Question:
Given \(0<x<y<z<10\), where \(x,y,z\) are integers:
Quantity A: \(-7\)
Quantity B: \(x + y - z\)
Given \(0<x<y<z<10\), where \(x,y,z\) are integers:
Quantity A: \(-7\)
Quantity B: \(x + y - z\)
Quantity A: \(-7\)
Quantity B: \(x + y - z\)
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When comparing an expression with a fixed number, check the possible range of values first.
Updated On: Oct 3, 2025
- Quantity B is greater.
- The two quantities are equal.
- Quantity A is greater.
- The relationship cannot be determined from the information given.
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The Correct Option is D
Solution and Explanation
Step 1: Possible range of \(x+y-z\).
Since \(0<x<y<z<10\), the smallest values possible are \(x=1, y=2, z=3\). Then: \(x+y-z = 1+2-3=0\).
Largest values: \(x=7, y=8, z=9\). Then: \(x+y-z = 7+8-9=6\).
So, \(x+y-z\) ranges between 0 and 6.
Step 2: Compare with Quantity A.
Quantity A = -7, Quantity B ranges from 0 to 6.
Step 3: Decide.
Clearly, Quantity B can vary but is always greater than -7. Final Answer: \[ \boxed{\text{Quantity B is greater.}} \]
Since \(0<x<y<z<10\), the smallest values possible are \(x=1, y=2, z=3\). Then: \(x+y-z = 1+2-3=0\).
Largest values: \(x=7, y=8, z=9\). Then: \(x+y-z = 7+8-9=6\).
So, \(x+y-z\) ranges between 0 and 6.
Step 2: Compare with Quantity A.
Quantity A = -7, Quantity B ranges from 0 to 6.
Step 3: Decide.
Clearly, Quantity B can vary but is always greater than -7. Final Answer: \[ \boxed{\text{Quantity B is greater.}} \]
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