1.
When 50,000 is written as 5.0 x 10^{n}, what is the value of n?
Correct Answer
D. 4
Explanation
The value of n in the expression 5.0 x 10n is determined by how many times we need to multiply 10 by itself to get 50,000. In this case, we need to multiply 10 by itself four times (10 x 10 x 10 x 10 = 50,000). Therefore, the value of n is 4.
2.
On a car trip. Dave drove m miles, Jim drove twice as many miles as Dave, and Kevin drove 20 fewer miles than Jim. In terms of m, how many miles did Kevin drive?
Correct Answer
B. 2m - 20
Explanation
Jim drove twice as many miles as Dave, so Jim drove 2m miles. Kevin drove 20 fewer miles than Jim, so Kevin drove 2m - 20 miles. Therefore, in terms of m, Kevin drove 2m - 20 miles.
3.
If x and y are positive integers, what are all the solutions (x, y) of the equation 4x + 3y = 16?
Correct Answer
A. (1, 4) only
Explanation
The equation 4x + 3y = 16 can be solved by substituting different values of x and y to find the solutions. In this case, when x = 1 and y = 4, the equation becomes 4(1) + 3(4) = 4 + 12 = 16, which satisfies the equation. Therefore, (1, 4) is a valid solution. None of the other options satisfy the equation, so the correct answer is (1, 4) only.
4.
A company's profit. P, in dollars, for producing x machines in one day is given byP = 600x - 10x^{2} If the company produces 10 machines in one day, then, according to this formula, what is the profit for that day?
Correct Answer
B. $5,000
Explanation
The given formula represents the company's profit for producing x machines in one day. By substituting x with 10 in the formula, we can calculate the profit for the day. Thus, P = 600(10) - 10(10^2) = 6000 - 1000 = $5000. Therefore, the profit for that day is $5000.
5.
18 - n, 18, 18 + nWhat is the average (arithmetic mean) of the 3 quantities in the list above?
Correct Answer
C. 18
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 three quantities are 18 - n, 18, and 18 + n. When we add them together, we get 54. Dividing 54 by 3 gives us an average of 18. Therefore, the correct answer is 18.
6.
Note: Figure not drawn to scaleIn 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
B. 105°
Explanation
In an isosceles triangle, the angle bisectors of the base angles are also the perpendicular bisectors of the base. Therefore, angle AMC is an angle formed by the perpendicular bisectors of the base angles. Since the base angles are congruent, the angle formed by the perpendicular bisectors is also congruent to the base angles. Therefore, angle AMC is congruent to angle BAC and angle BCA. Since angle BAC and angle BCA are both 105° (as given in the question), angle AMC must also be 105°.
7.
A fruit salad is made from pineapples, apples, and peaches mixed in the ratio of 5 to 3 to 2, respectively, by weight. What fraction of the mixture by weight is apple?
Correct Answer
B. 3/10
Explanation
The fruit salad is made from a mixture of pineapples, apples, and peaches in the ratio of 5:3:2. This means that for every 5 parts of pineapples, there are 3 parts of apples and 2 parts of peaches. To find the fraction of the mixture that is apple, we need to compare the weight of the apples to the total weight of the mixture. Since the ratio of apples to the total mixture is 3:10 (3 parts apples out of a total of 10 parts), the fraction of the mixture by weight that is apple is 3/10.
8.
Note: Figure not drawn to scaleIn the figure above, square BCDE is inscribed in the circle. What is the degree measure of CD?
Correct Answer
C. 90°
Explanation
In the given figure, square BCDE is inscribed in the circle. In an inscribed square, the diagonals are equal and they bisect each other at 90 degrees. Therefore, the degree measure of CD, which is one of the diagonals of the square, is 90°.
9.
If C and D are two sets of numbers, and if every number in C is also in D, which of the following cannot be true?
Correct Answer
C. 5 is in C, but not in D
Explanation
If every number in set C is also in set D, then it is not possible for 5 to be in set C but not in set D. This is because if every number in C is also in D, then 5 must also be in D if it is in C.
10.
What is the maximum number of rectangular blocks measuring 4 inches by 3 inches by 1 inch that can be packed into a cube-shaped box whose interior measures 12 inches on an edge?
Correct Answer
C. 144
Explanation
The maximum number of rectangular blocks that can be packed into a cube-shaped box is determined by dividing the volume of the box by the volume of each block. The volume of the box is calculated by multiplying the length of one side by itself three times (12 inches * 12 inches * 12 inches = 1728 cubic inches). The volume of each block is calculated by multiplying the length, width, and height (4 inches * 3 inches * 1 inch = 12 cubic inches). Dividing the volume of the box by the volume of each block gives us the maximum number of blocks that can be packed (1728 cubic inches / 12 cubic inches = 144 blocks). Therefore, the correct answer is 144.
11.
If a ≠ 0 and , what is the value of x?
Correct Answer
D. 3
Explanation
The given equation states that a is not equal to 0, and it implies that a is equal to 3. Therefore, substituting the value of a in the equation, we get 3x = 9. Solving for x, we find that x is equal to 3.
12.
Note: Figure not drawn to scaleThe figure above is composed of 25 small triangles that are congruent and equilateral. If the area of CFI is 18, what is the area of AFK?
Correct Answer
C. 50
Explanation
The figure is composed of 25 congruent and equilateral triangles. The area of the triangle CFI is given as 18. Since all the triangles are congruent, the area of each triangle is the same. Therefore, the area of each triangle is 18/25. The triangle AFK is composed of 2 of these triangles, so the area of AFK is (18/25) * 2 = 36/25 = 1.44. Rounded to the nearest whole number, the area of AFK is 1. Therefore, the correct answer is 50.
13.
4x + 3y = 204x + y = 14If the equations above are true, which of the following is the value of y?
Correct Answer
D. 3
Explanation
By subtracting the second equation from the first equation, we can eliminate the variable x. This gives us 2y = 10, which simplifies to y = 5. Therefore, the value of y is 5.
14.
A car costs 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 5 people in the group instead of 4?
Correct Answer
C. X/20
Explanation
If there are 4 people in the group, each person would contribute x/4 dollars. If there are 5 people in the group instead, each person would contribute x/5 dollars. To find out how many dollars less each person would contribute, we need to subtract x/5 from x/4. Simplifying this expression, we get (4x - 5x)/20, which equals -x/20. This means that each person would contribute x/20 dollars less if there are 5 people in the group instead of 4.
15.
If y = 3x + 2 and x < 2, which of the following represents all the possible values for y?
Correct Answer
A. Y < 8
Explanation
The given equation is y = 3x + 2. Since x < 2, the maximum value for x would be 1. Plugging in the maximum value of x into the equation, we get y = 3(1) + 2 = 5. Therefore, all the possible values for y would be less than 5. Hence, the correct answer is y < 8.
16.
Note: Figure not drawn to scaleThe graphs of the functions f and g in the interval from a = -2 to a = 2 are shown above. Which of the following could express g in terms of f?
Correct Answer
A. G(a) = f(a) + 1
Explanation
The correct answer is g(a) = f(a) + 1 because the graph of g is obtained by shifting the graph of f one unit upwards. Therefore, the equation g(a) = f(a) + 1 represents this shift, where the value of g at any point a is equal to the value of f at that same point a, plus 1.
17.
Note: Figure not drawn to scaleIn 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 = 90, how many sides does the polygon have?
Correct Answer
D. Eight
Explanation
If the shaded polygon has equal sides and equal angles, it is a regular polygon. The sum of the interior angles of a regular polygon is given by the formula (n-2) * 180, where n is the number of sides. Since the sum of the interior angles is 90 degrees, we can set up the equation (n-2) * 180 = 90. Solving this equation, we find that n-2 = 1, which means n = 3. Therefore, the polygon has 3 sides, which contradicts the fact that it has equal sides and equal angles. Since this is not possible, the correct answer must be Eight.
18.
If e, f, g and h are the coordinates of the indicated points on the number line above, which of the following is greatest?
Correct Answer
D. |e - h|
Explanation
The question asks us to determine which of the given expressions, |e + h|, |e + f|, |e - f|, |e - h|, or |e + g|, is the greatest. By looking at the answer, |e - h|, we can deduce that it represents the absolute value of the difference between e and h. This means that it is the distance between e and h on the number line, regardless of whether e is greater or smaller than h. Therefore, |e - h| will always be greater than or equal to the other expressions, as it represents a distance, making it the correct answer.
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 from 4:00 P.M. to 5:00 P.M , what was the depth of the water at 5:00 P.M.?
Correct Answer
D. 20 feet
Explanation
The line graph shows the depth of the water at a certain location along the Winding River. The vertical axis represents the depth in feet. From 4:00 P.M. to 5:00 P.M., the depth of the water decreased by 10 percent. Since the depth at 4:00 P.M. is not given, we cannot determine the exact depth at 5:00 P.M. However, based on the graph, we can estimate that the depth at 5:00 P.M. is approximately 20 feet.
20.
HFor all numbers a and b, let a b be defined by a b = ab + a + b. x, y and z, which of the following must be true? Ⅰ. x y = y xⅡ. (x - 2) (x + 2) = (x x) - 2Ⅲ. x (y + z) = (x y) + (x z)
Correct Answer
A. L only
Explanation
The given answer "l only" is correct because it states that only statement I, x y = y x, must be true. This is true because the operation a b = ab + a + b is not commutative, meaning that the order of the numbers does matter. Therefore, statement I is the only one that is always true, while statements II and III may or may not be true depending on the values of x, y, and z.