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OG12 OG15
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What is the average (arithmetic mean) of j and k ?(1)The average (arithmetic mean) of j + 2 and k + 4 is 11.(2)The average (arithmetic mean) of j, k, and 14 is 10.
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OG12 OG15
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A number of people each wrote down one of the first 30 positive integers. Were any of the integers written down by more than one of the people?(1)The number of people who wrote down an integer was greater than 40.(2)The number of people who wrote down an integer was less than 70.
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OG12 OG15 OG16
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In a certain office, 50 percent of the employees are college graduates and 60 percent of the employees are over 40 years old. If 30 percent of those over 40 have master's degrees, how many of the employees over 40 have master's degrees?(1)Exactly 100 of the employees are college graduates.(2)Of the employees 40 years old or less, 25 percent have master's degrees.
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OG12 OG15 OG16
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An employee is paid 1.5 times the regular hourly rate for each hour worked in excess of 40 hours per week, excluding Sunday, and 2 times the regular hourly rate for each hour worked on Sunday. How much was the employee paid last week?(1)The employee's regular hourly rate is $10.(2)Last week the employee worked a total of 54 hours but did not work more than 8 hours on any day.
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OG12 OG15
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In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?(1)Of the 300 students, 60 do not study Spanish.(2)A total of 240 of the students study Spanish.
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A certain salesperson's weekly salary is equal to a fixed base salary plus a commission that is directly proportional to the number of items sold during the week. If 50 items are sold this week, what will be the salesperson's salary for this week?(1)Last week 45 items were sold.(2)Last week's salary was $405.
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At Larry's Auto Supply Store, Brand X antifreeze is sold by the gallon and Brand Y motor oil is sold by the quart Excluding sales tax, what is the total cost for 1 gallon of Brand X antifreeze and 1 quart of Brand Y motor oil?(1)Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10 quarts of Brand Y motor oil is $58. (There is no quantity discount.)(2)Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12 quarts of Brand Y motor oil is $44. (There is no quantity discount.)
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OG12 OG15 OG16
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What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price?(1)x = 50(2)Full-price tickets sold for $20 each.
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OG12 OG15
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Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio $$\frac r s $$ is expressed as a decimal, is $$\frac r s$$ a terminating decimal?(1)$$90 < r < 100$$(2)$$s = 4$$
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排列组合
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If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is $$p >\frac1 2$$ ?(1)More than $$\frac1 2$$ of the 10 employees are women.(2)The probability that both representatives selected will be men is less than $$\frac1 {10}$$.
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OG12
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For all integers n, the function f is defined by $${f}({n})={a}^{n}$$, where a is a constant. What is the value of $$f (1)$$?(1)$$f (2) = 100$$(2)$$f (3) = -1,000$$
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OG12 OG15 OG16 OG17
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Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?(1)The first n people donated $$\frac1 {16}$$ of the total amount donated.(2)The total amount donated was $120,000.
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What is the value of the integer k?(1)$$k + 3 > 0$$(2)$${k}^{4}\le{0}$$
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The results of a certain experiment included 6 data values that were all multiples of the same number c, namely, c, 8c, 2c, 5c, 4c, and 4c. Was the average (arithmetic mean) of the 6 data values greater than 8?(1)c < 4(2)c > 2
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OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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 Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?(1)v + z = 6(2)s + t + u + x = 6
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OG12 OG15 OG16 OG17 OG18 OG19 OG20 OG2022
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If x is negative, is $$x < -3$$?(1)$${x}^{2} >{9}$$(2)$${x}^{3}<-{9}$$
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OG12
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If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?(1)t - p = p - m(2)t - m = 16
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If a, b, c, and d are positive integers, is $$(\frac {a} {b})(\frac {c} {d}) >\frac {c} {b}$$?(1)$$c > b$$(2)$$a > d$$
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If a certain machine produces bolts at a constant rate, how many seconds will it take the machine to produce 300 bolts?(1)It takes the machine 56 seconds to produce 40 bolts.(2)It takes the machine 1.4 seconds to produce 1 bolt.
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OG12 OG15 OG16 OG17
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A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?(1)$${x}=\frac {3y} {4}$$(2)The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
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