Question

Ten boys go to a neighbouring orchard. Each boy steals a few mangoes. What is the total number of mangoes they steal?
I. The first boy steals $4$ mangoes and the fourth boy steals $16$ mangoes and the eighth boy $32$ mangoes and the tenth boy steals $40$ mangoes.
II. The first boy stole the minimum number of mangoes and the tenth boy stole the maximum number of mangoes.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both statements I and II are needed to answer the question.
• D. If the question cannot be answered even with the help of both statements.

Hint:

In total-sum problems, unless all values are known or a fixed sequence rule is provided, partial data on a few members is not enough to determine the total.

Answer 1

The Correct Option is D

We need the total mangoes stolen by 10 boys. Without further structure (like arithmetic or geometric progression), we must know each boy’s count individually.

Step 1: From Statement I
We know: Boy 1 = $4$ mangoes, Boy 4 = $16$ mangoes, Boy 8 = $32$ mangoes, Boy 10 = $40$ mangoes.
We do not know mangoes stolen by Boys 2, 3, 5, 6, 7, 9. No fixed pattern (e.g., AP, GP) is stated. Therefore, Statement I alone is not sufficient.

Step 2: From Statement II
First boy stole the minimum, tenth boy stole the maximum. Without knowing counts for other boys or a distribution rule, we cannot get the total. Statement II alone is not sufficient.

Step 3: Combining Statements I and II
Even with both: From I: we have 4 boys’ counts. From II: we know 1st is smallest and 10th is largest. But the missing boys’ counts are still undetermined and no pattern is given to calculate them. Therefore, total mangoes cannot be found uniquely.
Hence, correct answer is (d).