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 Figures X and Y above show how eight identical triangular pieces of cardboard were used to form a square and a rectangle, respectively. What is the ratio of the perimeter of X to the perimeter of Y?
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At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
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Each of the marbles in a jar is either red or white or blue. If one marble is to be selected at random from the jar, what is the probability that the marble will be blue?(1) There are a total of 24 marbles in the jar, 8 of which are red.(2) The probability that the marble selected will be white is $$\frac{1}{2}$$.
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If sequence S has 120 terms, what is the 105th term of S?(1) The first term of S is −8.(2) Each term of S after the first term is 10 more than the preceding term.
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Three houses are being sold through a real estate agent. What is the asking price for the house with the second-largest asking price?(1) The difference between the greatest and the least asking price is $130,000.(2) The difference between the two greater asking prices is $85,000.
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Is $$x=\frac{1}{y}$$ ?(1) xy = 1(2) $$\frac{1}{xy}=1$$
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Do at least 60 percent of the students in Pat's class walk to school?(1) At least 60 percent of the female students in Pat's class walk to school.(2) The number of students in Pat's class who walk to school is twice the number of students who do not walk to school.
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If x and y are positive integers, what is the value of $$\sqrt{x}+\sqrt{y}$$ ?(1) x + y = 15(2) $$\sqrt{xy}= 6$$
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A certain truck uses $$\frac{1}{12}$$ + $${k}{v}^{2}$$ gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses $$\frac{5}{12}$$ gallon of fuel per mile?(1) The value of k is $$\frac{1}{10800}$$(2) When the truck travels at 30 miles per hour, it uses $$\frac{1}{6}$$ gallon of fuel per mile.
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If x = 2t and $${y}=\frac{t}{3}$$, what is the value of $${x}^{2}-{y}^{2}$$?(1) $${t}^{2}$$ − 3 = 6(2) $${t}^{3}$$ = −27
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A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00 and $9.50, respectively, and the selling prices per unit of P and Q are $10.00 and $13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000.00?(1) During the month, more units of P than units of Q were sold.(2) During the month, at least 100 units of Q were sold.
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A conveyor belt moves bottles at a constant speed of 120 centimeters per second. If the conveyor belt moves a bottle from a loading dock to an unloading dock, is the distance that the conveyor belt moves the bottle less than 90 meters? (1 meter = 100 centimeters)(1) It takes the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.(2) It takes the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.
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OG16 OG17 OG18 OG19 OG20 OG2022
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A telephone station has x processors, each of which can process a maximum of y calls at any particular time, where x and y are positive integers. If 500 calls are sent to the station at a particular time, can the station process all of the calls?(1) x = 600(2) 100 < y < 200
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If $${2}^{x+y}$$ = $${4}^{8}$$, what is the value of y?(1) $${x}^{2}$$ = 81(2) x − y = 2
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y = ax - 5y = x + 6y = 3x + bIn the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?(1) a = 2(2) r = 17
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 In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6. What is the perimeter of polygon PQWTUVR?(1) Triangle SWV has perimeter 9.(2) VW has length 3.5.
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City X has a population 4 times as great as the population of City Y, which has population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
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 The table shows the numbers of packages shipped daily by each of five companies during a 4-day period. The standard deviation of the numbers of packages shipped daily during the period was greatest for which of the five companies?
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If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200,then x must be a multiple of which of the following?
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In Western Europe, x bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?
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