# 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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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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