|
OG19 OG20 OG2022
|
In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7 ?
|
|
OG18-定量推理
|
Of all the students in a certain dormitory, $$\frac1 2$$ are first-year students and the rest are second-year students. If $$\frac4 5$$ of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
|
|
|
 The figure shown represents a board with 4 rows of pegs, and at the bottom of the board are 4 cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has the probability $$\frac1 2$$ of passing through the opening immediately to the left of that peg and probability $$\frac1 2$$ of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end in Cell 2?
|
|
|
At a monthly meeting, $$\frac2 5$$ of the attendees were males and $$\frac7 8$$ of the male attendees arrived on time. If $$\frac9 {10}$$ of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
|
|
|
A circular mat with diameter 20 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
|
|
|
A box contains exactly 24 balls, of which 12 are red and 12 are blue. If two balls are to be picked from this box at random and without replacement, what is the probability that both balls will be red?
|
|
|
In a certain English class, $$\frac1 4$$ of the number of girls is equal to $$\frac1 6$$ of the total number of students. What is the ratio of the number of boys to the number of girls in the class?
|
|
|
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
|
|
|
 In the figure, what is the area of triangular region BCD ?
|
|
PREP07 Test 1
|
If x is a negative integer, which of the following expressions has the LEAST value?
|
|
|
If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?
|
|
|
The sequence $${a}_{1}$$, $${a}_{2}$$, ..., $${a}_{n}$$, ... is such that $${a}_{n}=4a_{n-1}-{3}$$ for all integers $$n > 1$$. If $${a}_{3}={x}$$, then $${a}_{1}$$ =
|
|
|
 The figure shows two squares, and the points W, X, Y, and Z lie on a line. If the distance between W and X is equal to the distance between X and Y and to the distance between Y and Z, then the area of the smaller square is what fraction of the area of the larger square?
|
|
|
A gumball dispenser has 24 gumballs, 12 white and 12 black, which are dispensed at random. If the first 3 gumballs dispensed are black, what is the probability that the next gumball dispensed will be black?
|
|
|
Chris mixed 3 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?
|
|
|
A shipment of 8 television sets contains 2 black-and-white sets and 6color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
|
|
|
A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was $$\frac{1}{3}$$ full, and $$\frac{11}{4}$$ hours later it was $$\frac{3}{4}$$ full. What was the total number of hours that it took the pump to fill the pool?
|
|
Magoosh
|
If 0.25 + x = y and y/x = 0.2, then y =
|
|
Magoosh
|
If$$ \frac{w}{x} = \frac{2}{3} and\frac{ w}{y} = \frac{8}{15}$$, then $$({x + y})\over{y} $$=
|
|
Magoosh
|
If y is 80 percent greater than x, then x is what percent less than y?
|