Question

Suppose that 10 <
n
< 11. A possible value for n is
A) 100
B) 120
C) 130
D) 140

Answer 1

Given inequality is $10^2 < n < 11^2$

Now we have to find the possible values of n from the given choices.

To find that first we need to evaluate the given inequality for the value of n.

$10^2 < n < 11^2$

$10*10 < n < 11*11$

$100 < n < 121$

That means value of n can be any number between 100 and 121 but not 100 or 121.

From given choices only 120 belong to that category.

Hence choice B) 120 is the final answer.

Answer 2

The correct option is $\boxed{\bf option B}$.

Further explanation:  

In any inequality $a<b<c$ where $a,b\text{ and }c$ are the real numbers, the possible values for $b$ are all the real numbers that lies between $a$ and $c$.

Given:

The given inequality is $10^{2}<n<11^{2}$.

Step 1:

First we evaluate the expression $10^{2}$ and $11^{2}$ to put the value in the inequality.

The value of the expression $10^{2}$ is calculated as follows:

$\begin{aligned}10^{2}&=10\times10\\&=100\end{aligned}$

The value of the expression $11^{2}$ is calculated as follows:

$\begin{aligned}11^{2}&=11\times11\\&=121\end{aligned}$  

Step 2:

Now substitute the value of the expression $10^{2}$ and $11^{2}$ in the given inequality.

$\boxed{100<n<121}$

Step 3:

The given inequality is in the form of $a<b<c$ where $a,b\text{ and }c$ are the real numbers.

Compare: Given inequality with general inequality.

The possible values for $n$ are all the real numbers that lie between  $100\text{ and }121$.

Step 4:

Check all the possible values that lie between $100\text{ and }121$ from the given options.

The option A is $100$ which is incorrect as $100$ does not lie between $100\text{ and }121$.

The option B is $120$ which is correct as $120$ lies between $100\text{ and }121$.

The option C is $130$ which is incorrect as $130$ does not lie between $100\text{ and }121$.

The option D is $140$ which is incorrect as $140$ does not lie between $100\text{ and }121$.

Therefore, the value of $n$ which satisfies the given inequality is $\boxed{120}$ i.e., $\boxed{\bf option B}$

Learn more:  

1. A problem on simplification https://brainly.com/question/585147

2. A problem on division of algebraic expression https://brainly.com/question/365957

3. A problem on comparison https://brainly.com/question/120717

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Inequality

Keywords: Inequality, real numbers, possible values, expressions, exponent, lies between, substitution, evaluation, variable, constant, natural number, dotted line.