GMAT Avengers Study Group: Functions:

by on September 12th, 2014

A function is a rule that takes an input and gives an output. When we are told the equation of a function, that equation makes explicit the rule this particular function is following. For example, for the function f(x) = 1x-3, the rule is: whatever input x you give—and that input could be any real number—this function will multiply this input by 1 and then subtract 3 from the product: that difference is the output. If I put in an input of x = 2, then I get an output of 1(2)-3=-1, and the way we compactly write that fact with function notation is: f(2) = -1. In other words, an input of 2 gives an output of -3.

Typical misunderstandings of function notation

When we write f(x), many people new to function notation will misinterpret this as multiplication—as if there’s a thing “f” times the variable “x.” This is not correct. A function is a process through which the input goes.

Also be aware of the following notations:

  • f(x+5) # f(x) + 5
  • f(x-5) # f(x) - 5
  • f(x^2) # delim{|}{f(x)}{|}^2
  • f(5x) # f(x) * 5
  • f(x/5) # {f(x)}/5

It is also important to note that the GMAT often features quant questions with strange symbols. These symbols should not fluster you too much as long as you remember that they do not represent standard mathematical notation. Instead, the symbols pertain only to the problem and are defined by the GMAT.

List of the articles that we shared on our Facebook Event Page are listed below for a quick reference. We recommend going through these articles first before one plans to attempt the questions.

Problem Solving Practice

1) If n is a positive integer greater than 1, then p(n) represents the product of all the prime numbers less than or equal to n. The second smallest prime factor of p(12) + 11 is:

(A) 2

(B) 11

(C) 13

(D) 17

(E) 211

2) For which of the following functions f(x) is the relation f(f(x)) = f(f(f(f(x)))) NOT true for at least some values of x not equal to zero?

(A) f(x) = -delim{|}{f(x)}{|}

(B) f(x) = 2 - x

(C) f(x) = 3x

(D)   f(x) = 4/x

(E)  f(x) = 5

3) Given f(x) = 3x-5, for what value of x does 2*[f(x)-1] = f(3x-6)?

(A) 0

(B) 4

(C) 6

(D) 7

(E) 13

4) Given that f(x) = x/{x+1}, for what value of k does f(f(k) = 2/3?

(A) –2

(B) 5/3

(C) 1

(D) 2

(E) 8

5) The function F(n) is defined as the product of all the consecutive positive integers between 1 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is:

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

6) The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^{-at})+60, where F is in degrees Fahrenheit and a is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?

(A) 65

(B) 75

(C) 80

(D) 85

(E) 90

7) If f(x)=125/{x^3}, what is the value of f(5x)*f(x/5) in terms of f(x)?

(A) (f(x))^2

(B) f(x^2)

(C) (f(x))^3

(D)  f(x^3)

(E)  f(125x)

8) For which of the following does f(a)-f(b)=f(a-b) for all values of a and b?

(A) f(x)=x^2

(B) f(x)=x/2

(C) f(x)=x+5

(D) f(x)=2x-1

(E) f(x)=delim{|}{f(x)}{|}

9) If @X@ denotes the greatest integer that is less than or equal to X, then @-1@/@1@ =?

(A) -2

(B) -1

(C) 0

(D) 1

(E) 2

Data Sufficiency Practice

1) If [x] denotes the greatest integer less than or equal to x, is [x] = 0 ?

(1) 5x + 1 = 3 + 2x

(2) 0 < x < 1

2) If the operation # is one of the four arithmetic operations addition, subtraction, multiplication and division, is (6#2)#4 = 6#(2#4) ?

(1) 3#2 > 3

(2) 3#1 = 3

3) What is the minimal value of function f(x)?

(1) f(0) = 16

(2) f(x) = (x-4)^2

4) For all integers n, the function f is defined by f(n) = a^n, where a is a constant. What is the value of f(1)?

(1) f(2) = 100

(2) f(3) = -1,000

5) In the fraction x/y, where x and y are positive integers, what is the value of y?

(1) The least common denominator of x/y and 1/3 is 6.

(2) x = 1

6) If n is an integer and f(n) = f(n-1)-n, what is the value of f(4)?

(1) f(3) = 14

(2) f(6) = -1

7) If g(f(3)) = 19, what is f(g(3))?

(1) f(x) = 2x

(2) g(x) = 3x + 1

8) Max (x,y) is defined as the maximum of x and y, and Min(x,y) is defined as the minimum of x and y. What is the average of Max(x,60) and Min(40,x)?

(1) Min(x, 60) = x

(2) Max(40, x) = x

Answer Key

Problem Solving

  1. E
  2. C
  3. B
  4. A
  5. E
  6. B
  7. A
  8. B
  9. B

Data Sufficiency

  1. D - Each statement alone is sufficient to answer the question
  2. A - Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
  3. B - Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
  4. B - Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked
  5. E - Statements 1 and 2 together are not sufficient and more information is needed to answer the question asked
  6. D - Each statement alone is sufficient to answer the question
  7. C - Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone
  8. C - Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone

Make sure you check out the event Facebook page to see all the comments that were being exchanged during the live session.

***

RSVP NOW if you want to join me and fellow GMAT Avengers take on Quadrilaterals questions.

1 comment

  • Hi Rahul,

    Shouldn't the output in the last line of the first paragraph be (-1)?

    Regards,

    Aiena.

Ask a Question or Leave a Reply

The author Rahul Sehgal gets email notifications for all questions or replies to this post.

Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a Gravatar to have your pictures show up by your comment.