When the positive integer x is divided by 9, the remainder GMAT Problem Solving

Question: When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

  1. 0
  2. 1
  3. 3
  4. 4
  5. 6

Approach Solution (1)

X = 9K+5
3X = 3(9K + 5)
Then
(27K + 15) / 9
3K + (15 / 9)
15/9 ends with the remainder 6.

Correct option: E

Approach Solution (2)

Let n represent the quotient of the number.
We have been given that when the positive integer x is divided by 9, the remainder is 5. We can represent this information in an equation as:
x = 9n + 5

When 3x is divided by 9:
3x: 3(9n + 5)
27n + 15

Now, we need to break 15 into two numbers as:
27n + 9 + 6

Now, we will factor out 9 as:
9(3n + 1) + 6

Therefore, the remainder will be 6.

Correct option: E

Approach Solution (3)

Since the remainder from the division of x by 9 is 5, we can write x = 9s + 5 for some positive integers.
Multiplying by 3, we get:
3x = 27s + 15
= 27s + 9 + 6
= 9(3s + 1) + 6
Thus, the quotient is 3s + 1 and the remainder is 6

Correct option: E

“When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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