# Number Properties Puzzle -Critical Thinking 3

This is a great critical thinking challenge for those who love math challenges and puzzles. Let's see if you can solve it! Time to challenge your brain!

## Challenge:

When number y is divided by 7, the remainder equals to the quotient. What is the greatest value of y?

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The correct answer is 48.

First, let’s find some values of y. Let’s choose the smallest possible value for the quotient. It’s 0. Then, the remainder should also be 0. Therefore, the number y should be 0.

0 × 7 + 0 = 0

To find the next value of y, you should choose 1 for both quotient and remainder. Then, the value of y is 8.

1 × 7 + 1 = 8

What is the next value of y?

It’s 16. 2 × 7 + 2 = 16

Using the same pattern, you can find other values of y.

3 × 7 + 3 = 24

4 × 7 + 4 = 32

5 × 7 + 5 = 40

6 × 7 + 6 = 48

It is possible to choose 7 for both quotient and remainder?

Since, the remainder cannot be equal to the divisor (it’s 7 here), therefore, the greatest number you can choose for both quotient and remainder is 6. Then, the greatest value of y is 48.

When you divide 48 by 7, both quotient and remainder are 6.

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