Discrete Math Final Exam Review: Number Theory and Set Theory

A group of 28 people were randomly surveyed as they exited a gym about which types of exercises they incorporated into their workout routines. The results are recorded in the table shown.

Which statement below is false?

• One person does not do any of the three exercises.

• Three people do just sit-ups and pull-ups, but not push-ups.

• Ten people do exactly two of the exercises.

• No one does only push-ups and pull-ups

What is the value of the least positive integer n such that the expression below is a perfect cube?

(2³)(3⁴)(5⁵)(7⁶)(n)

What is the value of the least positive integer n such that the expression below is a perfect square?

(2³)(3⁴)(5⁵)(7⁶)(n)

• {1, 3, 17}

• {1, 3, 6}

• {1, 4, 17}

• {1, 4, 6}

Which statement is true in regards to the given sets?

• A\B = {4, 5, 6}

Which of the expressions below will always result in an even number for any positive integer n ?

800 people are selected at random in a particular town. 420 of them say they like to eat at Herman's Steakhouse, 360 of them say they like to eat at Joy's Steakhouse, and 140 of them say they like to eat at both places. How many of the people that were selected at random like to eat at just one of the two restaurants, but not both?

What is the greatest common factor of 693 and 735?

Which of the following represents the shaded area of the Venn diagram?