GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #61 : Understanding Functions

A sequence is formed the same way the Fibonacci sequence is formed. Its third and fourth terms are 16 and 30, respectively. What is its first term?

 

Possible Answers:

Correct answer:

Explanation:

A Fibonacci-style sequence starts with two numbers, with each successive number being the sum of the previous two. The second term is therefore the difference of the fourth and third terms, and the first term is the difference of the third and second.

Second term: 

First term: 

 

Example Question #62 : Understanding Functions

Define two real-valued functions as follows:

Determine .

Possible Answers:

The correct answer is not among the other responses.

Correct answer:

The correct answer is not among the other responses.

Explanation:

This is not among the given choices.

Example Question #63 : Functions/Series

Define function  as follows:

 has an inverse on each of the following domains except:

Possible Answers:

Correct answer:

Explanation:

 has an inverse on a given domain if and only if there are no two distinct values on the domain  such that .

The key to this question is to find the zeroes of the polynomial, which can be done as follows:

The zeroes are , or approximately .

The polynomial being cubic, its graph has two vertices; since all three zeroes are in the interval , so are both vertices. Therefore, this interval must have at least one pair  such that . Since a cubic polynomial has two "arms", one going up and one going down,  will continuously increase or decrease over the other intevals. The correct choice is .

Example Question #62 : Functions/Series

Define function  as follows:

 has an inverse on each of the following domains except:

Possible Answers:

None of the other responses gives a correct answer.

Correct answer:

Explanation:

 has an inverse on a given domain if and only if there are no two distinct values on the domain  such that .

If , then  can be defined to be .

This happens if 

, or

Similarly, if  can be defined to be , or .

Either way, on any interval that does not include the value , the function can be restated as a linear function, which must have an inverse on that domain. 

On the one interval that does contain this value, , two values  can be found such that . For example, 

 is the correct response.

 

Example Question #63 : Understanding Functions

Define function  as follows:

 has an inverse on each of the following domains except:

Possible Answers:

None of the other response gives a correct answer.

Correct answer:

None of the other response gives a correct answer.

Explanation:

 has an inverse on a given domain if and only if there are no two distinct values on the domain  such that .

 is a constantly increasing function, since it the equation of a line with positive slope. The cube root of a constantly increasing function is also constantly increasing, so 

 always increases as  increases.

Therefore, if  has an inverse on  and, subsequently, any domain.

Example Question #61 : Functions/Series

Define function  as follows:

 has an inverse on each of the following domains except:

Possible Answers:

None of the other choices gives a correct answer.

Correct answer:

Explanation:

 has an inverse on a given domain if and only if there are no two distinct values on the domain  such that .

 is a quadratic function, so its graph is a parabola. The key is to find the -coordinate of the vertex of the parabola, which can be found by completing the square:

The vertex occurs at , so the interval which contains this value will have at least one pair  such that . The correct choice is ..

Example Question #61 : Functions/Series

Define function  as follows:

 has an inverse on each of the following domains except:

Possible Answers:

Correct answer:

Explanation:

 has an inverse on a given domain if and only if there are no two distinct values on the domain  such that .

 has a sinusoidal wave as its graph, with period ; it begins at a relative maximum of  and has a relative maximum or minimum every  units. Therefore, any interval containing an integer multiple of  will have at least two distinct values  such that .

The only interval among the choices that includes a multiple of  is :

 .

This is the correct choice.

Example Question #1291 : Gmat Quantitative Reasoning

What is the sum of all terms from 0 to 30 inclusive ?

Possible Answers:

Correct answer:

Explanation:

We could solve this by actually adding up all terms the from 0 to 30, but it would take way too much time. There is a simple formula to remember for the summations of consecutive terms:  , which gives the sum of all terms from 0 to .

By substituting the value provided in our problem  into the formula, we can solve for the correct answer.

 

 

Example Question #1292 : Gmat Quantitative Reasoning

What is the sum of the even terms from 2 to 60?

Possible Answers:

Correct answer:

Explanation:

We should notice that since we have a sequence of even numbers, we can factor  out, so we can rewrite it as :

We can calculate the summation of all numbers from 1 to  with the formula ; so, we simply have to plug in 30 for  and multiply this formula by two:

Example Question #1293 : Gmat Quantitative Reasoning

What is the sum of the sequence of all terms from 120 to 160 inclusive? 

Possible Answers:

Correct answer:

Explanation:

The formula for the summation of consecutive terms is  , which gives the sum of all terms from 0 to . We can apply the formula to get the summation of all consecutive terms from 1 to 160. To figure out the summation starting from 120, we simply have to subtract the summation of all terms from 1 to 119. (We don't want to include 120 since we want it in our summation.)

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