Ethan is thinking of a negative number. This number is lower than $-4$ and higher than $-10$. The number is odd and a multiple of $3$. We need to find this number.

ArithmeticInteger PropertiesInequalitiesMultiples
2025/4/22

1. Problem Description

Ethan is thinking of a negative number. This number is lower than 4-4 and higher than 10-10. The number is odd and a multiple of 33. We need to find this number.

2. Solution Steps

The number is between 10-10 and 4-4. That means it is one of the following numbers:
9,8,7,6,5-9, -8, -7, -6, -5.
The number must be odd, so we can eliminate the even numbers:
9,7,5-9, -7, -5.
The number must be a multiple of 33, so it must be divisible by 33.
Out of the remaining numbers, only 9-9 is a multiple of 33 since 9=3×3-9 = 3 \times -3.
Therefore, the number Ethan is thinking of is 9-9.

3. Final Answer

-9

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