All GRE Math Resources
Example Questions
Example Question #1 :How To Simplify An Expression
a # b = (a * b) + a
What is 3 # (4 # 1)?
20
12
27
8
15
27
Work from the "inside" outward. Therefore, first solve 4 # 1 by replacing a with 4 and b with 1:
4 # 1 = (4 * 1) + 4 = 4 + 4 = 8
That means: 3 # (4 # 1) = 3 # 8. Solve this now:
3 # 8 = (3 * 8) + 3 = 24 + 3 = 27
Example Question #401 :Gre Quantitative Reasoning
Simplify the result of the following steps, to be completed in order:
1. Add 7xto 3y
2. Multiply the sum by 4
3. Addxto the product
4. Subtractx –yfrom the sum
29x+ 13y
28x- 13y
28x+ 13y
28x+ 11y
28x+ 12y
28x+ 13y
Step 1: 7x+ 3y
Step 2: 4 * (7x+ 3y) = 28x+ 12y
Step 3: 28x+ 12y+x= 29x+ 12y
Step 4: 29x+ 12y– (x–y) = 29x+ 12y–x+y= 28x+ 13y
Example Question #1 :How To Simplify An Expression
Quantitative Comparison
xandyare non-zero integers.
Quantity A: (x–y)2
Quantity B: (x+y)2
Quantity B is greater.
The two quantities are equal.
The answer cannot be determined from the information given.
Quantity A is greater.
The answer cannot be determined from the information given.
Quantity A: (x–y)2=x2– 2xy+y2
Quantity B: (x+y)2=x2+ 2xy+y2
Both havex2+y2so cancel those from both columns and just compare –2xyin Quantity A to 2xyin Quantity B. Ifx= 1 andy= 1, –2xy= –2 and 2xy= 2, so Quantity B is greater. But ifx= 1 andy= –1, –2xy= 2 and 2xy= –2, so Quantity A is greater. The contradiction means the answer cannot be determined.
Example Question #1 :Simplifying Expressions
Which is the greater quantity: the median of 5 positive sequential integers or the mean of 5 positive sequential integers?
The relationship cannot be determined
The mean is greater
The quantities are equal
The median is greater
The quantities are equal
If the first integer is, then
This is the same as the median.
Example Question #1 :How To Simplify An Expression
You are told thatcan be determined from the expression:
Determine whether the absolute value ofis greater than or less than 2.
The relationship cannot be determined from the information given.
The quantities are equal
The expression is simplified as follows:
Sincethe value of必须略大的莱斯时才17岁ed to the 4th power.
Example Question #1 :How To Simplify An Expression
Quantitative Comparison
Quantity A:
Quantity B:
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The relationship cannot be determined from the information given.
(x+y)2=x2+ 2xy+y2
Now, since there are no specifications on what x and y can equal, one or both of them could be 0, making the two columns equal. Any value other than 0 will make the columns unequal because of the additional 2xy term, so the answer cannot be determined.
Example Question #1 :How To Simplify An Expression
Which best describes the relationship betweenandif?
The relationship cannot be determined from the information given.
The relationship cannot be determined from the information given.
Use substitution to determine the relationship.
For example, we could plug inand.
So far it looks like the first expression is greater, but it's a good idea to try other values of x and y to be sure. This time, we'll try some negative values, say,and.
This time the first quantity is smaller. Therefore the relationship cannot be determined from the information given.
Example Question #21 :Simplifying Expressions
Ifand, then
Cannot be determined
We have three variables and only two equations, so we will not be able to solve for each independent variable. We need to think of another solution.
Notice what happens if we line up the two equations and add them together.
(x+y) + (3x –y+z)= 4x + z
and 5 + 3 = 8
Lets take this equation and multiply the whole thing by 3:
3(4x+z= 8)
Thus, 12x+ 3z= 24.
Example Question #2 :How To Simplify An Expression
Quantitative Comparison
is an integer.
Quantity A:
Quantity B:
Quantity A is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Quantity B is greater.
The two quantities are equal.
Plugging in numbers is not the best strategy here. Instead, let's see how we can equate the two expressions. Quantity A is actually a difference of squares. 256x2= (16x)2and 49y2= (7y)2. These look like the expressions in Quantity B. The formula to remember here is the difference of squares formula, a very important one for this test!a2–b2= (a+b)(a–b). Thus, ifa= 16xandb= 7y, 256x2– 49y2= (16x– 7y)(16x+ 7y), and the quantities are equal.