1. A recipe calls for 2 1/2 cups of flour for every 1 1/4 cups of sugar. If you want to make a larger batch using 5 cups of flour, how many cups of sugar will you need?
Solution
Correct: A
Let f be the amount of flour and s be the amount of sugar. We have the proportion f/s = 2.5/1.25. We are given f = 5. Thus, 5/s = 2.5/1.25. Cross-multiplying, we get 2.5s = 5 * 1.25 = 6.25. Dividing by 2.5 gives s = 6.25 / 2.5 = 2.5. So the answer is 2 1/2.
2. A store marks up a shirt by 40% and then puts it on sale for 20% off. If the shirt originally cost the store 15, what is the final sale price?
Solution
Correct: A
The shirt is marked up by 40%, so the new price is 15 + 0.40 * 15 = 15 + 6 = 21. Then it's discounted by 20%, so the final price is 21 - 0.20 * 21 = 21 - 4.20 = 16.80.
3. Solve for x: 3(x + 2) - 5 = 2(x - 1) + 4
Solution
Correct: B
Expanding, we get 3x + 6 - 5 = 2x - 2 + 4. This simplifies to 3x + 1 = 2x + 2. Subtracting 2x from both sides gives x + 1 = 2. Subtracting 1 from both sides gives x = 1.
4. What is the area of a circle with a circumference of 10π?
Solution
Correct: C
Circumference C = 2πr. We are given that 10π = 2πr, so r = 5. Area A = πr^2 = π(5^2) = 25π.
5. A train travels 120 miles in 2 hours. At the same rate, how long will it take to travel 300 miles?
Solution
Correct: B
The train's rate is 120 miles / 2 hours = 60 miles per hour. To travel 300 miles at 60 mph will take 300 / 60 = 5 hours.
7. A triangle has angles measuring x, 2x, and 3x degrees. What is the measure of the largest angle?
Solution
Correct: C
The angles of a triangle sum to 180 degrees. So x + 2x + 3x = 180, which means 6x = 180. Therefore, x = 30. The largest angle is 3x = 3(30) = 90 degrees.
8. If a = -2 and b = 3, what is the value of a^2 - 2ab + b^2?
Solution
Correct: C
Substituting, we get (-2)^2 - 2(-2)(3) + (3)^2 = 4 + 12 + 9 = 25.
9. A square has a perimeter of 36. What is the area of the square?
Solution
Correct: C
If the perimeter of a square is 36, then each side has length 36/4 = 9. The area of the square is 9*9 = 81.
10. What is 20% of 80% of 150?
Solution
Correct: B
80% of 150 is 0.80 * 150 = 120. 20% of 120 is 0.20 * 120 = 24.
11. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of selecting a blue marble at random?
Solution
Correct: B
The total number of marbles is 5 + 3 + 2 = 10. The probability of selecting a blue marble is the number of blue marbles divided by the total number of marbles, which is 3/10.
12. If x/3 + 2 = 7, what is the value of x?
Solution
Correct: C
Subtracting 2 from both sides gives x/3 = 5. Multiplying both sides by 3 gives x = 15.
13. Which of the following is equivalent to 3/8?
Solution
Correct: C
3/8 = 0.375.
14. Two complementary angles are in the ratio 2:3. What is the measure of the smaller angle?
Solution
Correct: B
Complementary angles add up to 90 degrees. Let the angles be 2x and 3x. So, 2x + 3x = 90, which means 5x = 90. Therefore, x = 18. The smaller angle is 2x = 2(18) = 36 degrees.
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