Question

The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer
What is the original number?
I. Sum of two digits of a number is 10. The ratio between the two digits is 1:4.
II. Product of two digits of a number is 16. Quotient of the two digits is 4.

• A. the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
• B. the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
• C. the data either in statement I alone or in statement II alone are sufficient to answer the question.
• D. the data even in both statements I and II together are not sufficient to answer the question.

Answer 1

The Correct Option is D

Let's analyze each statement:
Statement I:
● Sum of two digits of a number is 10.
● The ratio between the two digits is 1:4.
Statement II:
● Product of two digits of a number is 16.
● Quotient of the two digits is 4.
Now, let's consider each statement separately:
Statement I:
From the first part, "Sum of two digits of a number is 10," we can have multiple pairs of digits that sum up to 10, such as (1, 9), (2, 8), (3, 7), and so on. The ratio between the two digits being 1:4 does not uniquely determine the original number.
Statement II:
From the second part, "Product of two digits of a number is 16," we can have multiple pairs of digits that multiply to 16, such as (1, 16), (2, 8), and (4, 4). The quotient of the two digits being 4 does not uniquely determine the original number.
Now, let's consider both statements together: When we consider both statements together, we can narrow down the possibilities a bit. The sum of the digits being 10 and the product of the digits being 16 means that the two digits must be 2 and 8. However, this still doesn't uniquely determine the original number because we don't know their order. Since even with both statements together, we cannot uniquely determine the original number,
So, the correct option is: (D) the data even in both statements I and II together are not sufficient to answer the question.