# Aptitude - Problems on Numbers

- Problems on Numbers - Formulas
- Problems on Numbers - General Questions
- Problems on Numbers - Data Sufficiency 1
- Problems on Numbers - Data Sufficiency 2

*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. |

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, *x*^{2} = 36 *x* = 6.

So, 3*y* = 6 *y* = 2.

Therefore, Either I or II alone sufficient 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. |

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).

What is the two-digit number whose first digit is | |

I. | The number is multiple of 51. |

II. |
The sum of the digits |

**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.