate the magnitude of change for each based on its denominator ($d$). Since the numerator is always $5$, the fraction with the *largest* denominator will have the *smallest* change (inversely proportional vibes). Denominator of A ($d=3$) $\rightarrow$ Smallest denominator = Largest change. Denominator of D ($d=6$) $\rightarrow$ Largest denominator = Smallest change. Step 4: Rank them in ascending order (smallest change to largest change). Since the denominators are $6 > 5 > 4 > 3$, the changes are D < C < B < A. Final Answer: D < C < B < A