# 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

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

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

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.