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Problems on Numbers - General Aptitude

Q1:

What is the two-digit number? I. Sum of the digits is 7. II. Difference between the number and the number obtained by interchanging the digits is 9. III. Digit in the ten's place is bigger than the digit in the unit's place by 1.

A I and II only

B II and III only

C I and III only

D All I, II and III

E None of these

ANS:E - None of these

Let the tens and units digit be x and y respectively.   I. x + y = 7.  II. (10x + y) - (10y + x) = 9        x - y = 1. III. x - y = 1. Thus, I and II as well as I and III give the answer.  Correct answer is (E).