Exam 1: Critical Thinking

At a certain university, 5% and 17% of total students are mathematics majors (M) and business majors (B), respectively. If 3% of the total students are majoring in both mathematics and business, what percent of total students will be represented by the shaded region of the following Venn diagram?

Formulate the converse of the statement All math classes are difficult.

Suppose set M is mathematics majors and set B is business majors at a certain university. The shaded region in the following Venn diagram represents students majoring in:

The _____ is logically equivalent to the contrapositive.

Two sets are called _____ if they have no elements in common.

The number of blogs has grown rapidly. Assuming that two new blogs are created each second, how many blogs will be set up in one month (30 days)?

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: For the engineering division, what percentage of female applicants were hired?

It is estimated that in 2009 the United States consumed 18.69 million barrels of oil a day. A barrel of oil is 42 U.S. gallons. Assuming a U.S. population of 306 million, estimate per capita consumption in gallons. Round your answer to the nearest tenth.

Suppose that 100 students were given a biology exam and a chemistry exam. Assume that 36 passed the biology exam but not the chemistry exam, 25 passed the chemistry exam but not the biology exam, and 15 passed neither exam. How many passed the chemistry exam?

Consider the statement If it is Sunday, then I will go shopping. Formulate the converse.

Set B is a subset of set A if every element of A is also an element of B.

The Venn diagram shows the results of a survey asking registered voters if they would vote for proposition A or proposition B: How many surveyed would vote for only proposition B?

Logic is the study of methods and principles used to distinguish good from bad reasoning.

If you had $1 million in $10 bills, how many bills would you have?

One kilobyte of memory can store about two-thirds of a page of typical text (excluding formatting). Suppose the typical book is 500 pages. Could a 4-gigabyte flash drive hold tens, hundreds, thousands, or millions of such books?

Formulate the contrapositive of the statement My friends all play video games.

There are 1000 billions in a trillion.

The logic gate XOR corresponds to the exclusive use of or, in which we ask whether one or the other, but not both, is true. If the inputs to the XOR gate are 1 and 1, what is the output?

In a recent hiring period, XYZ Corporation hired 23% of the males who applied and 11% of the females. A lawsuit was contemplated because these numbers seemed to indicate that there was gender discrimination. On closer examination, it was found that XYZ was hiring for only two of its divisions: engineering and secretarial. Applicants applying by gender per department are given in the following table: Which of the following is NOT correct?

Use inductive reasoning to make a conclusion: Every observed score of test X is above 70 and Leo took test X.