Problems on Numbers - General Aptitude

Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read the both statements and
  • Give answer (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.
  • Give answer (B) if the 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.
  • Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
  • Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
  • Give answer(E) if the data in both Statements I and II together are necessary to answer the question.
Q1:

What is the two-digit number?
I.  The difference between the two digits is 9.
 II.  The sum of the digits is equal to the difference between the two digits.

A I alone sufficient while II alone not sufficient to answer

B II alone sufficient while I alone not sufficient to answer

C Either I or II alone sufficient to answer

D Both I and II are not sufficient to answer

E Both I and II are necessary to answer

ANS:E - Both I and II are necessary to answer

Let the tens and unit digits be x and y respectively. Then,  I. x - y = 9. II. x + y = x - y. From I and II, we get x - y = 9 and x + y = 9. On solving, we get x = 9 and y = 0.  Required number is 90. Thus, both I and II are needed to get the answer.  Correct answer is (E).