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Example Questions
Example Question #17 : Algebra
Given and
, find the values of
and
.
We can solve this problem by setting up a system of equations and using elimination:
We can eliminate the and solve for
by multiplying the bottom equation by
and adding the equations:
___________________
We can now find by substituting our
into any equation:
Example Question #1101 : Gmat Quantitative Reasoning
The product of two positive numbers, and
, yields
. If their sum is
, what is the value of
?
We have enough information to write out two equations:
Using the first equation, we can narrow our potential values to:.
Using the second equation, we can narrow down our values even further to . We are, however, being asked specifically for the value of
. Since we cannot state if the
or the
represents
and which represents
, we cannot answer this question. Additional data, such as
is less than
, would be required.
Example Question #14 : Algebra
Solve for .
We can solve this problem in the same way we would solve a system of equations using elimination. Since we are solving for we can manipulate the system to cancel out the
values:
We then add the equations. Notice how the values cancel out
leaving us with
Example Question #1101 : Gmat Quantitative Reasoning
Solve the following system of equations:
To solve, I used the elimination method by adding the tqo equations together. That eliminates y and leaves you with:
Therefore,
Example Question #22 : Algebra
Which of the following equations is parallel to the line given by the equation:
For lines to be parallel, their equations must have equal slopes. Therefore, we are looking for another line with a slope of -4/3. If we convert the equation:
into slope - intercept form, we get:
It has the same slope, and therefore is parallel to the original line.
Example Question #1102 : Gmat Quantitative Reasoning
The equations and
intersect at the point
. What is y?
The easiest way to solve the problem is to solve for y in one of the equations and then plug it into the other equation:
We can then plug that x-value into one of the original equations:
Example Question #1 : Exponents
cannot be determined
Putting these together,
Example Question #1 : Understanding Exponents
Then,
Example Question #1 : Understanding Exponents
Then putting them together,
Example Question #4 : Exponents
Which of the following expressions is equivalent to this expression?
You may assume that .
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