IPMAT Indore 2024 · Quantitative Ability · Question 5

Step 1 — introduce the multiplier. Let the counts be 3k, 6k and 7k for a positive integer k. The total is

3k+6k+7k=16k

Step 2 — apply the condition. The oranges, 3k, must be a multiple of both 5 and 6, i.e. a multiple of \text{lcm}\left( 5,6 \right)=30:

30∣3k \Rightarrow 10∣k

Step 3 — take the smallest k. The least such k is 10, giving

\text{oranges}=30, \text{apples}=60, \text{bananas}=70, \text{total}=16\left( 10 \right)=160

Check: 30 is divisible by 5 ✔ and by 6 ✔.

Answer: 160

Shortcut. Push the condition onto k. “3k is a multiple of 30” is just “k is a multiple of 10”. Minimum k=10, total =16k=160. The common slip is to set the total to a multiple of 30 and answer 30 — but the condition is on the oranges alone.