How to find value with a number line - GRE Quantitative Reasoning

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract from to get .

Open circles mean the values are excluded from the set.

The number line shows the set is between and exclusive.

The only value in that set would be .

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

is and that value is the same as . Therefore we eliminate the choice because will always be greater than those values raised to the power.

Next is . We elminate both the positive and negative range of . If we look at the difference between and , it's over .

Then, we should guess that will definitely be greater than so therefore answer is .

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

Since perimeter of equilateral triangle is and we have three equal sides, we just divide that vaue by to get . To find height, we can set-up a proportion.

The height is opposite the angle . Side opposite is and the side of equilateral triangle which is opposite is .

Cross multiply.

Divide both sides by

Let's simplify by factoring out to get a final answer of .

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.

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.

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract from to get .

Open circles mean the values are excluded from the set.

The number line shows the set is between and exclusive.

The only value in that set would be .

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

is and that value is the same as . Therefore we eliminate the choice because will always be greater than those values raised to the power.

Next is . We elminate both the positive and negative range of . If we look at the difference between and , it's over .

Then, we should guess that will definitely be greater than so therefore answer is .

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

Since perimeter of equilateral triangle is and we have three equal sides, we just divide that vaue by to get . To find height, we can set-up a proportion.

The height is opposite the angle . Side opposite is and the side of equilateral triangle which is opposite is .

Cross multiply.

Divide both sides by

Let's simplify by factoring out to get a final answer of .

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.

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.

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract from to get .

Open circles mean the values are excluded from the set.

The number line shows the set is between and exclusive.

The only value in that set would be .

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

is and that value is the same as . Therefore we eliminate the choice because will always be greater than those values raised to the power.

Next is . We elminate both the positive and negative range of . If we look at the difference between and , it's over .

Then, we should guess that will definitely be greater than so therefore answer is .

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

Since perimeter of equilateral triangle is and we have three equal sides, we just divide that vaue by to get . To find height, we can set-up a proportion.

The height is opposite the angle . Side opposite is and the side of equilateral triangle which is opposite is .

Cross multiply.

Divide both sides by

Let's simplify by factoring out to get a final answer of .

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.

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.

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract from to get .

Open circles mean the values are excluded from the set.

The number line shows the set is between and exclusive.

The only value in that set would be .

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

is and that value is the same as . Therefore we eliminate the choice because will always be greater than those values raised to the power.

Next is . We elminate both the positive and negative range of . If we look at the difference between and , it's over .

Then, we should guess that will definitely be greater than so therefore answer is .

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

Since perimeter of equilateral triangle is and we have three equal sides, we just divide that vaue by to get . To find height, we can set-up a proportion.

The height is opposite the angle . Side opposite is and the side of equilateral triangle which is opposite is .

Cross multiply.

Divide both sides by

Let's simplify by factoring out to get a final answer of .