| Quantity A | Quantity B |
| \((\sqrt{3} + \sqrt{3} + \sqrt{3})^{2}\) | \((\sqrt{54/2})^{2}\) |
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Solution
x 4 = 81; 8y 3 = 64
| Quantity A | Quantity B |
| x | y |
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Solution
The area of the circle above, with center C, is 36π, and x > 90.
| Quantity A | Quantity B |
| The area of the triangle | 18 |
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A student’s average test score in algebra is 88 after eight tests have been taken. When the teacher drops the student’s two lowest test scores, the student’s average score increases to 92. What is the average score of the two tests that were dropped?
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The sum of the first 100 positive integers is how much greater than the sum of the first 80 positive integers?
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In the xy-plane, the distance between the point P (1,3) and Q (9,y) is 17. If y > 0, then what is the value of y?
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The weights of python snakes are normally distributed with a mean of 110 kg and a standard deviation of 8 kg. If 68% of pythons weigh within one standard deviation of the mean and 95% of pythons weigh within two standard deviations of the mean, what percent of pythons weigh from 94 to 102 kg?
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How many 2 × 4 × 6 boxes will fit in a 14 × 16 × 18 storage locker? (The boxes and locker are rectangular solids, and all units are in feet.)
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Let m be the 1,003rd digit to the right of the decimal point in the repeated decimal expansion \(\overline{0.13579}\) , and let n equal the 78th digit to the right of the decimal point in the repeated decimal expansion \(\overline{0.2468}\). What is the value of mn ?
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A jar contains 30 red marbles, 40 blue marbles, 50 green marbles, and no other marbles. After x blue marbles are added to the jar, the probability of selecting a blue marble on a random draw is equal to \(\frac{7}{9}\) What is the value of x?
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At School Y, 60% of all students are male, and 40% of all male students are transfer students. If two students at the school are selected at random from the entire student body of 25 students, what is the probability that both students will be male transfer students?
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If \(\frac{4n^{2}}{15}\) is an integer, then which of the following could be n?
Indicate all that apply.
A. −75
B. −9
C. 4
D. 135
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Solution
Four numbers are placed in the number circle above so that one number is equal to the sum of the other three. Which of the following could be the value of x?
Indicate all that apply.
A. 5
B. 17
C. 39
D. 51
E. 2,856
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Solution
(A, D) Sum implies addition, so this problem requires the three numbers in the circle to add up to the fourth. One possibility is x = 6 + 17 + 28, and x = 51. Another possibility is for 28, the largest given number, to equal the sum of the other three. Then x + 6 + 17 = 28. So x = 28 − 23 = 5. The answer is (A) and (D).
Questions are based on the following data, which shows the amount of money that an average student at College Z spent on tuition, rent, and food from the year 2007 through the year 2010. Figures at left are in dollars.
The data supports which of the following statements for the period shown?
Indicate all that apply.
A. The average student’s tuition expenses increased each year.
B. The average student’s rent expenses increased each year.
C. The average student’s total expenses for food, rent, and tuition combined increased each year.
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Solution
(A, C) Tuition is the bottom part of each bar, which grew each year, so (A) is correct. Rent is the middle part of each bar. In 2007, rent spans more than two horizontal lines and is thus greater than $2,000. In 2008, rent spans fewer than two horizontal lines, and is thus less than $2,000. So rent decreased from 2007 to 2008, and (B) is not correct. (C) is correct, because rent plus food plus tuition equals the height of the full bar, which clearly grew each year. The answer is (A) and (C).
Questions are based on the following data, which shows the amount of money that an average student at College Z spent on tuition, rent, and food from the year 2007 through the year 2010. Figures at left are in dollars.
In which year did the average student spend less on food than in the previous year?
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Solution
(B) Compare the sizes of the top part of each bar, food, and notice that this is smallest in 2008. So in 2008, (B), food expenses were less than in the previous year.
Questions are based on the following data, which shows the amount of money that an average student at College Z spent on tuition, rent, and food from the year 2007 through the year 2010. Figures at left are in dollars.
By approximately what percent did the average student’s tuition increase from 2007 to 2010?
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Solution
Questions are based on the following data, which shows the amount of money that an average student at College Z spent on tuition, rent, and food from the year 2007 through the year 2010. Figures at left are in dollars.
Considering the costs of tuition and rent only, the average student’s expenses increased by an average of how much per year over the period shown?
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Solution
