Quantity A | Quantity B |
a | b |
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2m = 32
Quantity A | Quantity B |
3m | m3 |
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(A) Solve for m by trial and error. Observe that 2 5 = 2 × 2 × 2 × 2 × 2 = 8 × 4 = 32, so m = 5. Then (A) is 3 5 = 3 × 3 × 3 × 3 × 3 = 243, while (B) is 5 3 = 5 × 5 × 5 = 125, and (A) is greater.
Quantity A | Quantity B |
The area of the parallelogram | 2,000 |
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x 2 + 5x = 6
Quantity A | Quantity B |
(x + 6)(x – 1) | 1 |
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Country X is in the shape of a rectangle 80 km wide by 100 km long.
Ann lives on the border of Country X, and
her three children each live inside the country.
Quantity A | Quantity B |
The sum of the distances from Ann’s house to each of her three children’s houses | 300km |
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(D) There are a couple of different ways to draw the picture:
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Five people in a room weigh an average of 120 pounds each. When a sixth person enters, the average weight in the room increases to 125 pounds per person. What does the sixth person weigh?
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Questions are based on the following graph, which shows the number of hours that 10 students studied for a quiz plotted against each student’s subsequent quiz score. The line of best fit (trend line) has been plotted for the data. Each dot represents an individual student.
What was the quiz score of the student whose score least fit the general pattern of data?
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Questions are based on the following graph, which shows the number of hours that 10 students studied for a quiz plotted against each student’s subsequent quiz score. The line of best fit (trend line) has been plotted for the data. Each dot represents an individual student.
Which of the following statements appear to be true from the data?
Indicate all that apply.
A. The data supports the statement, “Students who studied for more hours tended to receive higher quiz scores.”
B. No student who studied for fewer than two hours received a score above six.
C. The mode quiz score was greater than the median quiz score.
D. Some students received the same quiz scores as each other, even though the number of hours they studied differed by more than 1 full hour.
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(A, B, C, D) (A) The trend line, or line of best fit, has a positive slope. It inclines upward as we move from left to right, implying that scores rise with more hours studied. (B) There are three students who studied for less than 2 hours, the 3 points in the lower left. Two of these students scored a 6, but none scored above 6. (C) The most frequently recurring quiz score, or mode quiz score, is 8. The median, or middle value on the list, must be below 8, because only four of the scores are as high as 8, while six of the scores are below 8. Specifically, the median of 10 scores will always be the average of the 5th and 6th highest scores, both of which, here, are less than 8. (D) The two students who scored a 7 differed in their number of hours studied by more than 2 full hours.
3 20 + 3 22 is how many times greater than 3 20 ?
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Eight less than the square of x is less than eight. Which of the following expresses all possible values of x?
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Five different video games are to be tested on five consecutive weekdays, one game per day.
How many different orderings of these games are possible?
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(120) Many students will not get past the initial thought that the answer must be 5 × 5 and will quickly enter 25, which is incorrect. To solve, take a “fill in the blank” approach. Write out five blanks to represent the five weekdays, say Monday through Friday:_____ _____ _____ _____ _____.
In each blank, write the number of ways that particular blank can be filled. On Monday, there are five possible games we could test, so write 5 in the first blank. On Tuesday, there are only four choices left, because the same game will not be tested again. Since five different games need to be tested in the 5-day period, repeats are precluded. Write 4 in the second blank. On Wednesday, there are only three choices remaining, and so forth. By the Basic Counting Principle, the total number of combinations equals the product of these numbers. Therefore, there are 5 × 4 × 3 × 2 × 1 or 120 total orderings.
The sum of two numbers is 40 and their difference is 26. What is their product?
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Questions are based on the following table, which shows student enrollment at College Y over a 7-year period.
In the year 2007 (not shown), n male students and 300 female students enrolled in College Y, and the median total enrollment for the 8 years from 2000 through 2007 became 834.5. What is the value of n?
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Questions are based on the following table, which shows student enrollment at College Y over a 7-year period.
What was the greatest percentage decrease in total enrollment from one year to the next?
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(E) Look only at the total enrollment column at the right. This shows a few small yearly decreases and three larger decreases of 42, 41, and 40, in the periods from 2000 to 2001, 2001 to 2002, and 2005 to 2006, respectively. Put each decrease over the starting value of that period, to determine the percent change. The calculator shows that the greatest is 40/800 = 0.05 = 5%
Children who ride the roller coaster must be between 24 and 52 inches tall. If x represents the height in inches of a child who may ride the roller coaster, which of the following absolute value inequalities represents all possible values of x?
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The ratio of programmers to scientists at a company was 8:5 in the year 2000 and 3:4 in the year 2010. If the total number of programmers and scientists at the company was 52 in the year 2000 and 196 in the year 2010, how many more scientists were at the company in 2010 than in 2000?
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