1.
When 70,000 is written as 7.0 x 10^{n} , what is the value of n ?
Correct Answer
D. 4
Explanation
The value of n can be determined by counting the number of decimal places needed to shift the decimal point in 70,000 to obtain 7.0. In this case, the decimal point needs to be shifted 4 places to the left, indicating that n is equal to 4.
2.
On a car trip Sam drove m miles, Kara drove twice as many miles as Sam, and Darin drove 20 fewer miles than Kara. In terms of m, how many miles did Darin drive?
Correct Answer
B. 2m - 20
Explanation
Kara drove twice as many miles as Sam, which can be represented as 2m. Darin drove 20 fewer miles than Kara, so his distance can be represented as 2m - 20. Therefore, the answer is 2m - 20.
3.
If x and y are positive integers, what are all the solutions (x, y) of the equation 3x + 2y = 11 ?
Correct Answer
D. (1, 4) and (3, 1)
Explanation
The equation 3x + 2y = 11 can be solved by substituting different values of x and y to find the solutions. By trying different combinations, we find that (1, 4) and (3, 1) are the only solutions that satisfy the equation. For (1, 4), when x = 1 and y = 4, 3(1) + 2(4) = 11. Similarly, for (3, 1), when x = 3 and y = 1, 3(3) + 2(1) = 11. Therefore, the correct answer is (1, 4) and (3, 1).
4.
A companyâ€™s profit, P, in dollars, for producing x machines in one day is given by P = 500x - 20x^{2}. If the company produces 10 machines in one day, then, according to this formula, what is the profit for that day?
Correct Answer
C. $3,000
Explanation
The given formula for calculating profit is P = 500x - 20x^2. To find the profit for the day when 10 machines are produced, substitute x = 10 into the formula. P = 500(10) - 20(10)^2 = 5000 - 2000 = $3000. Therefore, the profit for that day is $3000.
5.
12 - n, 12, 12 + nWhat is the average (arithmetic mean) of the 3 quantities in the list above?
Correct Answer
B. 12
Explanation
The average of the three quantities in the list can be found by adding them together and then dividing by 3. In this case, the sum of the three quantities is 12 + 12 + 12 = 36. Dividing 36 by 3 gives us an average of 12.
6.
In isosceles triangle ABC above, AM and CM are the angle bisectors of angle BAC and angle BCA. What is the measure of angle AMC ?
Correct Answer
A. 110 degrees
Explanation
In an isosceles triangle, the angles opposite the equal sides are also equal. In triangle AMC, angles MAC and MCA are equal since AM and CM are angle bisectors. Therefore, the measure of angle AMC is twice the measure of angle MAC or MCA. Since the measure of angle MAC or MCA is 55 degrees (half of 110 degrees), the measure of angle AMC is 110 degrees.
7.
A fruit salad is made from pineapples, pears, and peaches mixed in the ratio of 2 to 3 to 5, respectively, by weight. What fraction of the mixture by weight is pineapple?
Correct Answer
A. 1/5
Explanation
The fruit salad is made from pineapples, pears, and peaches mixed in the ratio of 2 to 3 to 5, respectively. This means that for every 2 parts of pineapples, there are 3 parts of pears and 5 parts of peaches. In total, there are 2 + 3 + 5 = 10 parts of the mixture. To find the fraction of the mixture that is pineapple, we divide the number of parts of pineapples (2) by the total number of parts (10), which gives us 2/10. Simplifying this fraction gives us 1/5.
8.
In the figure above, square RSTU is inscribed in the circle. What is the degree measure of arc ST ?
Correct Answer
C. 90 degrees
Explanation
The degree measure of arc ST is 90 degrees because in a circle, an inscribed angle is always half the measure of its intercepted arc. Since arc ST is the intercepted arc of angle SUT, which is a right angle, the degree measure of arc ST is 90 degrees.
9.
If P and Q are two sets of numbers, and if every number in P is also in Q, which of the following CANNOT be true?
Correct Answer
C. 6 is in P, but not in Q.
Explanation
If every number in P is also in Q, it means that P is a subset of Q. This means that every element in P is also an element in Q. Therefore, it is not possible for a number to be in P but not in Q. Hence, option 6 cannot be true.
10.
What is the maximum number of rectangular blocks measuring 3 inches by 2 inches by 1 inch that can be packed into a cube-shaped box whose interior measures 6 inches on an edge?
Correct Answer
D. 36
Explanation
The cube-shaped box has an interior measurement of 6 inches on each side. Since the rectangular blocks measure 3 inches by 2 inches by 1 inch, we can fit 2 blocks along the length (6/3), 3 blocks along the width (6/2), and 6 blocks along the height (6/1). Multiplying these numbers together gives us a total of 36 blocks that can be packed into the box.
11.
If a â‰ 0 and (5/x) = (5 + a)/(x + a), what is the value of x?
Correct Answer
E. 5
Explanation
The given equation states that the ratio of 5 to x is equal to the ratio of 5+a to x+a. We can cross-multiply to get 5(x+a) = x(5+a). Expanding both sides of the equation, we have 5x + 5a = 5x + ax. The x terms cancel out, leaving us with 5a = ax. Since a is not equal to 0, we can divide both sides of the equation by a to get 5 = x. Therefore, the value of x is 5.
12.
The figure above is composed of 25 small triangles that are congruent and equilateral. If the area of DFH is 10, what is the area of AFK ?
Correct Answer
B. 42.5
Explanation
Each small triangle in the figure has the same area since they are congruent and equilateral. The area of the triangle DFH is given as 10. Since the figure is composed of 25 small triangles, the total area of the figure is 25 times the area of one small triangle. Therefore, the total area of the figure is 25 * 10 = 250. The triangle AFK is one of the small triangles, so its area is also 10. However, we are asked for the area of AFK in terms of the total area of the figure. Therefore, the area of AFK is 10/250 * 100 = 4%. This is equivalent to 42.5, so the correct answer is 42.5.
13.
3x +2y+ 2z = 193x +y +z = 1413. If the equations above are true, which of the followingis the value of y+z? �=+ z ?
Correct Answer
E. 5
Explanation
The given equations can be solved using the method of substitution or elimination. By solving the equations, we find that y = 6 and z = -1. Therefore, the value of y + z is 6 + (-1) = 5.
14.
A boat costs x dollars, and this cost is to be shared equally by a group of people. In terms of x, how many dollars less will each person contribute if there are 4 people in the group instead of 3 ?
Correct Answer
A. X/12
Explanation
If there are 3 people in the group, each person would contribute x/3 dollars. If there are 4 people in the group instead, each person would contribute x/4 dollars. Therefore, each person would contribute x/3 - x/4 = (4x - 3x)/12 = x/12 dollars less.
15.
If y = 2x+3 and x < 2, which of the followingrepresents all the possible values for y ?
Correct Answer
A. Y < 7
Explanation
The equation y = 2x + 3 represents a linear function with a slope of 2 and a y-intercept of 3. Since x < 2, the values of x that satisfy this inequality are all numbers less than 2. Plugging in the maximum value of x, which is 2, we get y = 2(2) + 3 = 7. Therefore, all possible values of y are less than 7, which is represented by y < 7.
16.
The graphs of the functions f and g in the interval from x = -2 to x = 2 are shown above.Which of the following could express g in terms of f ?
Correct Answer
B. G (x) = f(x) + 1
Explanation
The correct answer is g(x) = f(x) + 1 because it is evident from the graph that the graph of g(x) is obtained by shifting the graph of f(x) one unit upward. This can be observed by comparing the y-values of corresponding points on the graphs of f(x) and g(x). Therefore, adding 1 to f(x) will result in the graph of g(x).
17.
In the figure above, a shaded polygon which has equal sides and equal angles is partially covered with a sheet of blank paper. If x + y = 80, how many sides doesthe polygon have?
Correct Answer
B. Nine
Explanation
The given information states that a shaded polygon with equal sides and equal angles is partially covered with a sheet of blank paper. This implies that the shaded polygon is a regular polygon. Since a regular polygon has equal sides and equal angles, it can be concluded that the polygon has 9 sides.
18.
If s, t, u, and v are the coordinates of the indicated points on the number line above, which of the following is greatest?
Correct Answer
D. |s-v|
Explanation
The greatest value among the given options is |s-v|. This can be determined by considering the absolute difference between the coordinates of s and v on the number line. Since absolute values only yield positive values, |s-v| will always be greater than or equal to 0. In comparison, |s+t|, |s-t|, |s+v|, and |s+u| may have negative values depending on the relative positions of the coordinates on the number line. Therefore, |s-v| is the greatest option.
19.
On the day of a rainstorm, the depth of the water at a certain location along the Winding River was recorded hourly, and the results are indicated in the line graph above. Each unit on the vertical axis represents 1 foot. If the depth of the water decreased 10 percent from3:00 P.M. to 4:00 P.M., what was the depth of the water at 4:00 P.M.?
Correct Answer
C. 18 feet
Explanation
The line graph shows the depth of the water at different times. From 3:00 P.M. to 4:00 P.M., the depth of the water decreased by 10 percent. Therefore, we need to find the depth of the water at 4:00 P.M. by subtracting 10 percent from the depth at 3:00 P.M. The depth at 3:00 P.M. is 20 feet, so 10 percent of 20 feet is 2 feet. Subtracting 2 feet from 20 feet gives us a depth of 18 feet at 4:00 P.M.
20.
Correct Answer
D. I and II only