All GRE Math Resources
Example Questions
Example Question #61 : How To Evaluate Algebraic Expressions
When the integer is increased by , the result is less than times the integer . What is ?
The trick for this problem is to translate "When the integer is increased by , the result is less than times the integer ." into mathematical terms. Let's do it piece by piece:
When the integer :
When the integer is increased by :
When the integer is increased by , the result is:
When the integer is increased by , the result is less than:
When the integer is increased by , the result is less than times the integer :
Now that we have this, solve for
Now plug this value in for the problem question:
Example Question #62 : How To Evaluate Algebraic Expressions
When the integer is mulitplied by , the result is greater than the product of and the integer . What is ?
To solve this problem, translate "When the integer is mulitplied by , the result is greater than the product of and the integer " into mathematical terms. Step-by-step it is:
When the integer :
When the integer is mulitplied by :
When the integer is mulitplied by , the result is:
When the integer is mulitplied by , the result is greater than:
When the integer is mulitplied by , the result is greater than the product:
When the integer is mulitplied by , the result is greater than the product of and the integer :
Now, solve for
Now, plug this value into the problem question:
Example Question #61 : Evaluating Expressions
For any integer , let
Quantity A:
Quantity B:
Quantity A is greater.
The two quantities are equal.
The relationship cannot be determined.
Quantity B is greater.
Quantity B is greater.
Follow the condition given, namely to evaluate each quantity:
Quantity A:
Quantity B:
Quantity B is greater.
Example Question #64 : How To Evaluate Algebraic Expressions
For any positive integer ,
Quantity A:
Quantity B:
The two quantities are equal.
The relationship cannot be determined.
Quantity A is greater.
Quantity B is greater.
Quantity B is greater.
To solve this problem, follow the operation given for each quantity:
,
Quantity A:
Quantity B:
Quantity B is greater.
Example Question #65 : How To Evaluate Algebraic Expressions
For any positive integer ,
Quantity A:
Quantity B:
The two quantities are equal.
Quantity B is greater.
The relationship cannot be determined.
Quantity A is greater.
Quantity A is greater.
To perform this problem, simply perform the operation , for each quantity:
Quantity A:
Quantity B:
Quantity A is greater.
Example Question #62 : Evaluating Expressions
For any integer ,
Quantity A:
Quantity B:
The relationship cannot be determined.
Quantity B is greater.
Quantity A is greater.
The two quantities are equal.
The two quantities are equal.
To solve this problem, evaluate each quantity using the property :
Quantity A:
Quantity B:
The two quantities are equal.
Example Question #67 : How To Evaluate Algebraic Expressions
A counselor found that in a group of students, were taking a foreign language, were taking math, and were taking neither. How many students were taking both?
For group problems, we may use the group equation:
Our unknown value is the number of students in both groups:
Example Question #65 : How To Evaluate Algebraic Expressions
In a group of employees, can use the cash register, can use the price gun, and can use both. How many employees cannot use either?
For group problems, we may use the group equation:
Example Question #69 : How To Evaluate Algebraic Expressions
In a group of artists, are able to use traditional media, can use both traditional and digital media, and cannot use either (they work with novel and untraditional methods.) How many artists can only use digital media?
For group problems, we may use the group equation:
Example Question #70 : How To Evaluate Algebraic Expressions
In a group of high school athletes, can play baseball, can play soccer, and can play neither (playing American football instead). How many athletes can play both baseball and soccer?
For group problems, we may use the group equation: