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What is the remainder when the positive integer n is divided by 5? – OG 2020 Question #310 with Solution

OG 2020: Question No. 310

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

  1. When n is divided by 3, the quotient is 4 and the remainder is 1.
  2. 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

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

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

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)

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

Hence, the correct answer choice is option A.

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