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 two – digit number whose first digit is 'a' and the second digit is 'b'?
I. The sum of both the digits is 6.
II. The number is a multiple of 51.

• 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 E

if the data in both statements I and II together are necessary to answer the question.

Number = 10b +a
II. 10b + a = 51 $\times c$ , where c = 1, 2, 3 etc.
I. a + b = 6
Taking c = 1, we get 10b + (6 - b) = 51 $\iff$ 9b = 45 $\iff$ b = 5
$\therefore$ a = 1, b = 5
So, number = 51
Thus, I and II together give the answer.