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Problems on Numbers - General Aptitude

Q1:

What is the two-digit number?
I.  The difference between the two-digit number and the number formed by interchanging the digits is 27.
II.  The difference between the two digits is 3.
 III.  The digit at unit's place is less than that at ten's place by 3.

A I and II only

B I and III only

C All I, II and III

D I, and either II or III

E Even with all I, II and III, answer cannot be give.

ANS:E - Even with all I, II and III, answer cannot be give.

Let the tens and units digit be x and y respectively.   I. (10x + y) - (10y + x)        x - y = 3.  II. x - y = 3. III. x - y = 3. Thus, even all the given three statements together do not give the answer.  Correct answer is (E).