Each year for 4 years, an insect species increased its population within a region by a number of individuals equal to half of the population of the preceding year. If there were 16,200 insects of the species in the region at the end of the four-year period, how many insects of the species were in the region at the beginning of the four-year period?

Of 41 reviews of a particular restaurant, 20 cited good service, 7 cited the quality of the desserts, and 20 cited neither good service nor the quality of the desserts. How many of the reviews cited good service and the quality of the desserts?

If , then $$

In the figure above, the coordinates of point A could be which of the following?

The present ratio of apples to oranges within a basket is 10 to 1. If 18 apples and 3 oranges were added, the ratio of apples to oranges would be 7 to 1. How many apples are in the basket?

In the rectangular coordinate system above, A is at the origin, B has coordinates (1, 0), and line L is a line parallel to AB that passes through (0, 5). If a point C along line L is chosen to form a triangle with the segment AB, what is the area of triangle ABC?

Working simultaneously at their respective constant rates, Machines  and  produce 20 widgets in  hours. Working alone at its constant rate, Machine  produces 20 widgets in  hours. In terms of  and , how many hours does it take Machine , working alone at its constant rate, to produce 10 widgets?

If , then

For the positive integers and , represents the number of zeros between the decimal point and the first nonzero digit to the right of the decimal point in the reciprocal of the product of and , when that reciprocal is expressed as a terminating decimal. What is the value of ?

What is the smallest positive integer that is divisible by every odd integer between 1 and 10, inclusive?

If is an integer greater than 6, then all of the following must be divisible by 3 EXCEPT

A company's profits obtained from Product A, Product B, and Product C are in the ratio 47:1:2, respectively. If the total profits from these three products is $16,000, what is the profit from Product C?

Of the 50 members of a staff, 40 percent worked the day shift and the remaining 60 percent worked the night shift in a given week. Of the staff members, 80 percent prefer working the day shift and the remaining 20 percent prefer working the night shift. What is the minimum number of staff members who failed to receive his or her preference of shift that week?

What is the area of the shape in the figure above?

Carbon dioxide comprises, on average, about 397 parts per million of the Earth's atmosphere, on a molecular basis. In an even sample of the Earth's atmosphere consisting of 4 billion molecules, approximately how many of those molecules would be expected to be carbon dioxide? (1 billion = 1,000,000,000)

Upon making a sale, Pat receives a 9 percent commission on the price of the item in excess of $9,000. If Pat's commission on a sale was $405, what was the price of the item?

If a + 3|b| = 50, what are a and b?

(1) 3|b| = a - 20

(2) |b| $+\frac{a}{3}=\frac{50}{3}$

The sum of the prices of handbag A and handbag B is $50.00. If 30% of the price of handbag A is 45% of the price of handbag B, what is the price of handbag B?

Sequence is composed of integers, where , whose arithmetic mean is . If each element of is multiplied by 3, the arithmetic mean of the resulting integers remains . Which statement(s) below must be true?

1. 
2. The largest and smallest members of have the same absolute value.
3. contains both positive and negative numbers.