Identify a Number Between 10,999 and 11,101

Q: How do I read the inequality symbols correctly?

The symbol < means "less than". So \( 10,999 reads: "x is greater than 10,999 AND less than 11,101". Think of the symbol as an arrow pointing to the smaller number!

Q: What if a number equals exactly 10,999 or 11,101?

Since we use strict inequalities (< not ≤), the number cannot equal the boundaries. It must be strictly between 10,999 and 11,101, not including these values.

Q: Is there only one correct answer in this range?

No! There are many correct answers in this range (like 11,000, 11,050, 11,100). The question asks you to select from the given choices, so pick the one that fits.

Q: How can I quickly eliminate wrong choices?

Start by checking the obvious violations: Is 10,990 even greater than 10,999? No, so eliminate it immediately. Then check if remaining choices exceed 11,101.

Q: What does the box symbol mean in math?

The □ (box) symbol represents an unknown value that you need to find or select. It's like a placeholder asking "what number goes here?"

Number Comparisons with Range Constraints

Select a suitable number for the given range:

$10,999 < \Box < 11,101$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Select a suitable number for the given range:

$10,999 < \Box < 11,101$

Step-by-step solution

To solve this problem, we need to determine which of the given choices falls between 10,999 and 11,101.

Check each choice against the bounds of the range:
Choice 1: $11,003$ — Is $11,003$ greater than $10,999$ ? Yes. Is $11,003$ less than $11,101$ ? Yes. Thus, $11,003$ fits within the range.
Choice 2: $11,109$ — Is $11,109$ greater than $10,999$ ? Yes. Is $11,109$ less than $11,101$ ? No.
Choice 3: $10,990$ — Is $10,990$ greater than $10,999$ ? No.
Choice 4: $11,202$ — Is $11,202$ greater than $10,999$ ? Yes. Is $11,202$ less than $11,101$ ? No.

Therefore, the only choice that fits within the specified range is $11,003$ .

Final Answer

$11,003$

Key Points to Remember

Essential concepts to master this topic

Range Rule: Number must be greater than lower bound and less than upper bound
Technique: Check each choice: Is 11,003 > 10,999 AND < 11,101? Yes
Check: Verify both inequalities are satisfied for the chosen number ✓

Common Mistakes

Avoid these frequent errors

Checking only one boundary condition
Don't just verify if a number is greater than 10,999 and ignore the upper limit = accepting wrong answers! A number might exceed 10,999 but still be too large for the range. Always check that your number satisfies BOTH the lower AND upper boundary conditions.

Practice Quiz

Test your knowledge with interactive questions

Select the appropriate sign:

$24,909\Box24,990$

FAQ

Everything you need to know about this question

How do I read the inequality symbols correctly?

The symbol < means "less than". So $10,999 < x < 11,101$ reads: "x is greater than 10,999 AND less than 11,101". Think of the symbol as an arrow pointing to the smaller number!

What if a number equals exactly 10,999 or 11,101?

Since we use strict inequalities (< not ≤), the number cannot equal the boundaries. It must be strictly between 10,999 and 11,101, not including these values.

Is there only one correct answer in this range?

No! There are many correct answers in this range (like 11,000, 11,050, 11,100). The question asks you to select from the given choices, so pick the one that fits.

How can I quickly eliminate wrong choices?

Start by checking the obvious violations: Is 10,990 even greater than 10,999? No, so eliminate it immediately. Then check if remaining choices exceed 11,101.

What does the box symbol mean in math?

The □ (box) symbol represents an unknown value that you need to find or select. It's like a placeholder asking "what number goes here?"

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