Question

What is the two digit number where the digit at the unit place is smaller?
I. The difference between the two digits is 5.
II. The sum of the two digits is 7.

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

Answer 1

The correct option is E Data in both the statements I and II together are necessary to answer the question.

Let the unit's digit be x and ten's digit be y and x < y.
$\therefore$ Number = 10y+x
From statement I,
$y-x=5\dots \left(i\right)$
From statement II,
$y+x=7\dots \left(ii\right)$
From (i) and (ii), x, y can be calculated and two digit number can be found.