Aptitude - Problems on Numbers

Exercise :: Problems on Numbers - Data Sufficiency 1

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.
1. 

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

Answer: Option C

Explanation:

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.


2. 

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

Answer: Option E

Explanation:

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).


3. 

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

Answer: Option A

Explanation:

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.