Question

The numbers represented by variables a and c are integers.

If c > b > a, under which of the following conditions could the expression b > 5 be true? Select ALL that apply.
A. when and a = -5 and c = 5

B. when and a = 0 and c = 10

C. when and a = 7 and c = 3

D. when and a = 2 and c = 8

E.
when and

Answer 1

To determine which conditions allow the expression \( b > 5 \) to be true under the constraint that \( c > b > a \), let's analyze each option:

### A. when \( a = -5 \) and \( c = 5 \)
- Since \( c = 5 \) and \( a = -5 \), we need to find \( b \) such that \( -5 < b < 5 \).
- Here, \( b \) can take values \( -4, -3, -2, -1, 0, 1, 2, 3, 4 \).
- None of these values is greater than 5.
- **Not valid**.

### B. when \( a = 0 \) and \( c = 10 \)
- Here \( 10 > b > 0 \).
- Possible integer values for \( b \) can be \( 1, 2, 3, 4, 5, 6, 7, 8, 9 \).
- All of these values are greater than 5.
- **Valid**.

### C. when \( a = 7 \) and \( c = 3 \)
- This condition contradicts \( c > b > a \) because \( c = 3 < a = 7 \).
- **Not valid**.

### D. when \( a = 2 \) and \( c = 8 \)
- Here \( 8 > b > 2 \).
- Possible integer values for \( b \) can be \( 3, 4, 5, 6, 7 \).
- Only \( 6 \) and \( 7 \) are greater than 5.
- **Valid**.

### E. Additional condition not specified.
Since there seems to be no specific condition given in option E, we cannot evaluate it.

### Conclusion:
The valid options under the condition \( c > b > a \) and \( b > 5 \) are:
- **B** (when \( a = 0 \) and \( c = 10 \))
- **D** (when \( a = 2 \) and \( c = 8 \))

Thus, the answers are **B and D**.