Question

Which expression can have a remainder greater than 7?


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Math item response image

Math item response image

Math item response image

Answer 1

To determine which expression can have a remainder greater than 7, we need to analyze the potential remainders when dividing by specific numbers. The context often involves modular arithmetic.

1. For an expression to have a remainder greater than 7, it must be divided by a number that has a potential remainder range including values greater than 7.

2. If we consider the expression \( x \mod n \):
- The possible remainders when dividing by \( n \) are 0, 1, 2, ..., \( n-1 \).
- Therefore, for a remainder to be greater than 7, \( n \) must be greater than 7. This means we could potentially have remainders of 8, 9, ..., up to \( n-1 \).

Thus, if the divisor \( n \) in any of the expressions is greater than 7, then it is possible for that expression to yield a remainder greater than 7.

Without specific expressions or values provided, I cannot identify exactly which expression allows for a remainder greater than 7. But in general, any expression where the divisor is greater than 7 can have a remainder greater than 7.

If you have specific expressions or additional context, please share, and I can provide a more tailored analysis!