GRE Math : How to find value with a number line

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Example Question #1 : How To Find Value With A Number Line

The range of the earnings for architecture graduates is $\$14,000$ $\displaystyle \$14,000$ , and the range of the salaries for engineering graduates is $\$11,500$ $\displaystyle \$11,500$ .

Which of the following statements individually provide(s) sufficient additional information to determine the range of the salaries of all graduates between the two professions?

A: The median salary for the engineers is $\$5,000$ $\displaystyle \$5,000$ greater than that of the architects.

B: The average (arithmetic mean) of the engineers is $\$7,500$ $\displaystyle \$7,500$ greater than that of the architects.

C: The lowest salary of the engineers is $\$2,000$ $\displaystyle \$2,000$ less than the lowest of the architects.

Possible Answers:

B only

A, B, and C

C only

A and C only

A only

Correct answer:

C only

Explanation:

The provision of the bottom-end of the engineering range is the only additional information that provides us a fixed endpoint from which we can build off of by supplementing with the ranges provided in the question, to give us the full range between both engineering and achitecture graduates. See the diagram provided to understand how this can be done.

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Even if the mean and medians were provided, these additional values give us no information on the endpoints of the salaries, and the question only asks for the range.

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Example Question #113 : Arithmetic

What's the distance between $\displaystyle 1$ and $\displaystyle 8$ on a number line?

Possible Answers:

$\displaystyle 7$

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 6$

$\displaystyle 5$

Correct answer:

$\displaystyle 7$

Explanation:

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract $\displaystyle 1$ from $\displaystyle 8$ to get $\displaystyle 7$ .

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Example Question #1 : Number Line

Which of the following answer best fits in the picture below?

Possible Answers:

0.9 $\displaystyle 0.9$

6.5 $\displaystyle 6.5$

8.1 $\displaystyle 8.1$

9.1 $\displaystyle 9.1$

$\displaystyle 8$

Correct answer:

6.5 $\displaystyle 6.5$

Explanation:

Open circles mean the values are excluded from the set.

The number line shows the set is between $\displaystyle 1$ and $\displaystyle 8$ exclusive.

The only value in that set would be 6.5 $\displaystyle 6.5$ .

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Example Question #114 : Arithmetic

If $\displaystyle x^4=1000000$ , then where on the number line lies $\displaystyle x$ ?

Possible Answers:

$\displaystyle (29, 30)$

$\displaystyle (-30, -31)$

$\displaystyle (-31, -32)$

(32,33) $\displaystyle (32,33)$

$\displaystyle (30, 31)$

Correct answer:

$\displaystyle (-31, -32)$

Explanation:

Because a number line contains both positive and negative integers, we need to consider both possibilities.

30^4 $\displaystyle 30^4$ is 810000 $\displaystyle 810000$ and that value is the same as (-30)^4 $\displaystyle (-30)^4$ . Therefore we eliminate the 29, 30 $\displaystyle 29, 30$ choice because 1000000 $\displaystyle 1000000$ will always be greater than those values raised to the 4th $\displaystyle 4th$ power.

Next 31^4 $\displaystyle 31^4$ is 923521 $\displaystyle 923521$ . We elminate both the positive and negative range of 30, 31 $\displaystyle 30, 31$ . If we look at the difference between 31^4 $\displaystyle 31^4$ and 30^4 $\displaystyle 30^4$ , it's over 100000 $\displaystyle 100000$ .

Then, we should guess that 32^4 $\displaystyle 32^4$ will definitely be greater than 1000000 $\displaystyle 1000000$ so therefore answer is $\displaystyle -31, -32$ .

Remember, a negative value raised to an even power will always have a positive value.

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Example Question #2 : How To Find Value With A Number Line

If perimeter of equilateral triangle is $9\sqrt{6}$ $\displaystyle 9\sqrt{6}$ , what is the height of the triangle?

Possible Answers:

$3\sqrt{6}$ $\displaystyle 3\sqrt{6}$

$\frac{3\sqrt{2}}{2}$ $\displaystyle \frac{3\sqrt{2}}{2}$

$3\sqrt{2}$ $\displaystyle 3\sqrt{2}$

$\frac{9\sqrt{2}}{2}$ $\displaystyle \frac{9\sqrt{2}}{2}$

$9\sqrt{2}$ $\displaystyle 9\sqrt{2}$

Correct answer:

$\frac{9\sqrt{2}}{2}$ $\displaystyle \frac{9\sqrt{2}}{2}$

Explanation:

Since perimeter of equilateral triangle is $9\sqrt{6}$ $\displaystyle 9\sqrt{6}$ and we have three equal sides, we just divide that vaue by $\displaystyle 3$ to get $3\sqrt{6}$ $\displaystyle 3\sqrt{6}$ . To find height, we can set-up a proportion.

The height is opposite the angle $\displaystyle 60$ . Side opposite $\displaystyle 60$ is $\sqrt{3}$ $\displaystyle \sqrt{3}$ and the side of equilateral triangle which is opposite $\displaystyle 90$ is $\displaystyle 2$ .

$\frac{3\sqrt{6}}{2}=\frac{h}{\sqrt{3}}$ $\displaystyle \frac{3\sqrt{6}}{2}=\frac{h}{\sqrt{3}}$ Cross multiply.

$3\sqrt{18}=2h$ $\displaystyle 3\sqrt{18}=2h$ Divide both sides by $\displaystyle 2$

$\frac{3\sqrt{18}}{2}=h$ $\displaystyle \frac{3\sqrt{18}}{2}=h$

Let's simplify by factoring out $\sqrt{9}$ $\displaystyle \sqrt{9}$ to get a final answer of $\frac{9\sqrt{2}}{2}$ $\displaystyle \frac{9\sqrt{2}}{2}$ .

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GRE Math : How to find value with a number line

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Find Value With A Number Line

Example Question #113 : Arithmetic

Example Question #1 : Number Line

Example Question #114 : Arithmetic

Example Question #2 : How To Find Value With A Number Line

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