Question

The given question consists of a set of statements. Find out whether the data provided in the statements are sufficient to answer the question and mark the option:

What is the number?
I. The sum of the two digits is 8 and the ratio of the two digits is 1:3.
II. The product of two digits of a number is 12 and the quotient of two digits is 3.

• A. if 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. if 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. if the data even in both Statements I and II together are not sufficient to answer the question.
• D. if the data even in both Statements I and II together are not sufficient to answer the question.
• E. if the data in both statements I and II together are necessary to answer the question.

Answer 1

The correct option is B

if 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.

Let the tens and units digit be x and y respectively.
I. x+y = 8 and $\frac{x}{y}=\frac{1}{3}$
II. xy = 12 and $\frac{x}{y}=\frac{3}{1}$

$\therefore$ statement II gives, x${}^2$ = 36 $\iff$ x = 6
So, 3y = 6 $\iff$ y = 2
Thus, II alone can give the answer, but I alone cannot give the answer.