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题目列表

题目内容
Let a, b, and c be integers greater than or equal to 2. When b is divided by c, the remainder is 0. When a is divided by b, the remainder is c. Which of the following is equal to the remainder when a is divided by c?


In triangle ABC shown, what is the length of line segment AD ?
In the xy-plane, the point (t, t-1) lies on the line with equation y = $$ - \frac{1}{2}$$ x +$$\frac{1}{3}$$ . What is the value of t?
Two seating arrangements of people around a circular table are called the same if, for each seated person, the same person is seated to that person's immediate right in both arrangements.

Quantity A

The number of different seating arrangements of 4 people around a circular table

Quantity B

8
There are 25 students in Ms. Ware's class-15 of these students take French, 12 of these students take Spanish, and 8 of these students take Latin. If all 25 students in Ms.Ware's class take at least one of these three language courses, which of the following is the greatest possible number of students in the class who could be taking all three language courses?
Each time a certain coin is tossed, the probability is $$\frac{1}{2}$$ that it will land head up and $$\frac{1}{2}$$ that it will land tail up. If the coin is tossed 3 times, what is the probability that it will land heads up exactly twice?
If both the sum and the product of the four positive integers a, b, c and d are even, while the product of a, b, c and d is multiple of 8, but not multiple of 16, then what is the number of these integers that could be even?
0 < s < t

Quantity A

$$\frac{s}{t}$$ +0.4

Quantity B

$$\frac{5s+2t}{5t}$$
The average (arithmetic mean) of the 4 integers q, r, s and t is 0.

Quantity A

The average of the 4 integers q+10, r, s and t

Quantity B

The average of the 5 integers q, r, s, t, and 10


The circumference of a circle with radius 3 is divided into 4 areas of lengths w, x, y, and z, as shows.

Quantity A

The average (arithmetic mean) of w, x, y, and z

Quantity B

2π
Line segment QT has length 28. Point P is on QT, and line segment PT has length 15. Point X is also on QT, and line segment XP has length 3.

Quantity A

The length of line segment QX

Quantity B

The length of line segment QP
Jim paints $$\frac{1}{5}$$ of a garage, and Katrin paints 1/6 of the remainder of the garage.

Quantity A

The fraction of the garage not painted by Jim and Katrin

Quantity B

19/30
It costs $$d$$ dollars to buy $$s$$ sandwiches. At this rate, what is the cost of $$s+2,850$$ sandwiches, in dollars?
A store is shipping 7 items to a single address. The items can be packed into 1, 2 or 3 different containers for shipping. If a container is used for shipping, it must be packed with at least 2 items. Which of the following statements about the different combinations of packing must be true?

Indicate all such statements.
Club X has 40 members and Club Y has 28 members. If 8 people are members of both clubs, how many people are members of at least one of the two clubs?
In quadrant I of the xy-plane, a triangle has vertices at $$(r, r)$$, $$(4r, r)$$, and $$(r, 3r)$$. For what value of $$r$$ is the area of the triangle equal to $$300$$?
A circle is inscribed in a square. If a point is to be chosen at random from the square region, what is the probability that the point chosen will lie inside the circular region?
How many of the 900 positive 3-digit integers have a units digit of 2 and are the square of an integer?
Each of the people who took a data entry test made 0, 1, 2, 3, or 4 errors. Of those people, 65 percent made fewer than 4 errors, 46 percent made fewer than 3 errors, and 24 percent made fewer than 2 errors.

Quantity A

The percent of the people who took the data entry and made exactly 2 errors

Quantity B

20%

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