IPMAT Indore 2024 · Quantitative Ability · Question 24

Step 1 — read off the magnitudes. Scale so that \left| a \right|=1. Then

\left| \frac{c}{a}\right|=4 \Rightarrow \left| c \right|=4, \left| \frac{a}{b}\right|=\frac{1}{3}\Rightarrow \left| b \right|=3

Consistency check with the third condition: \left| \frac{b}{c}\right|=\frac{3}{4} ✔ matches \left| b \right|/\left| c \right|=3/4.

Step 2 — fix the signs.

ac>0: a and c have the same sign.

\frac{b}{c}=-\frac{3}{4}<0: b and c have opposite signs.

Take a=1 (the ratio asked for is sign-invariant under a\to -a, as all three of a, b, c flip together). Then c=+4 and b=-3.

Step 3 — evaluate.

\frac{b+c}{a}=\frac{-3+4}{1}=1

Verify with a=-1: then c=-4, b=3, and \frac{3-4}{-1}=1 ✔ — the same value.

Answer: Option 4 — 1

Shortcut. Magnitudes then signs — never together. Set \left| a \right|=1, read \left| b \right|=3, \left| c \right|=4 off the two modulus equations (the third one only confirms they are consistent). Now only \frac{b}{c}<0 and ac>0 matter: b is the odd one out, so b and c carry opposite signs while a matches c. That gives \frac{b+c}{a}=\frac{-3+4}{1}=1. Options 7 and -7 are there for anyone who adds \left| b \right|+\left| c \right| without the sign.