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ISEE Lower Level Quantitative : How to find length of a line

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

Example Question #1 : How To Find Length Of A Line

On a number line, what is the length of a line that stretches from $\dpi{100} -3$ $\displaystyle \dpi{100} -3$ to $\dpi{100} 13$ $\displaystyle \dpi{100} 13$?

Possible Answers:

$\dpi{100} 3$ $\displaystyle \dpi{100} 3$

$\dpi{100} 16$ $\displaystyle \dpi{100} 16$

$\dpi{100} 10$ $\displaystyle \dpi{100} 10$

$\dpi{100} 13$ $\displaystyle \dpi{100} 13$

Correct answer:

$\dpi{100} 16$ $\displaystyle \dpi{100} 16$

Explanation:

$\dpi{100} -3$ $\displaystyle \dpi{100} -3$ is $\dpi{100} 3$ $\displaystyle \dpi{100} 3$ units to the left of zero on the number line. $\dpi{100} 13$ $\displaystyle \dpi{100} 13$ is $\dpi{100} 13$ $\displaystyle \dpi{100} 13$ units to the right of zero on the number line.

The length of the line would then be $\dpi{100} 13+ 3=16$ $\displaystyle \dpi{100} 13+ 3=16$.

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Example Question #1 : How To Find Length Of A Line

If the radius of a circle is equal to $\frac{1}{4}x$ $\displaystyle \frac{1}{4}x$, then what is the value of the diameter?

Possible Answers:

$\displaystyle 2x$

$\displaystyle x$

$\frac{1}{4}x$ $\displaystyle \frac{1}{4}x$

$\frac{1}{2}x$ $\displaystyle \frac{1}{2}x$

Correct answer:

$\frac{1}{2}x$ $\displaystyle \frac{1}{2}x$

Explanation:

The length of a dimater is twice the length of the radius. Given that the length of the radius is $\frac{1}{4}x$ $\displaystyle \frac{1}{4}x$, the dimater will be equal to $\frac{1}{4}x\cdot2=\frac{2}{4}x=\frac{1}{2}x$ $\displaystyle \frac{1}{4}x\cdot2=\frac{2}{4}x=\frac{1}{2}x$.

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Example Question #3 : How To Find Length Of A Line

The length of $\displaystyle AD$ is $\displaystyle x$ and the length of $\displaystyle AC$ is $\displaystyle y$.

Screenshot_2015-03-29_at_2.20.22_pm

What is the length of $\displaystyle CD$ in terms of $\displaystyle x$ and $\displaystyle y$?

Possible Answers:

x^2 $\displaystyle x^2$

x+y $\displaystyle x+y$

y-x $\displaystyle y-x$

x-y $\displaystyle x-y$

y+x $\displaystyle y+x$

Correct answer:

x-y $\displaystyle x-y$

Explanation:

Using the segment addition postulate, we know that $\displaystyle AC+CD=AD$. We can substitute $\displaystyle x$ and $\displaystyle y$ for $\displaystyle AC$ and $\displaystyle AD$ and solve for $\displaystyle CD$.

Substitute: y+CD=x $\displaystyle y+CD=x$

Subtract y from both sides: $\displaystyle -y$ $\displaystyle -y$

Simplify: CD=x-y $\displaystyle CD=x-y$

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Example Question #4 : How To Find Length Of A Line

The length of BC is x and the length of CE is y.

Screenshot_2015-03-29_at_2.20.22_pm

What is the length of segment $\displaystyle BE$?

Possible Answers:

x+y $\displaystyle x+y$

y-x $\displaystyle y-x$

$x\cdot y$ $\displaystyle x\cdot y$

x-y $\displaystyle x-y$

x+x+y+y $\displaystyle x+x+y+y$

Correct answer:

x+y $\displaystyle x+y$

Explanation:

Segments $\displaystyle BC$ and $\displaystyle CE$ make up segment $\displaystyle BE$. Using the segment addition postulate, add the lengths of $\displaystyle BC$ and $\displaystyle CE$ to find the length of $\displaystyle BE$.

$\displaystyle BC+CE=BE$

Substitute $\displaystyle x$ and $\displaystyle y$: x+y=BE $\displaystyle x+y=BE$

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Example Question #5 : How To Find Length Of A Line

The length of $\displaystyle AD$ is $\displaystyle x$ and the length of $\displaystyle AE$ is $\displaystyle y$.

Screenshot_2015-03-29_at_2.20.22_pm

What is the length of segment $\displaystyle DE$?

Possible Answers:

x+y $\displaystyle x+y$

y-x $\displaystyle y-x$

$2\cdot x$ $\displaystyle 2\cdot x$

x-y $\displaystyle x-y$

$x\cdot y$ $\displaystyle x\cdot y$

Correct answer:

y-x $\displaystyle y-x$

Explanation:

Using the segment addition postulate, we know that $\displaystyle AD+DE=AE$. We can substitute $\displaystyle x$ and $\displaystyle y$ for $\displaystyle AD$ and $\displaystyle AE$ and solve for $\displaystyle DE$.

Substitute: x+DE=y $\displaystyle x+DE=y$

Subtract y from both sides: $\displaystyle -x$ $\displaystyle -x$

Simplify: DE=y-x $\displaystyle DE=y-x$

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Example Question #6 : How To Find Length Of A Line

The length of $\displaystyle BD$ is $\displaystyle x$ and the length of $\displaystyle AB$ is $\displaystyle y$.

Screenshot_2015-03-29_at_2.20.22_pm

What is the length of segment $\displaystyle AD$ in terms of $\displaystyle x$ and $\displaystyle y$?

Possible Answers:

x+y $\displaystyle x+y$

$x\cdot y$ $\displaystyle x\cdot y$

y-x $\displaystyle y-x$

$2\cdot y$ $\displaystyle 2\cdot y$

x-y $\displaystyle x-y$

Correct answer:

x+y $\displaystyle x+y$

Explanation:

Segments $\displaystyle AB$ and $\displaystyle BD$ make up segment $\displaystyle AD$. Using the segment addition postulate, add the lengths of $\displaystyle AB$ and $\displaystyle BD$ to find the length of $\displaystyle AD$.

$\displaystyle AB+BD=AD$

Substitute $\displaystyle x$ and $\displaystyle y$: x+y=AD $\displaystyle x+y=AD$

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : How to find length of a line

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #1 : How To Find Length Of A Line

Example Question #1 : How To Find Length Of A Line

Example Question #3 : How To Find Length Of A Line

Example Question #4 : How To Find Length Of A Line

Example Question #5 : How To Find Length Of A Line

Example Question #6 : How To Find Length Of A Line

All ISEE Lower Level Quantitative Resources

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