All GRE Math Resources
Example Questions
Example Question #361 : Ssat Upper Level Quantitative (Math)
If a line has an equation of , what is the slope of a line that is perpendicular to the line?
Putting the first equation in slope-intercept form yields .
A perpendicular line has a slope that is the negative inverse. In this case, .
Example Question #2 : How To Find Out When An Equation Has No Solution
Solve for .
No solutions.
No solutions.
Cross multiplying leaves , which is not possible.
Example Question #31 : Algebra
If is defined for all numbers and to be , then what is ?
In evaluating, we can simply plug in 4 and 2 for and respectively. We then get .
Example Question #31 : Algebra
Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?
The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives
.
Example Question #31 : Algebra
John goes on a trip of kilometers at a speed of kilometers an hour. How long did the trip take?
If we take the units and look at division, will yield hours as a unit. Therefore the answer is .
Example Question #34 : How To Find The Solution To An Equation
With a head wind a plane can fly a certain distance in five hours. The return flight takes an hour less. How fast was the plane flying?
In general, .
The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes .
Solving for gives .
Example Question #32 : Algebra
How much water should be added to of 90% cleaning solution to yield 50% cleaning solution?
Pure water is 0% and pure solution 100%. Let = water to be added.
in general where is the volume and is the percent.
So the equation to solve becomes
and
Example Question #31 : Linear / Rational / Variable Equations
Solve and
This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of to get and then substutite the into the second equation to get
.
Solving this equation gives and substituting this value into one of the original equations gives , thus the correct answer is .
Example Question #43 : Linear / Rational / Variable Equations
Joy bought some art supplies. She bought colored pencils for $1.25 per box and sketch pads for $2.25 each. Joy bought one more sketch pad than colored pencil boxes and spent $9.25. How many sketch pads did she buy?
Let = # of color pencil boxes and = # of sketch pads purchased.
So the equation to solve becomes .
Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.
Example Question #36 : How To Find The Solution To An Equation
This question deals with absolute value equations which will normally gives you two solutions.
You need to solve two sets of equations for absolute value problems:
and