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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 number?
I.  The sum of the two digits is 8. The ratio of the two digits is 1 : 3.
 II.  The product of the two digit of a number is 12. The quotient of two digits is 3.

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:C - Either I or II alone sufficient to answer

Let the tens and units digit be x and y respectively. Then,

 I. x + y = 8 and x = 1
y 3
 I gives, 4y = 24        y = 6. So, x + 6 = 8        x = 2.
II. xy = 12 and x = 3
y 1
 II gives, x2 = 36        x = 6. So, 3y = 6        y = 2. Therefore, Either I or II alone sufficient to answer.