## OG 2020: Question No. 310

What is the remainder when the positive integer n is divided by 5?

- When n is divided by 3, the quotient is 4 and the remainder is 1.
- When n is divided by 4, the remainder is 1.

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Number Properties |

Sub-Topic | Divisibility & Remainders |

Difficulty | Easy – Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given

- The number n is a positive integer.

We need to determine

- The remainder, when n is divided by 5.

To find the remainder when n is divided by 5, we need to know the value of n or the units digit of n.

As we do not have any pertinent information about n in the question stem, let us now analyse the individual statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, when n is divided by 3, the quotient is 4 and the remainder is 1.

- Therefore, the value of n = 3 × 4 + 1 = 12 + 1 = 13

As we can determine the value of n, we will also be able to find the remainder when n is divided by 5.

Hence, statement 1 is sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

As per the information given in statement 2, when n is divided by 4, the remainder is 1.

However, in this division, we have no information about the quotient.

- If the quotient is 1, then n = 4 × 1 + 1 = 5, which is divisible by 5.
- If the quotient is 2, then n = 4 × 2 + 1 = 9, which is not divisible by 5.

As we cannot determine the unique value of n, statement 2 is not sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

Since we can determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer choice is option A.