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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 two-digit number whose first digit is a and the second digit is b?. The number is greater than 9.
I.  The number is multiple of 51.
 II.  The sum of the digits a and b is 6.

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:A - I alone sufficient while II alone not sufficient to answer

From statement I: A two digit number, greater than 9 and multiple of 51 should be 51 itself. Because, 2 x 51 = 102 (3 digit number). Therefore, I alone sufficient to answer. From statement II: A two digit number, greater than 9 and sum of the digit is 6. It can be 15, 24, 33, 42, 51. So we cannot determine the required answer from the statement II alone. Thus, I alone give the answer while II alone not sufficient to answer.