Aptitude - Problems on Numbers

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Data Sufficiency 1
Data Sufficiency 2

"To err is human; to forgive, divine."

- Alexander Pope

Directions to Solve

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.

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

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

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