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40 DVDs (17 are about psychology, 14 are about biology, and 9 are about history) need to be arranged in a bookshelf such that the 9 history-related DVDs are, on the whole, arranged in chronological order. In how many ways can these DVDs be arranged?
From a class of 8 students, of which 5 students are female, a president and a vice president are to be chosen at random. If a student cannot be both the president and the vice president, what is the probability that the president and the vice president will both be female? Give your answer as a fraction.
$x$ is defined as the 3-digit integer formed by reversing the digits of integer $x$ ; for instance, $258$ is equal to $852$ . $R$ is a 3-digit integer such that its units digit is $2$ greater than its hundreds digit. Quantity A $R*-R$ Quantity B $200$
Let a be the greatest integer such that $5^{a}$ is a factor of 1,500, and let b be the greatest integer such that $3^{b}$ is a factor of 33,333,333. Which of the following statements are true? Indicate all such statements.
Quantity A The remainder when 123,456,789 is divided by 9 Quantity B 1
Quantity A The number of tenths equal to 1.4 Quantity B The number of hundredths equal to 1.3
Sam, Jan, and Kate all bought the same style of jacket. Jan paid 17 percent more for the jacket than Sam paid, and Kate paid 12 percent more for the jacket than Jan paid. The amount that Kate paid was what percent greater than the amount that Sam paid? Give your answer to the nearest whole percent.
Vladimir invested $10,000 for one year.He invested some of the amount at 4 percent simple annual interest and the rest of the amount at 6 percent simple annual interest. If the total interest earned for the year was between $450 and $550, which of the following statements must be true?. Indicate all such statements.
x> $\sqrt{5}$ Quantity A 3x Quantity B $\sqrt{45}$
Professor Lopez is teaching three different courses with an average (arithmetic mean) enrollment of 32 students per course. If 5 students are taking two of these courses, 3 other students are taking all three courses, and all of the others are taking only one of the courses, what is the total number of different students enrolled in the three courses?
Sequence $S$ : $a_{1}, a_{2}, a_{3},......,a_{n}$ ........ In sequence $S$ , $a_{1}$ is an integer and $a_{n}=2a_{n-1}$ for all integers n greater than 1. If no term of sequence S is a multiple of 100, which of the following could be the value of $a_{1}$ ? Indicate all such values.
Eugene and Penny started a job in sales on the same day. Eugene's sales for the first month were r dollars and each month after the first his sales for that month were twice his sales for the preceding month. Penny's sales for the first month were 10r dollars, and each month after the first her sales for that month were 10r dollars more than her sales for the preceding month. Which of the following statements are true? Indicate all such statements.
The figure above shows a rectangle and five circles. Each circle is tangent to the other circles and to the sides of the rectangle that it touches. If the diameter of each circle is 4, what is the area of the rectangle?
The length of each side of a smaller cube is 2. What is the surface area of the bigger cube formed out of 125 such cubes?
The 25 students in an English class took a literature test. Jovan, one of the 25 students, originally received a score on the test that was 6.2 points above the average (arithmetic mean) score for the 25 students. Each student was then given an opportunity to earn 10 additional points on the test by completing an extra project, and the average was then recalculated. If Jovan earned the 10 additional points and no other student earned additional points, Jovan's new score was how many points above the recalculated average score?
The boxplot above summarizes a list of 240 numbers. Which of the following statements must be true? Indicate all such expressions.
Four different persons will be selected from 2 men and 5 women to serve on a committee. If at least 1 man and 1 woman must be among thoses selected, how many different selections of the 4 persons are possible?
Point A (a, b) is in the xy-plane where both a and b are positive integers. What is the number of point A such that a+b < 200?
X=1!+2!+3!+4!+5!+6!+7!+8!+9!+10! What is the remainder when X is divided by 20?
k is a positive integer Quantity A The remainder when k is divided by 7 Quantity B The remainder when 2k is divided by 7

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