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:

The difference between the digits of a two – digit number is 4. What is the digit in the unit's place?
I. The difference between the number and the number obtained by interchanging the positions of the digits is 36.
II. The sum of both the digits is 12.

• 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 I alone are sufficient to answer the question, while the data in Statement II 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 III together are necessary to answer the question.

Answer 1

The correct option is B

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.

Let the ten's digit be x and unit's digit be y.
Then, x - y = $\pm$4
I. (10x +y) - (10y + x) = 36 $\iff$ x - y = 4
II. x + y = 12
Thus, (i) and (iii) together give the answer.
$\therefore$ II alone gives the answer and I alone does not give the answer.