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The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B?
How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ?
What is the range of the average costs for the eight home remodeling projects listed?
In City X, the percent increase from 1997 to 1999 in the average cost of a deck addition was 45 percent, and the percent increase from 1994 to 1997 in the average cost of a deck addition was 26 percent. Which of the following expressions represents the average cost, in dollars, of a deck addition in City X in 1994 ?
For how many of the remodeling projects listed is the average return on the project when the home is sold less than 75 percent of the average cost of the project?
A grocery store had 105 pieces of fruit for sale consisting of apples, mangoes, and peaches.

Which of the following statements individually provide(s) sufficient additional information to determine the number of apples for sale at the grocery store?

Indicate all such statements.
Of the 36 students in a certain class, 10 are in the chess club and 13 are in the bridge club. If 20 of the students are not in either club, how many of the students are in only one of the two clubs?
x(x+3)(x-5)>0

Which of the following inequalities specify values of x that satisfy the inequality above?

Indicate all such inequalities.


The figure shows a circle with center A and radius 10, and a circle with center D and radius 3. AD intersects the two circles at points F and E, respectively. Line is tangent to the two circles at points B and C, respectively. If the length of FE is 12, what is the length of BC ?

Length of BC:_____
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x is a positive two-digit integer with units digit 6, and y is a positive two-digit integer with tens digit 8.

Quantity A

The least possible value of x+y

Quantity B

96


Each of six consecutive positive integers is divided by 6.

Quantity A

The average (arithmetic mean) of the 6 resulting remainders

Quantity B

3.5


x, y, and z are positive integers.

3x+2y+z=42

Quantity A:x+y+z

Quantity B:18


The center of the circle is O and RS>ST.

Quantity A

x

Quantity B

y


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m+t=1

m < t

Quantity A

mt

Quantity B

$$m^2$$


x is an integer.

Quantity A:$$\frac{10^{3x+1}}{10^{x+3}}$$

Quantity B:$$\frac{10^{x+1}}{10^{1-x}}$$

Quantity A

The number of possible values of the product pt, where p and t are even positive integers and 30< pt< 34

Quantity B

1




A submarine`s depth, in meters below sea level, at a time t minutes after it began to dive below the sea surface is equal to $$g_{(x)}$$ for 0≤t≤6. Its diving speed, measured in meters per minute, is the rate of change in depth.

Quantity A

The average diving speed of the submarine for 0≤t≤3

Quantity B

Quantity B:The average diving speed of the submarine for 3≤t≤6


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The table shows the distribution of the grades on a chemistry exam taken by a class of 40 students. If one of the students is to be chosen at random, what is the probability that the student chosen will be one whose grade on the exam is greater than or equal to 90 ?

Give your answer as a fraction.
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In a certain store, notebooks that normally sell for 59 cents each are on sale for 2 for 99 cents. If a person buys 2x of these notebooks at the sale price, what is the value of x if the total amount saved compared to buying at the normal price is 95 cents?

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