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All of the 80 science students at a certain school are enrolled in at least one of three science courses: biology, chemistry, and physics. There are 60 students enrolled in biology, 50 students enrolled in chemistry, and 35 students enrolled in physics. None of the students are enrolled in all three courses. Which of the following could be the number of students enrolled in both chemistry and physics?
Indicate all such numbers.
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?
There are 500 students in a class. 450 of them take Course A, 300 of them take Course B, and 150 of them take Course C. Each student has to take at least one course, and 100 of them take all the three classes simultaneously. The number of students who take both Course A and Course B, but not Course C could be?
Indicate all such possible values.
Three students need to read 50 proposals. Each proposal has to be read by at least one student. Student A read 38 of them, Student B read 36 of them, while Student C read 28 of them. At least how many proposals are read by at least two students?
In a group of people, 40% of like red, 50% of them like blue, while 60% of them like green. 9% of them only like red, 10% only like blue and 11% only like green. 20% of them like all the three colors simultaneously. What percent of people like both red and green, but not blue?
List A: 4, 6, 8, 10, 12, 14-
The above list of numbers is formed by adding 2 to each of the preceding term What is the 54th term of the list?
The first term of sequence K is 7 and the last term is 217. Each term after the first is 2 greater than the previous term. How many terms are in sequence K?
A certain holiday is always on the fourth Tuesday of Month X. If Month X has 30 days, on how many different dates of Month X can the holiday fall?
In a sequence, for any integer n greater than 1, $$a_{n}$$ is greater than its preceding term by 3 and $$a_{17}$$ is 55.

Quantity A

$$a_{98}$$

Quantity B

300
What is the sum of all the odd integers between 3 and 97, inclusive?
$$Q_{n}=3Q_{n-1}$$

Quantity A

$$Q_{28}$$

Quantity B

$$Q_{11}$$
In a sequence, $$S_{1}=5$$, $$S_{n}=2*S_{n-1}$$
Quantity A: $$S_{8}$$
Quantity B: $$S_{21}/S_{13}$$
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.
In a sequence, $$a_{1}$$=1, for any integer n greater than 1, $$a_{n}$$ is 12 times the square of its preceding term. If $$a_{5}$$=$$12^{n}$$, then what is the value of n
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.
In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 2 and then subtracting 3 from the product. If the 4th term in the sequence is 19, which of the following numbers are in the sequence?
Indicate all such numbers.
Sequence A: 1, –3, 4, 1, –3, 4, 1, –3, 4, ...
In the sequence above, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 150th term to the 154th term?
$$a_{1}=1$$, $$a_{2}=1$$, $$a_{n}=0.2a_{n-1}(n≥3)$$

Quantity A

$$a_{6}$$

Quantity B

$$25^{3}(0.2)^{10}$$
$$a_{1}$$, $$a_{2}$$, $$a_{3}$$,..........., $$a_{n}$$,.............

A sequence of numbers as shown above is defined by $$a_{n}=a_{n-1}-a_{n-2}$$ for n > 2. If $$a_{1}=-5$$, and $$a_{2}=4$$, what is the sum of the first 100 terms of the sequence?
A list of numbers could be summarized into $$a_{n}=(-1)^{n+1}*n$$ (n is a positive integer), and $$a_{1}=1$$
What is the sum of $$a_{1}$$, $$a_{2}$$, $$a_{3}$$,...........,$$a_{97}$$, $$a_{98}$$, $$a_{99}$$?

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