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Problems on Numbers - General Aptitude

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
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).