IPMAT Indore 2025 · Quantitative Ability · Question 9

Step 1 — read the condition geometrically. On a number line, \left| a-b \right| is the distance from a to b. The equation says

\left( \text{distance}a\to b \right)+\left( \text{distance}b\to c \right)=\left( \text{distance}a\to c \right)

Going from a to c via b costs exactly the same as going straight. That happens only when b lies between a and c. (If b were outside, the detour would be strictly longer — the triangle inequality.)

Step 2 — push b as high as possible. We need one of a, c to be larger than b. Natural numbers less than 100 go up to 99, and all three must be distinct.

Could b=99? Then we would need some a or c greater than 99, which is not allowed. ✗

Try b=98: take a=99 and c=97. Check: \left| 99-98 \right|+\left| 98-97 \right|=1+1=2, and \left| 97-99 \right|=2. ✓

Answer: 98