Number Line - GRE Quantitative Reasoning
Card 0 of 12
The range of the earnings for architecture graduates is 
, and the range of the salaries for engineering graduates is 
.
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 
greater than that of the architects.
B: The average (arithmetic mean) of the engineers is 
greater than that of the architects.
C: The lowest salary of the engineers is 
less than the lowest of the architects.
The range of the earnings for architecture graduates is
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
B: The average (arithmetic mean) of the engineers is
C: The lowest salary of the engineers is
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.
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.
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What's the distance between 
and 
on a number line?
What's the distance between
Let's draw a number line.
Since a number line is straight and contains the numbers consecutively, we just subtract 
from 
to get 
.
Let's draw a number line.
Since a number line is straight and contains the numbers consecutively, we just subtract
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Which of the following answer best fits in the picture below?
Which of the following answer best fits in the picture below?
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 
.
Open circles mean the values are excluded from the set.
The number line shows the set is between
The only value in that set would be
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If 
, then where on the number line lies 
?
If
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.
Because a number line contains both positive and negative integers, we need to consider both possibilities.
Next
Then, we should guess that
Remember, a negative value raised to an even power will always have a positive value.
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If perimeter of equilateral triangle is 
, what is the height of the triangle?
If perimeter of equilateral triangle is
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 
.
Since perimeter of equilateral triangle is
The height is opposite the angle
Let's simplify by factoring out
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On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?
On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?
The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.
|14- (-4)| = |14+4| = |18| = 18
The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.
|14- (-4)| = |14+4| = |18| = 18
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Which of the following is a graph for the values of 
defined by the inequality stated above?
Which of the following is a graph for the values of
Begin by solving for 
:
Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:
Begin by solving for
Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:
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Which of the following is a graph for the values of 
defined by the inequality stated above?
Which of the following is a graph for the values of
To begin, you must simplify so that you "isolate" 
, (i.e. at least eliminate any coefficients from it). To do this, divide allof the members of the inequality by 
:
Now, this inequality represents all of the numbers between 13 and 32. However, it does include 
(hence, getting a closed circle for that value) and does not include 
(hence, getting an open circle for that value). Therefore, it looks like:
To begin, you must simplify so that you "isolate"
Now, this inequality represents all of the numbers between 13 and 32. However, it does include
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Which of the following inequalities is represented by the number line shown above?
Which of the following inequalities is represented by the number line shown above?
Since the inequality represents one range of values between two end points (both of which are included, given the sign being "less than or equal"), you know that whatever you answer, it must be convertible to the form:
Now, you know that it is impossible to get this out of the choices that have no absolute values involved in them. Therefore, the only options that make sense are the two having absolute values; however, here you should choose only the ones that have a 
, for only that will yield a range like this. Thus, we can try both of our options.
The wrong answer is simplified in this manner:
And you can stop right here, for you know you will never have 
for the left terminus.
The other option is simplified in this manner:
This is just what you need!
Since the inequality represents one range of values between two end points (both of which are included, given the sign being "less than or equal"), you know that whatever you answer, it must be convertible to the form:
Now, you know that it is impossible to get this out of the choices that have no absolute values involved in them. Therefore, the only options that make sense are the two having absolute values; however, here you should choose only the ones that have a
The wrong answer is simplified in this manner:
And you can stop right here, for you know you will never have
The other option is simplified in this manner:
This is just what you need!
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Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
It is not necessary to solve this problem by multiplying terms out. Notice that between quantities A and B, the last three terms switch places for the two large numbers. as such they can be rewritten:
Quantity A:
Quantity B:
Both quantities A and B share the exact same terms, save for two:
Quantity A: 
Quantity B: 
From visual inspection, it is clear that B is larger.
It is not necessary to solve this problem by multiplying terms out. Notice that between quantities A and B, the last three terms switch places for the two large numbers. as such they can be rewritten:
Quantity A:
Quantity B:
Both quantities A and B share the exact same terms, save for two:
Quantity A:
Quantity B:
From visual inspection, it is clear that B is larger.
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Which of the following is true?
Which of the following is true?
Since 
is always positive, and 
, it follows that 
for all possible values.
For the A, it is possible to choose values that make the statement false, for example 
and 
.
C is always false.
Since
For the A, it is possible to choose values that make the statement false, for example
C is always false.
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Which of the statements is always true?
Which of the statements is always true?
Although C may approach zero for large values of 
and values of 
, it will never actually reach it for real values.
A and B, however, have x and y values which make them false:
For A, an example is 
For B, 
would make the value zero.
Although C may approach zero for large values of
A and B, however, have x and y values which make them false:
For A, an example is
For B,
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