Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

The sum of three natural numbers is 50. What will be the number of digits in their product?

I. Largest number among them is 41.

II. At least one of the three numbers has 2 digits.

A The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

B The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

C The data in statement I alone or in statement II alone is sufficient to answer the question.

D The data in both the statements I and II is not sufficient to answer the question.

E The data in both the statements I and II together is necessary to answer the question.

Solution

Correct Answer: Option A

From statement I:

Largest number among them is 41.

⇒ The remaining two numbers can be at most 8 and at least 1. Possible pairs are (1, 8), (2, 7), (3, 6), (4, 5). In each of the cases the product of three numbers will be a 3 digit number.

∴ Statement I alone is sufficient to answer the question.

From statement II:

At least one of the three numbers has 2 digits.

We see that this is a statement that is always true and provides no extra information. Three natural numbers whose sum is 50 cannot be all 1 digit numbers, as sum would not exceed 27 in that case.

∴ Statement II alone is sufficient to answer the question.

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