IPMAT Indore 2025 · Quantitative Ability · Question 21

Step 1 — count the sample space. n is a three-digit number with hundreds digit 1, 2 or 3, and digits summing to 10. For each hundreds digit h, the tens and units must satisfy t+u=10-h:

\text{Total}=10+9+8=27

Step 2 — the divisibility test. A number is divisible by 4 exactly when the number formed by its last two digits is divisible by 4.

Step 3 — hunt through each block.

h=1, t+u=9: the two-digit endings are 09,18,27,36,45,54,63,72,81,90. Divisible by 4: 36, 72 → 136, 172 (2)

h=2, t+u=8: endings 08,17,26,35,44,53,62,71,80. Divisible by 4: 08, 44, 80 → 208, 244, 280 (3)

h=3, t+u=7: endings 07,16,25,34,43,52,61,70. Divisible by 4: 16, 52 → 316, 352 (2)

\text{Favourable}=2+3+2=7

Step 4 — the probability.

P=\frac{7}{27}

Answer: Option 2 — \frac{7}{27}