If a Positive Integer n is Divided by 5, the Remainder is 3 GMAT Problem Solving

Question: If a positive integer n is divided by 5, the remainder is 3. Which of the numbers below yields a remainder of 0 when it is divided by 5?

1. n + 3
2. n + 2
3. n - 1
4. n - 2
5. n + 1

Correct Answer: B

Solution and Explanation:
Approach Solution 1:
The problem statement states that:
Given:

• If a positive integer n is divided by 5, the remainder is 3.

The problem statement asks to find the number that yields a remainder of 0 when it is divided by 5

Let us solve the problem in the following way
It is given that n divided by 5 yields a remainder equal to 3
The above statement can be written as follows
n = 5 k + 3 , where k is an integer
Now let us add 2 to both sides of the above equation
We will get the equation as-
n + 2 = 5 k + 5
n + 2 = 5(k + 1)
According to the preceding, n + 2 divided by 5 yields a remainder of zero.
Therefore, the number that yields a remainder of 0 when it is divided by 5 is n + 2

Approach Solution 2:
There is another way to approach this question is as follows-

We know that

\(\frac{n}{5}\)= p+3
n = 5p + 3.
As it can be seen that 5p is divisible by 5 but 3 is not. we have to add 2
n + 2 = 5p + 3 + 2 .
n + 2 = 5p + 5
n + 2 = 5(p+1)
Now it is seen that 5(p + 1) is divisible by 5.
Therefore, the number that yields a remainder of 0 when it is divided by 5 is n + 2

“If a positive integer n is divided by 5, the remainder is 3”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “501 GMAT Questions”. The GMAT Problem Solving questions enable the candidates to access data in order to crack numerical problems. The candidate must posses solid knowledge in arithmetic, geometry and algebra to solve the quantitative problems effectively. GMAT Quant practice papers assist the candidates to analyse different sorts of questions that will enhance their mathematical understanding.

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