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$$a$$ and $$b$$ are positive integers and $$a \lt b$$.

Quantity A

$$\frac{1}{\frac{1}{a}+\frac{1}{15}+\frac{1}{14}+\frac{1}{13}+\frac{1}{12}}$$

Quantity B

$$\frac{1}{\frac{1}{b}+\frac{1}{15}+\frac{1}{14}+\frac{1}{13}+\frac{1}{12}}$$


The reduced price of a certain television was x percent less than the television's original price. The ratio of the reduced price of the television to the original price was 5 to 6.

Quantity A

x

Quantity B

20


A certain factory has two work shifts. There are 840 employees on the day shift and 700 on the evening shift. The ratio of the number of male employees to the number of female employees is the same for both shifts. If the number of female employees on the day shift is 252, what is the number of male employees on the evening shift?


The table above shows a family`s monthly budget for last month and a comparison of this month`s budget with last month`s budget. Which of the following could be the amount budgeted for discretionary spending this month?

Indicate all such amounts.
A certain store sells circular rugs at a constant price per square foot. If a circular rug with diameter 5 feet costs $250, what is the cost of a circular rug with diameter 9 feet?
Two water faucets are used to fill a certain tank. Running individually at their respective constant rates, these faucets fill the empty tank in 12 minutes and 20 minutes, respectively. If no water leaves the tank, how many minutes will it take for both faucets running simultaneously at their respective rates to fill the empty tank?

Give your answer as a decimal.
x ≠ 0

$$(a+\frac{1}{a})^{2}$$=5

Quantity A

$$a^{2}$$+$$(\frac{1}{a})^{2}$$

Quantity B

3


Which of the following is equal to $$\frac{1}{\frac{\sqrt{2}+1}{\sqrt{2}-1}}$$?
The equation $$x^{3}$$ - $$x^{2}$$-2x=0 has three different roots.

Quantity A

The product of the three roots

Quantity B

-2


The operation is defined by x✸y=$$\frac{x^{2}}{y}$$+$$\frac{x}{y}$$ for all numbers $$x$$ and $$y$$, where $$y \neq 0$$. What is the value of $$(9✸ (-9))+((-9) ✸9)$$?


Quantity A

y

Quantity B

115




A thin metal plate in the shape of a parallelogram has an area of 80 square inches and is cut into two pieces using two cuts. Each cut is parallel to a side of the plate, as shown, and the ratio of the length of each cut to the length of the side of the plate to which the cut is parallel is 3 to 4. What is the area, in square inches, of the piece of the plate represented by the shaded region?


In the figure, AC=15 and BC=12. If f+g=90, then the area of the triangular region is ?


In the sequence $$a_1$$, $$a_2$$, $$a_3$$,......., the $$n^{th}$$ term an is the distance in the xy-plane between (0, 1) and (n, 0) for each positive integer n. The figure shows the first four terms of the sequence.

Quantity A

$$a_{20}$$

Quantity B

$$\sqrt{401}$$


Each digit of a 20-digit number is either a 1, 2, 3, 4, or 5. If the average (arithmetic mean) of 15 of the 20 digits of the number is 2.8 and if M is the average of all 20 digits of the number, then M must satisfy which of the following inequalities?


The table above shows a certain store`s weekly revenue and expenses for five weeks. What is the store`s median weekly profit for the five weeks?
Each of 7 fish in an aquarium has a different weight, and the total weight of the 7 fish is 172 pounds. The total weight of the 4 heaviest fish is 114 pounds.The average (arithmetic mean) weight of the 4 lightest fish is 20.5 pounds. What is the median weight,in pounds, of the 7 fish?

_____pounds

Quantity A

The average (arithmetic mean) of the integers from 1 to 31, inclusive

Quantity B

16


r < s < t

The average (arithmetic mean) of r, s, and t is equal to the median of r, s, and t .

Quantity A

s-r

Quantity B

t-s


23, 21, 20, 32, 34, 35, 26, 31, 30, 24

For which integer in the list above are 90 percent of the integers in the list less than that integer?

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