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OG18 OG19 OG20 OG2022
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In the xy-plane, the origin O is the midpoint of line segment PQ. If the coordinates of P are (r,s), what are the coordinates of Q ?
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OG18 OG19 OG20 OG2022
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If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?
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OG18 OG19 OG20 OG2022
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What number is 108 more than two-thirds of itself?
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OG18 OG19 OG20 OG2022
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125% of 5 =
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OG18-数学分册
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The sequence $$a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$$ is such that $$a_{n} = a_{n ‒ 1} + 5$$ for 2 ≤ n ≤ 5. If $$a_{5} = 31$$, what is the value of $$a_{1} $$?
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OG18-数学分册
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Each machine at a toy factory assembles a certain kind of toy at a constant rate of one toy every 3 minutes. If 40 percent of the machines at the factory are to be replaced by new machines that assemble this kind of toy at a constant rate of one toy every 2 minutes, what will be the percent increase in the number of toys assembled in one hour by all the machines at the factory, working at their constant rates?
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OG18-数学分册
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Of the following, which is least?
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OG18-数学分册
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How many integers between 1 and 16, inclusive, have exactly 3 different positive integer factors?(Note: 6 is NOT such an integer because 6 has 4 different positive integer factors: 1, 2, 3, and 6.)
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OG18-数学分册
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List S consists of 10 consecutive odd integers, and list T consists of 5 consecutive even integers. If the least integer in S is 7 more than the least integer in T, how much greater is the average (arithmetic mean) of the integers in S than the average of the integers in T ?
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OG18-数学分册
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A school club plans to package and sell dried fruit to raise money. The club purchased 12 containers of dried fruit, each containing 16$$\frac{3}{4}$$ pounds. What is the maximum number of individual bags of dried fruit, each containing $$\frac{1}{4}$$ pounds, that can be sold from the dried fruit the club purchased?
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OG18-数学分册
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If a and b are positive integers and $${(2^{a})}^{b} = 2^{3}$$, what is the value of $$2^{a}2^{b}?$$
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OG18-数学分册
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If x – y = R and xy = S, then (x – 2)(y + 2) =
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OG18-数学分册
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If the sum of the reciprocals of two consecutive odd integers is $$\frac{12}{35}$$, then the greater of the two integers is
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OG18-数学分册
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If S = {0, 4, 5, 2, 11, 8}, how much greater than the median of the numbers in S is the mean of the numbers in S ?
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OG18-数学分册
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A group of store managers must assemble 280 displays for an upcoming sale. If they assemble 25 percent of the displays during the first hour and 40 percent of the remaining displays during the second hour, how many of the displays will not have been assembled by the end of the second hour?
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OG18-数学分册
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2x + 2y = -44x + y = 1 In the system of equations above, what is the value of x?
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OG18-数学分册
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Is the positive integer n odd?(1) $$n^{2} + {(n+1)}^{2} + {(n+2)}^{2}$$ is even.(2) $$n^{2} - {(n+1)}^{2} - {(n+2)}^{2}$$ is even.
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OG18-数学分册
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If x > 0, what is the value of $$x^{5}$$?(1) $$\sqrt{x}=32$$(2) $$x^{2}=2^{20}$$
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OG18-数学分册
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What is the average (arithmetic mean ) of x and y?(1) The average of x and 2y is 10.(2) The average of 2x and 7y is 32.
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OG18-数学分册
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What is the value of $$\frac{r}{2} + \frac{s}{2}$$?(1) $$\frac{r +s}{2} = 5$$(2) r + s =10
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