Question 1

If x, y, and z are integers with x?y and y>z, which of the following could x, y, and z represent (respectively)?

Accepted Answer

­ x = ­?3, y =­­­­­ ?2, and z =­ ?3.?3 is less than or equal to ­?2, and­­ ?2 is greater than ­?3.

Question 2

Which of the following uses the doubling method of informal counting to solve the following:3+4=

Accepted Answer

The doubling method would be 3 + 4 = (3 + 3) +1 = 6 + 1 = 7. Using the doubling method of informal counting involves taking apart a number so that it is the same number as the one being added to it and then adding the difference. It is a way to do mental math easily in one's head.

Question 3

Which property is the following equation an example of?9 x 1/9 = 9

Accepted Answer

9 x 1/9 = 9 is an example of the multiplicative inverse property. The multiplicative inverse property involves multiplying a number by its reciprocal, or putting it into a fraction with 1 as the numerator. When you multiply it by its reciprocal, you get the original number.

Question 4

According to the US Standard system, which of the following would be used to measure the volume of water in a bath tub?

Accepted Answer

According to the US Standard system, gallons would be used to measure the volume of water in a bath tub. Other countries do not use gallons as a way of measurement. A US Standard liquid gallon is approximately 4.5 liters.

Question 5

Sally, Nick, Bobby, and Kenny are standing in a line. How many different ways can they be ordered?

Accepted Answer

Sally, Nick, Bobby, and Kenny can be ordered 24 different ways in line. You get the answer by multiplying 4 by each number that precedes it. Since there are 4 children, then 4 x 3 x 2 x 1 = 24.

Question 6

What is the perimeter of a rectangle that has 2 sides measuring 4 cm and 2sides measuring 6 cm?

Accepted Answer

A rectangle that has 2sides measuring 4 cm and 2sides measuring 6 cm has a perimeter of 20. To get this answer, you add the sum of all sides: 4+4+6+6=20.

Question 7

Tim ate 8/10 of a pizza. State the fraction for the amount of pizza that was left over in its simplest form.

Accepted Answer

Tim had 1/5 of the pizza left, as stated in simplest form. Since Tim ate 8/10 of the pizza, he had 2/10 remaining. 2/10 in its simplest form is 1/5.

Question 8

Is 40÷5>, =, or < 49÷7?

Accepted Answer

40÷5 > 49÷7. In other words, 8 > 7.

Question 9

In a jar of candy there are 127 red candies, 92 orange ones, 108 yellow ones, 77 green ones, and 13 blue candies. If a person reaches into the jar without looking and grabs one piece of candy, what is the probability of that piece being red?

Accepted Answer

A person reaching into the candy jar would have a 30% chance of pulling out a piece of red candy. There are 417 pieces of candy in the jar altogether, which means the person has 127 chances in 417 to pull out a piece of red candy (or 127/417 if the candy is red). To convert that to a percentage, divide the number of chances to get a red candy (127) by the total number of pieces (417), then multiply the quotient by 100.

Question 10

A company just distributed candy bars wrapped with golden tickets hidden within ordinary shipments of their product. The company spokesperson announces that there is a "one in one thousand chance" of someone finding a golden ticket when they open a candy bar, and that 500,000 candy bars have been distributed in the golden ticket promotion. If a person buys three of the candy bars, what is their chance of finding a golden ticket?

Accepted Answer

A person with three eligible candy bars has a 0.3% chance of receiving one of the golden tickets. There is one golden ticket in every 1000 candy bars and there are 500,000 candy bars that could possibly have the prize. That means there are 500 golden tickets waiting to be found, and each candy bar has a 0.1% chance of having a ticket (500/500,000). If the person has three candy bars, that triples their 0.1% chance of finding a golden ticket.

Question 11

Data that is weighted toward one end of the numerical range in which it occurs is:

Accepted Answer

Data that is asymmetrically concentrated at one end of a numerical range is skewed. This may be the result of faulty data collection (such as a poor poll or survey) or may be a completely natural phenomenon. A skewed graph or data set is not necessarily an indication of fault, flaw or wrongdoing, but may merely demonstrate a disproportionate relationship.

Question 12

A variable that affects the data collected but is not accounted for or demonstrated in the statistical measure of the data is a:

Accepted Answer

A lurking variable is information directly related to the independent and dependent variables in statistical analysis, that has an effect on the data being analyzed, but is not accounted for in the analysis. Lurking variables that are not accounted for in data analysis can cause the resulting predictions to be inaccurate or incomplete. Lurking variables can also be called confounding variables.

Question 13

People who score in the 95th percentile on an exam:

Accepted Answer

A test taker who scores in the 95th percentile scored as well or better than 95% of the people who took the exam. It is a comparative measure of success that has nothing to do with the number of questions on the exam, the number of correct responses given or the "score" of the exam in a 1 to 100 grading scheme. Early education exams are typically evaluated solely on this measure. Secondary school, higher education and professional exams vary in their emphasis on this method, but most report comparative percentile scores as a frame of reference.

Question 14

The test scores for eight students are 97, 94, 98, 97, 89, 92, 68 and 96. What would the seventh score be considered?

Accepted Answer

A piece of data that is atypical or significantly different from the rest of its data set is called an outlier. While true outliers are often easy to spot with critical thinking skills alone, there is also a mathematical precept for assessing these anomalies. Generally, a number that is two or more standard deviations from the mean is considered an outlier. In some cases, outliers can skew data significantly, which is why identifying them is critical. Occasionally, an outlier can be removed justifiably from a data set to improve the data's reliability.

Question 15

What is the mode for the numbers 34, 62, 58, 49, 37, 85, 22, 44, 37 and 52?

Accepted Answer

The mode for the number set above is 37. It is the number that occurs most frequently in a number set. 37 occurs twice, while all of the other numbers occur once. The order of the numbers is not relevant nor is the number of entrants in the set.

Question 16

What is the mean for the following test scores? 92%, 87%, 75%, 88%, 96%, 95%, 94%, 82%, 88%

Accepted Answer

The mean for the data set above is 88.56% The mode is 88% and the median or middle number when the numbers are in ascending order (75%, 82%, 87%, 88%, 88%, 92%, 94%, 95%, 96%) is 88%.

Question 17

What is the mode for the following set of numbers? 1, 7, 8, 7, 9, 1, 2, 4, 5, 1, 3, 6, 6, 0, 9, 3, 0, 1, 4, 6

Accepted Answer

The mode (the number that occurs most frequently in the set) for the number set above is 1, which occurred four times in the 20 number series. 4.15 is the mean; 4 is the median or middle number when the numbers are in ascending order: 0, 0, 1, 1, 1, 1, 2, 3, 3, 4, 4, 5, 6, 6, 6, 7, 7, 8, 9, 9.

Question 18

In a game, one card is drawn from a complete deck of playing cards without jokers. If the card is a club or a queen, the gambler wins double his bet. Otherwise, the dealer keeps the money. How much better are the dealer's odds in this game?

Accepted Answer

In a game where the dealer keeps a gambler's wager if he draws any card but a club or queen, his odds are 38% better than the gambler's of winning the money. There are 52 cards in a deck and 13 cards in each suit, including clubs. There are four queens in each deck, but the queen of clubs has already been counted, so only the queens of hearts, diamonds and spades count toward the gambler's list of winning cards. Therefore, the gambler needs one of 16 cards to be pulled in order to win, which make his odds of winning 31%. If his odds are 31%, the gambler's odds are the far superior 69%, which is better by 38%.

Question 19

To find the percentage (p) of any number (n), which formula can be used?

Accepted Answer

To find the percentage of any number, such as 42% of 677, for example, multiply the percentage in its whole value by the number, then divide the product by 100. (42 x 677) ÷ 100 = 284.34.

Question 20

Seven/Twelve has $4 million in sales over the past week. What were the approximate sales per day?

Accepted Answer

$571,000. $4 million divided by 7 days is an average of $571,429 per day.
Key Takeaway: Dividing by seven is an important skill because of the week unit is frequently used. If you remembered the repeating decimal we gave you earlier, all you have to do is move it over in this question.
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142

Quiz 25: Mathematics

If x, y, and z are integers with x?y and y>z, which of the following could x, y, and z represent (respectively) ?