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Multiple Choice
Multiple Choice
Multiple Choice
Multiple Choice
Mr. Rosales Test
100
If and what is the value of m? (A) -7/2 (B) -3 (C) -5/2 (D) -2 (E) -3/2
Correct Answer: C Explanation: Since can be written as and can be written as the left side of the equation is Since the value of m is
100
Note: Figure not drawn to scale. If two sides of the triangle above have lengths 5 and 6, the perimeter of the triangle could be which of the following? I. 11 II. 15 III. 24 (A) I only (B) II only (C) III only (D) II and III only (E) I, II, and III
Correct Answer: B Explanation: In questions of this type, statements I, II, and III should each be considered independently of the others. You must determine which of those statements could be true.  Statement I cannot be true. The perimeter of the triangle cannot be 11, since the sum of the two given sides is 11 without even considering the third side of the triangle.  Continuing to work the problem, you see that in II, if the perimeter were 15, then the third side of the triangle would be 15 – (6 + 5), or 4. A triangle can have side lengths of 4, 5, and 6. So the perimeter of the triangle could be 15.  Finally, consider whether it is possible for the triangle to have a perimeter of 24. In this case, the third side of the triangle would be 24 – (6 + 5)= 13. The third side of this triangle cannot be 13, since the sum of the other two sides is not greater than 13. By the Triangle Inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the correct answer is II only.
100
The total weight of a tin and the cookies it contains is 2 pounds. After ¾ of the cookies are eaten, the tin and the remaining cookies weigh 0.8 pounds. What is the weight of the empty tin in pounds? A. 0.2 B. 0.3 C. 0.4 D. 0.5 E. 0.6
Correct Answer: C Explanation: Let the weight of the empty tin = w (2 - w) = weight of the cookies; and one quarter of the cookies weigh (2 - w)/4 One quarter of the cookies + tin = 0.8 = w + (2 - w)/4 Multiply through by 4; 3.2 = 4w + 2 - w 1.2 = 3w; w = 0.4
100
6. Which of the following pairs of angles must be equal? A. a and e only B. a and e, and c and d only C. c and d only D. d and e only E. c and d and d and e only
Correct Answer: B Explanation: This question is testing that you know that the angle between a tangent to a circle and a chord (angle c is such an angle) is equal to the angle in the opposite segment (angle d is in the segment opposite to c in this case). Similarly, angle a is equal to angle e for the same reason.
100
Simplify, change to a decimal and then change to a percentage 32/64
1/2,.5, 50%
200
The projected sales volume of a video game cartridge is given by the function where s is the number of cartridges sold, in thousands; p is the price per cartridge, in dollars; and a is a constant. If according to the projections, 100,000 cartridges are sold at $10 per cartridge, how many cartridges will be sold at $20 per cartridge? (A) 20,000 (B) 50,000 (C) 60,000 (D) 150,000 (E) 200,000
Correct Answer: C Explanation: For 100,000 cartridges sold at $10 per cartridge, s = 100 (since s is the number of cartridges sold, in thousands) and p = 10. Substituting into the equation yieldsSolving this equation for a yields Since a is a constant, the function can be written as To determine how many cartridges will be sold at $20 per cartridge, you need to evaluate Since s is given in thousands, there will be 60,000 cartridges sold at $20 per cartridge.
200
6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The percentage alcohol in the new solution is A. 16 B. 15 C. 14 D. 13 E. 12
Correct Answer: A Explanation: Total new volume is 10 pints. The first solution contributes 0.2 x 6 pints alcohol, and the second contributes 0.1 x 4. Total alcohol = 1.6. Percentage alcohol = (1.6 / 10) x 100 = 16
200
10. The graph shows a quadratic function with a minimum at (-1,1) If f(a) = f(1), which if the following could be the value of a? A. 2 B. 0 C. -1 D. -2 E. -3
Correct Answer: E Explanation: We can see that f(1) will be the y-coordinate of the point on the graph where the x coordinate is 1. Reading from the graph this is 3 If f(a) is also 3, the value of a will be the x-coordinate of the other point on the graph where y = 3. Reading from the graph we get -3
200
7. The average bonus per employee was A. 81 B. 91 C. 100 D. 101 E. 105
Correct Answer: D Explanation: To calculate the total spent in bonuses we have to multiply the bonus by the number of employees for each bonus amount: (50 x 7)+ (100 x 37)+ (150 x 4)+ (200 x 2) = 5050. Now divide by the total number of employees to find the average = 5050/50 = 101
200
Translate the numbers from roman numerals MMDCXLVII
2647
300
If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers? (A) k + 5 (B) k + 15 (C) k + 20 (D) k + 30 (E) k + 45
Correct Answer: D Explanation: Since k is divisible by 2, 3, and 15, k must be a multiple of 30, as 30 is the least common multiple of 2, 3, and 15. Some multiples of 30 are 0, 30, 60, 90, and 120.  If you add two multiples of 30, the sum will also be a multiple of 30. For example, 60 and 90 are multiples of 30 and their sum, 150, is also a multiple of 30.  If you add a multiple of 30 to a number that is not a multiple of 30, the sum will not be a multiple of 30. For example, 60 is a multiple of 30 and 45 is not. Their sum, 105, is not a multiple of 30.  The question asks which answer choice is divisible by 2, 3, and 15; that is, which answer choice is a multiple of 30. All the answer choices are in the form of "k plus a number." Only choice (D), k + 30, has k added to a multiple of 30. The sum of k and 30 is also a multiple of 30, so the correct answer is choice (D).
300
If x ¤ y = (x + y)² - (x - y)² Then √5 ¤ √5 = A. 0 B. 5 C. 10 D. 15 E. 20
Correct Answer: E Explanation: The strange symbol tells us what to do to x and y. We then follow these directions for the actual values for x and y given in the problem. Hence, (2 √5)2 - (0)2 = 4.5 =20
300
3x + y = 19 , and x + 3y = 1. Find the value of 2x + 2y A. 20 B. 18 C. 11 D. 10 E. 5
What is Correct Answer: D Explanation: To solve a pair of simultaneous equations such as those given we can add or subtract them. Adding we get 4x + 4y = 20 Therefore 2x + 2y = 10
300
NOONTIME TEMPERATURES IN HILO, HAWAII Mon Tue Wed Thu Fri Sat Sun 66 78 75 69 78 77 70 The table above shows the temperatures, in degrees Fahrenheit, in a city in Hawaii over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a? (A) a < m < f (B) a < f < m (C) m < a < f (D) m < f < a (E) a = m < f
Correct Answer: A Explanation: To determine the correct order of m, ƒ, and a, it is helpful to first place the seven temperatures in ascending order as shown below. 66 69 70 75 77 78 78 The median temperature is the middle temperature in the ordered list, which is 75, so m = 75. The temperature that occurs most often, or the mode, is 78, so f = 78. To determine the average, you can add the seven numbers together and divide by 7. However, you can determine the relationship between the average and the median by inspection. The three numbers greater than 75 are closer to 75 than are the three numbers smaller than 75. Therefore, the average of the seven numbers will be less than 75. The correct order of m, ƒ, and a is a < m < f.
300
Courtney set up an ice bath in the lab to cool a solution in a beaker. The solution began at room temperature (18 degrees C) and cooled to 5 degrees C every 6 minutes. What was the temperature change in the beaker after an hour?
-32 degrees C
400
If m = n and p < q , then: A. m - p < n - q B. p - m > q - n C. m - p > n - q D. mp > nq E. m + q < n + p
The correct answer is C. We know that m and n are equal and that p is less than q. Therefore, it must be the case that subtracting p from m yields a larger number than subtracting q from n. Therefore, C is correct: m - p > n - q. If you have trouble doing this reasoning on your own, try plugging in numbers. For example, let m and n equal 10, let p equal 2, and let q equal 3. Now plug those numbers into all of the answer choices to see that only choice (C) is true.
400
DOUBLE JEOPARDY!!!!!!!!!!! A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen? (A) 1/8 (B) 2/9 (C) 2/7 (D) 3/8 (E) 1/2
Correct Answer: D Explanation: To determine the probability that a senior's name will be chosen, you must determine the total number of seniors' names that are in the lottery and divide this number by the total number of names in the lottery. Since each senior's name is placed in the lottery 3 times, there are 3 × 100 = 300 seniors' names. Likewise, there are 2 × 150 = 300 juniors' names and 1 × 200 = 200 sophomores' names in the lottery. The probability that a senior's name will be chosen is .
400
The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of A. 45% B. 40% C. 35% D. 32.5% E. 30%
Correct Answer: B Explanation: Let the original price of the cycle be 100. After the first reduction the price will be 75. This new price is then reduced by 20% = 0.8 x 75 = 60 60 represents a reduction of 40 percent on the original.
400
In the xy-coordinate plane above, line contains the points (0,0) and (1,2). If line m (not shown) contains the point (0,0) and is perpendicular to , what is an equation of m? (A) (B) (C) (D) (E)
Correct Answer: A Explanation: Since the coordinates of two points on line are given, the slope of is Line m, which is perpendicular to will have a slope of since slopes of perpendicular lines are negative reciprocals of each other. The equation of m can be written as Since line m also contains point (0,0), it follows that Therefore, an equation of line m is
400
Find 15% of 80
12
500
2. ASB is a quarter circle. PQRS is a rectangle with sides PQ = 8 and PS = 6. What is the length of the arc AQB ? A. 5π B. 10π C. 25 D. 14 E. 28
Correct Answer: A Explanation: Arc AQB is one quarter the perimeter of the circle (because angle S is a right angle). To find the radius we need to see that the diagonal SQ of the rectangle= radius. Now use Pythagoras to find the diagonal; 82 + 62 = r2 So r = 10 (You could have spotted that this is a 3-4-5 triangle and so saved this part of the calculation) The length of the arc = ¼ 20 π = 5π
500
4. Which of the following describes the relationship between A and B as shown in the pairs of numbers in the table above? A. B = A + 4 B. B = 2A + 1 C. B = 3A - 1 D. B = A² + 1 E. B = A² - 1
Correct Answer: D Explanation: You can try out the relationships using at least two pairs from the table to see whether the relationship holds. But it is relatively easy to spot that the first number squared + 1 gives the second number in each case.
500
5. BCD is a line segment and Angle BAC = ¼ Angle ACB ; Angle ACD = ? A. 140 B. 100 C. 120 D. 60 E. it cannot be determined from the information given
Correct Answer: E Explanation: If a value x is selected for angle ACB and one quarter of the value is taken for angle BAC, we could work out the value for the other angle of the triangle. Also angle ACD would be 180 - x. The problem is that we could choose a range of different values for x and still make them fit the given information. Therefore we cannot work out any one value for angle ACD.
500
9. Which of the following is the equation of a line passing through the origin and parallel to the line 2x – y = 5? A. 5x – y = 0 B. 2x – y = 0 C. 2x + y = 5 D. 2x + y = 0 E. x + 2y = 0
Correct Answer: B Explanation: First rearrange the equation into the form y = mx + c; y = 2x – 5 From this we know the slope is 2 and so the equation we are looking for must have the ‘m’ value = 2. We are also told that the equation must pass through the origin; this means that the ‘c’ value must be 0. In B we can rearrange to get y = 2x which fulfills both requirements.
500
The initial population of protists in a culture is 4,781. The final population after one week was 8,204.the population increased by what percent over the week? Round your answer to the nearest hundreth of a percent.
What is 171.6%