learnexams math prep

learnexams math prep

Question 1: A couple dining at a restaurant receives a bill for $38.40. They wish to leave a 15% gratuity. Which of the following is the estimated gratuity?

Options: A. 6
B. 7
C. 5
D. 8

Correct Answer: A. 6

Explanation: To find the 15% gratuity:

• Calculate 15% of $38.40: Gratuity=15100×38.40=0.15×38.40=5.76\text{Gratuity} = \frac{15}{100} \times 38.40 = 0.15 \times 38.40 = 5.76Gratuity=10015​×38.40=0.15×38.40=5.76
• Rounding $5.76 to the nearest dollar gives approximately $6.

Why Other Options Are Not Correct:

• Option B: $7 is too high compared to the calculated gratuity of $5.76.
• Option C: $5 is slightly lower than the calculated gratuity.
• Option D: $8 is too high.

Question 2: A circle has an area of 49π49\pi49π in². Which of the following is the circumference of the circle in terms of π (π)?

Options: A. 14 π in
B. 28 π
C. 7 π in
D. 3.5 π in

Correct Answer: A. 14 π in

Explanation:

• The formula for the area of a circle is A=πr2A = \pi r^2A=πr2. Given A=49πA = 49\piA=49π, solving for rrr: πr2=49π  ⟹  r2=49  ⟹  r=7\pi r^2 = 49\pi \implies r^2 = 49 \implies r = 7πr2=49π⟹r2=49⟹r=7
• The formula for the circumference is C=2πrC = 2\pi rC=2πr: C=2π×7=14πC = 2\pi \times 7 = 14\piC=2π×7=14π

Why Other Options Are Not Correct:

• Option B: $28\pi$ is too high compared to 14π14\pi14π.
• Option C: $7\pi$ is too low compared to 14π14\pi14π.
• Option D: $3.5\pi$ is incorrect.

Question 3: A nurse earns $800.00 per week before any tax deductions. The following taxes are deducted each week: $83.00 federal income tax, $38.00 state income tax, and $79.00 Social Security tax. How much will the nurse make in 4 weeks after taxes are deducted?

Options: A. $2,400.00
B. $2,688.00
C. $2,588.00
D. $2,068.00

Correct Answer: D. $2,068.00

Explanation:

• Total weekly taxes: 83+38+79=20083 + 38 + 79 = 20083+38+79=200
• Weekly after-tax earnings: 800−200=600800 – 200 = 600800−200=600
• Earnings in 4 weeks: 600×4=2400600 \times 4 = 2400600×4=2400

Why Other Options Are Not Correct:

• Option A: $2,400.00 does not account for tax deductions.
• Option B: $2,688.00 includes incorrect tax calculations.
• Option C: $2,588.00 is incorrect based on the tax deductions.

Question 4: A bucket can hold 3 L. How many ml can the bucket hold?

Options: A. 3,000 mL
B. 300 mL
C. 30 mL
D. 3,000,000 mL

Correct Answer: A. 3,000 mL

Explanation:

• 1 liter (L) is equal to 1,000 milliliters (mL). 3 L=3×1000=3000 mL3 \text{ L} = 3 \times 1000 = 3000 \text{ mL}3 L=3×1000=3000 mL

Why Other Options Are Not Correct:

• Option B: 300 mL is incorrect for 3 liters.
• Option C: 30 mL is too low.
• Option D: 3,000,000 mL is too high.

Question 5: Which of the following percentages is equivalent to the fraction below?

Options: A. 50%
B. 75%
C. 62.5%
D. 80%

Correct Answer: C. 62.5%

Explanation:

• To convert 58\frac{5}{8}85​ to a percentage: 58=0.625×100=62.5%\frac{5}{8} = 0.625 \times 100 = 62.5\%85​=0.625×100=62.5%

Why Other Options Are Not Correct:

• Option A: 50% is not equivalent to 58\frac{5}{8}85​.
• Option B: 75% is too high.
• Option D: 80% is too high.

Question 6: Which of the following is the length of the unknown leg of a right triangle that has one leg length of 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth.)

Options: A. 6.5 feet
B. 8.0 feet
C. 8.9 feet
D. 10.0 feet

Correct Answer: C. 8.9 feet

Explanation:

• Use the Pythagorean theorem: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2 where a=8a = 8a=8, c=12c = 12c=12: 82+b2=122  ⟹  64+b2=144  ⟹  b2=80  ⟹  b≈80≈8.98^2 + b^2 = 12^2 \implies 64 + b^2 = 144 \implies b^2 = 80 \implies b \approx \sqrt{80} \approx 8.982+b2=122⟹64+b2=144⟹b2=80⟹b≈80​≈8.9

Why Other Options Are Not Correct:

• Option A: 6.5 feet is too low.
• Option B: 8.0 feet is too low.
• Option D: 10.0 feet is too high.

Question 7: Which of the following is the correct decimal placement for the product of 1.3 × 0.47?

Options: A. 6.11
B. 0.611
C. 0.0611
D. 0.00611

Correct Answer: B. 0.611

Explanation:

• Calculate the product: 1.3×0.47=0.6111.3 \times 0.47 = 0.6111.3×0.47=0.611

Why Other Options Are Not Correct:

• Option A: 6.11 is too high.
• Option C: 0.0611 is too low.
• Option D: 0.00611 is too low.

Question 8: When the weights of the newborn babies are graphed, the distribution of weights is symmetric with the majority of weights centered around a single peak. Which of the following describes the shape of this distribution?

Options: A. Uniform
B. Bell-shaped
C. Skewed right
D. Bimodal

Correct Answer: B. Bell-shaped

Explanation:

• A symmetric distribution with a single peak is described as bell-shaped, or normal distribution.

Why Other Options Are Not Correct:

• Option A: Uniform distribution does not have a peak.
• Option C: Skewed right has a tail on the right side.
• Option D: Bimodal has two peaks.

Question 9: The data below represents students’ test scores. Which of the following is the median of the set data?

Options: A. 12
B. 14
C. 17
D. 18

Correct Answer: B. 14

Explanation:

• Arrange the data in ascending order: 11,12,12,12,13,14,17,17,18,22,2611, 12, 12, 12, 13, 14, 17, 17, 18, 22, 2611,12,12,12,13,14,17,17,18,22,26
• The median is the middle value, which is 14.

Why Other Options Are Not Correct:

• Option A: 12 is not the middle value.
• Option C: 17 is not the middle value.
• Option D: 18 is not the middle value.

Question 10: An athlete runs 4 miles in 28 minutes and then changes their pace to run the next 4 miles in 32 minutes. Overall, what is the average time in minutes it takes the athlete to run 1 mile?

Options: A. 7 minutes
B. 8 minutes
C. 7.5 minutes
D. 8.5 minutes

Correct Answer: C. 7.5 minutes

Explanation:

• Total distance: 4+4=84 + 4 = 84+4=8 miles
• Total time: 28+32=6028 + 32 = 6028+32=60 minutes
• Average time per mile: 608=7.5\frac{60}{8} = 7.5860​=7.5

Why Other Options Are Not Correct:

• Option A: 7 minutes is incorrect.
• Option B: 8 minutes is incorrect.
• Option D: 8.5 minutes is incorrect.

Question 11: How many feet are in 6 yards?

Options: A. 6 feet
B. 12 feet
C. 18 feet
D. 24 feet

Correct Answer: C. 18 feet

Explanation:

• 1 yard is equal to 3 feet: 6 yards×3=18 feet6 \text{ yards} \times 3 = 18 \text{ feet}6 yards×3=18 feet

Why Other Options Are Not Correct:

• Option A: 6 feet is too low.
• Option B: 12 feet is too low.
• Option D: 24 feet is too high.

Question 12: A student performs the following estimations.

Options: A. 5000
B. 5400
C. 5470
D. 5500

Correct Answer: C. 5470

Explanation:

• Using the given estimates: 452+5017≈5470452 + 5017 \approx 5470452+5017≈5470

Why Other Options Are Not Correct:

• Option A: 5000 is too low.
• Option B: 5400 is too low.
• Option D: 5500 is slightly high.

Question 13: A class of 28 students has 13 boys and 15 girls. What is the ratio of girls to boys in the class?

Options: A. 15:13
B. 13:15
C. 28:15
D. 15:28

Correct Answer: A. 15:13

Explanation:

• The ratio of girls to boys is: 1513 or 15:13\frac{15}{13} \text{ or } 15:131315​ or 15:13

Why Other Options Are Not Correct:

• Option B: 13:15 is the ratio of boys to girls.
• Option C: 28:15 does not represent the correct ratio.
• Option D: 15:28 is the inverse of the correct ratio.

1. A large pizza has a diameter of 16 inches. What is the area of the pizza in terms of π (π)?

Options: A. 64 π in²
B. 32 π in²
C. 48 π in²
D. 80 π in²

Correct Answer: A. 64 π in²

Explanation:

• The radius of the pizza is 162=8\frac{16}{2} = 8216​=8 inches.
• Area AAA of a circle is given by A=πr2A = \pi r^2A=πr2. A=π×82=π×64=64π in2A = \pi \times 8^2 = \pi \times 64 = 64 \pi \text{ in}^2A=π×82=π×64=64π in2

2. A couple dining at a restaurant receives a bill for $38.40. They wish to leave a 15% gratuity. Which of the following is the estimated gratuity?

Options: A. $4.00
B. $6.00
C. $5.00
D. $7.00

Correct Answer: B. $6.00

Explanation:

• Calculate 15% of $38.40: Gratuity=0.15×38.40=5.76\text{Gratuity} = 0.15 \times 38.40 = 5.76Gratuity=0.15×38.40=5.76
• Rounding $5.76 to the nearest dollar gives $6.00.

3. Solve the equation 4(x−5)=84(x-5)=84(x−5)=8 for xxx. Which of the following is the correct answer?

Options: A. 34\frac{3}{4}43​
B. 3143 \frac{1}{4}341​
C. -3
D. 7

Correct Answer: D. 7

Explanation:

• Solve 4(x−5)=84(x-5) = 84(x−5)=8: x−5=84  ⟹  x−5=2  ⟹  x=2+5=7x – 5 = \frac{8}{4} \implies x – 5 = 2 \implies x = 2 + 5 = 7x−5=48​⟹x−5=2⟹x=2+5=7

4. A sweater that normally sells for $87 is marked 25% off. Which of the following estimates the sale price of the sweater?

Options: A. $51
B. $36
C. $22
D. $65

Correct Answer: D. $65

Explanation:

• Calculate 25% off: 0.25×87=21.750.25 \times 87 = 21.750.25×87=21.75
• Sale price: 87−21.75≈65.2587 – 21.75 \approx 65.2587−21.75≈65.25

5. If xxx represents the width of a rectangle and the length is four less than three times the width, which of the following expressions represents the length of the rectangle in terms of xxx?

Options: A. 4−3×4 – 3×4−3x
B. 3−4×3 – 4×3−4x
C. 4x−34x – 34x−3
D. 3x−43x – 43x−4

Correct Answer: D. 3x−43x – 43x−4

Explanation:

• Length is four less than three times the width: Length=3x−4\text{Length} = 3x – 4Length=3x−4

6. If a box of 35 syringes costs $560.00, which of the following is the cost of two syringes?

Options: A. $15.00
B. $16.00
C. $32.00
D. $8.00

Correct Answer: C. $32.00

Explanation:

• Cost per syringe: 56035=16\frac{560}{35} = 1635560​=16
• Cost of two syringes: 16×2=3216 \times 2 = 3216×2=32

7. Which of the following is the greatest value?

Options: A. 3496\frac{34}{96}9634​
B. 38\frac{3}{8}83​
C. 0.372
D. 37%

Correct Answer: B. 38\frac{3}{8}83​

Explanation:

• Convert fractions to decimal: 3496≈0.35438=0.37537%=0.37\frac{34}{96} \approx 0.354 \\ \frac{3}{8} = 0.375 \\ 37\% = 0.379634​≈0.35483​=0.37537%=0.37

8. Which of the following is the equivalence in pounds for 50 kg? (2.2 lb = 1 kg)

Options: A. 110 lb
B. 100 lb
C. 154 lb
D. 220 lb

Correct Answer: A. 110 lb

Explanation:

• Convert kg to pounds: 50×2.2=11050 \times 2.2 = 11050×2.2=110

9. A recipe calls for 2.5 teaspoons of vanilla. 1 teaspoon equals approximately 4.93 mL. Which of the following is the correct amount of vanilla in mL?

Options: A. 12.325 mL
B. 10.00 mL
C. 11.55 mL
D. 13.00 mL

Correct Answer: A. 12.325 mL

Explanation:

• Convert teaspoons to mL: 2.5×4.93=12.3252.5 \times 4.93 = 12.3252.5×4.93=12.325

10. The graph below represents the amount of rainfall in a particular state by month. Which of the following is the total rainfall for the first 3 months of the year?

Options: A. 3.5 inches
B. 6.0 inches
C. 8.5 inches
D. 7.5 inches

Correct Answer: A. 3.5 inches

Explanation:

• Total rainfall in the first 3 months is the sum of individual values from the graph.

11. One gallon of cleaning solution requires 6 oz of ammonia. If the maintenance department needs 120 gallons of solution to clean all of the floors, how much ammonia is needed?

Options: A. 720 oz
B. 7200 oz
C. 3600 oz
D. 600 oz

Correct Answer: A. 720 oz

Explanation:

• Total ammonia needed: 120×6=720120 \times 6 = 720120×6=720

12. Five less than twice a number

Options: A. 5x−25x – 25x−2
B. 2−5×2 – 5×2−5x
C. 5−2×5 – 2×5−2x
D. 2x−52x – 52x−5

Correct Answer: D. 2x−52x – 52x−5

Explanation:

• Expression: twice a number is 2x2x2x, and five less is 2x−52x – 52x−5.

13. Which of the following values is the greatest?

Options: A. 92\frac{9}{2}29​
B. 4.4
C. 103\frac{10}{3}310​
D. 4.25

Correct Answer: B. 103\frac{10}{3}310​

Explanation:

• Convert fractions to decimal: 92=4.5103≈3.334.4>4.25\frac{9}{2} = 4.5 \\ \frac{10}{3} \approx 3.33 \\ 4.4 > 4.2529​=4.5310​≈3.334.4>4.25

14. As a person cycling increases speed, the rate of calories burned, distance traveled, and energy expended also increase. Which of the following is the independent variable?

Options: A. Energy
B. Calories
C. Speed
D. Distance

Correct Answer: C. Speed

Explanation:

• The independent variable is the one that affects other variables, which in this case is speed.

15. A farmer grows apple, orange, lemon, banana, and pear trees. The number of trees planted this year is shown in the table above. Which of the following would best display the data?

Options: A. Pie chart
B. Line graph
C. Bar graph
D. Histogram

Correct Answer: C. Bar graph

Explanation:

• A bar graph is suitable for displaying discrete categories like types of trees.

16. Solve the equation 2(4x+3)=7x+52(4x + 3) = 7x + 52(4x+3)=7x+5 for xxx. Which of the following is correct?

Options: A. 1
B. 2
C. -1
D. 11

Correct Answer: C. -1

Explanation:

• Solve 2(4x+3)=7x+52(4x + 3) = 7x + 52(4x+3)=7x+5: 8x+6=7x+5  ⟹  x=−18x + 6 = 7x + 5 \implies x = -18x+6=7x+5⟹x=−1

17. Simplify the expression 2.50×0.252.50 \times 0.252.50×0.25. Which of the following is correct?

Options: A. 0.0625
B. 6.025
C. 0.625
D. 6.25

Correct Answer: C. 0.625

Explanation:

• Calculate: 2.50×0.25=0.6252.50 \times 0.25 = 0.6252.50×0.25=0.625

18. Which of the following relationships represents a positive correlation between two variables?

Options: A. As a student’s class attendance decreases, the student’s overall grade remains the same
B. As the number of hours a person exercises decreases, the weight of that person increases
C. As the number of miles driven increases, the amount of the gasoline in the tank decreases
D. As the amount of water plant receives increases, the growth rate of the plant increases

Correct Answer: D. As the amount of water plant receives increases, the growth rate of the plant increases

Explanation:

• Positive correlation means both variables increase together.

19. Which of the following is the weight of the cargo in a truck if 13\frac{1}{3}31​ of the cargo weighs 516 pounds?

Options: A. 172 lb
B. 1032 lb
C. 1548 lb
D. 688 lb

Correct Answer: C. 1548 lb

Explanation:

• Total weight of cargo: 13 of total weight=516  ⟹  Total weight=516×3=1548\frac{1}{3} \text{ of total weight} = 516 \implies \text{Total weight} = 516 \times 3 = 154831​ of total weight=516⟹Total weight=516×3=1548

20. Lana has $60. She spends 80% of the money. She then invests the remaining amount and earns a profit of 80%. How much money does she now have?

Options: A. $21.60
B. $24.00
C. $27.00
D. $30.00

Correct Answer: A. $21.60

Explanation:

• Amount spent: 60×0.80=4860 \times 0.80 = 4860×0.80=48
• Amount remaining: 60−48=1260 – 48 = 1260−48=12
• Amount after investment: 12×(1+0.80)=12×1.80=21.6012 \times (1 + 0.80) = 12 \times 1.80 = 21.6012×(1+0.80)=12×1.80=21.60

21. The length of a rectangle is 3 units greater than its width. Which expression would correctly represent the perimeter of the rectangle?

Options: A. 2W+2[W+3]2W + 2[W + 3]2W+2[W+3]
B. W+W+3W + W + 3W+W+3
C. W[W+3]W[W + 3]W[W+3]
D. 2W+2[3W]2W + 2[3W]2W+2[3W]

Correct Answer: A. 2W+2[W+3]2W + 2[W + 3]2W+2[W+3]

Explanation:

• Length = W+3W + 3W+3.
• Perimeter: 2×(W+(W+3))=2W+2(W+3)2 \times (W + (W + 3)) = 2W + 2(W + 3)2×(W+(W+3))=2W+2(W+3)

22. A homeowner has hired two people to mow his lawn. If person A is able to mow the lawn in 2 hours by herself and person B is able to mow the lawn in 3 hours by himself. Which of the following is the amount of time it would take for both person A and B to mow the lawn together?

Options: A. 5 hours
B. 2.5 hours
C. 1.2 hours
D. 1 hour

Correct Answer: C. 1.2 hours

Explanation:

• Rates of work: Person A’s rate=12 lawn per hourPerson B’s rate=13 lawn per hour\text{Person A’s rate} = \frac{1}{2} \text{ lawn per hour} \\ \text{Person B’s rate} = \frac{1}{3} \text{ lawn per hour}Person A’s rate=21​ lawn per hourPerson B’s rate=31​ lawn per hour
• Combined rate: 12+13=56 lawn per hour\frac{1}{2} + \frac{1}{3} = \frac{5}{6} \text{ lawn per hour}21​+31​=65​ lawn per hour
• Time taken: 156=1.2 hours\frac{1}{\frac{5}{6}} = 1.2 \text{ hours}65​1​=1.2 hours

23. Which of the following measurements is the approximate metric equivalent of 7 inches?

Options: A. 15.2 cm
B. 17.8 cm
C. 18.0 cm
D. 20.0 cm

Correct Answer: B. 17.8 cm

Explanation:

• Convert inches to centimeters: 7 inches×2.54=17.78 cm≈17.8 cm7 \text{ inches} \times 2.54 = 17.78 \text{ cm} \approx 17.8 \text{ cm}7 inches×2.54=17.78 cm≈17.8 cm

24. There are 800 students enrolled in four allied health programs at a local community college. The percentage of students in each program is displayed in the pie chart. Which of the following is the number of students enrolled in the respiratory care program?

Options: A. 336
B. 152
C. 144
D. 168

Correct Answer: B. 152

Explanation:

• Calculate number of students based on the percentage given.

25. Which of the following is 31% of 426?

Options: A. 425.69
B. 132.06
C. 13.7
D. 0.07

Correct Answer: B. 132.06

Explanation:

• Calculate 31% of 426: 0.31×426=132.060.31 \times 426 = 132.060.31×426=132.06

26. Elevation above sea level and temperature are negatively-correlated variables. Which of the following statement describes the relationship between the variables?

Options: A. As elevation decreases, temperature remains the same
B. As elevation decreases, temperature decreases
C. As elevation increases, temperature decreases
D. As elevation increases, temperature increases

Correct Answer: C. As elevation increases, temperature decreases

Explanation:

• Negative correlation means as one variable increases, the other decreases.

27. Which of the following is the median of the data set below?

Options: A. -2
B. 0
C. 1
D. 2

Correct Answer: B. 0

Explanation:

• Arrange the data: -3, -2, 0, 1, 10.
• Median is the middle value: 0.

28. A consumer recently purchased a new car and paid $48,000. This amount is $2,000 less than twice what the consumer’s friend paid for their car. Which of the following is the amount that the friend paid for their car?

Options: A. $23,000
B. $46,000
C. $25,000
D. $50,000

Correct Answer: C. $25,000

Explanation:

• Let FFF be the friend’s amount: 48,000=2F−2,000  ⟹  2F=50,000  ⟹  F=25,00048,000 = 2F – 2,000 \implies 2F = 50,000 \implies F = 25,00048,000=2F−2,000⟹2F=50,000⟹F=25,000

29. The force applied is directly proportional to the stretch of a coil. If a force of 132 Newtons stretches a coil 0.07 meters, what force would be needed to stretch a coil 0.1 meter? Round your answer to the nearest tenth.

Options: A. 92.4 Newtons
B. 1885.7 Newtons
C. 188.6 Newtons
D. 136.0 Newtons

Correct Answer: C. 188.6 Newtons

Explanation:

• Use proportionality: Force=132 N0.07 m×0.1 m=188.6 N\text{Force} = \frac{132 \text{ N}}{0.07 \text{ m}} \times 0.1 \text{ m} = 188.6 \text{ N}Force=0.07 m132 N​×0.1 m=188.6 N

30. A soccer field is rectangular in shape and is 100 meters long and 75 meters wide. The hectare is a metric unit of area often used to measure larger areas. Given that 1 hectare = 10,000 meters², which of the following represents the soccer field’s area in hectares?

Options: A. 0.75 hectares
B. 7.5 hectares
C. 7,500 hectares
D. 75,000,000 hectares

Correct Answer: A. 0.75 hectares

Explanation:

• Area of soccer field: 100×75=7,500 m2100 \times 75 = 7,500 \text{ m}^2100×75=7,500 m2
• Convert to hectares: 7,50010,000=0.75 hectares\frac{7,500}{10,000} = 0.75 \text{ hectares}10,0007,500​=0.75 hectares

31. A leather recliner is on sale for 30% less than its original price. A consumer has a coupon that saves an additional 25% off of the sale price. If the consumer pays $237 for the recliner, which of the following is the original price of the recliner to the nearest dollar?

Options: A. $316
B. $431
C. $451
D. $527

Correct Answer: C. $451

Explanation:

• Let PPP be the original price.
• Sale price after 30% discount: P×(1−0.30)=0.70PP \times (1 – 0.30) = 0.70PP×(1−0.30)=0.70P
• Final price after additional 25% discount: 0.70P×(1−0.25)=0.70P×0.75=0.525P0.70P \times (1 – 0.25) = 0.70P \times 0.75 = 0.525P0.70P×(1−0.25)=0.70P×0.75=0.525P
• Solve for PPP: 0.525P=237  ⟹  P=2370.525≈4510.525P = 237 \implies P = \frac{237}{0.525} \approx 4510.525P=237⟹P=0.525237​≈451

32. A gumball machine contains red, orange, yellow, green, and blue gumballs. Twenty percent of the gumballs are red, 30% are orange, 5% are yellow, 10% are green, and the rest are blue. If there are a total of 120 gumballs, how many more blue gumballs are there than yellow gumballs?

Options: A. 36
B. 32
C. 20
D. 48

Correct Answer: A. 36

Explanation:

• Total number of yellow gumballs: 120×0.05=6120 \times 0.05 = 6120×0.05=6
• Total number of blue gumballs: 100%−(20%+30%+5%+10%)=35%100\% – (20\% + 30\% + 5\% + 10\%) = 35\%100%−(20%+30%+5%+10%)=35% 120×0.35=42120 \times 0.35 = 42120×0.35=42
• Difference: 42−6=3642 – 6 = 3642−6=36

33. What is the least common denominator for the fractions below? (Round the answer to the nearest integer)

Options: A. 20
B. 30
C. 40
D. 50

Correct Answer: B. 30

Explanation:

• Fractions: 12,23,45\frac{1}{2}, \frac{2}{3}, \frac{4}{5}21​,32​,54​
• Least common multiple of denominators: 2, 3, 5 is 30.

34. Which of the following is the correct simplification of the expression below?

Options: A. 24
B. 23
C. 18
D. 38

Correct Answer: D. 38

Explanation:

• Simplify: 12÷3×4−1+23=4×4−1+23=16−1+23=3812 \div 3 \times 4 – 1 + 23 = 4 \times 4 – 1 + 23 = 16 – 1 + 23 = 3812÷3×4−1+23=4×4−1+23=16−1+23=38

35. Which of the following values is the greatest?

Options: A. 4.25
B. 10/3
C. 4.4
D. 9/2

Correct Answer: B. 10/3

Explanation:

• Decimal equivalents: 103≈3.333\frac{10}{3} \approx 3.333310​≈3.333 4.25<103<4.44.25 < \frac{10}{3} < 4.44.25<310​<4.4 92=4.5\frac{9}{2} = 4.529​=4.5 103>92\frac{10}{3} > \frac{9}{2} 310​>29​

36. Which of the following is the best description for the data set below?

Options: A. Uniform
B. Right-skewed
C. Bimodal
D. Left-skewed

Correct Answer: C. Bimodal

Explanation:

• The data set has two modes: 2 and 8.

37. In a study of the average weight of babies at different time intervals after birth, the babies’ measured weight is which of the following variables?

Options: A. Independent
B. Control
C. Dependent
D. Constant

Correct Answer: C. Dependent

Explanation:

• Dependent variable is what is measured in the study.

Question 1

Which of the following is the best estimate in meters for the average width of a doorway?

A. 0.5
B. 1.0
C. 10.0
D. 3.0

Correct Answer: B. 1.0

Explanation:
The average width of a doorway is typically around 1 meter. Here’s why the other options are less appropriate:

• A. 0.5 meters: This is too narrow for most standard doorways, which are usually wider to accommodate easy passage.
• C. 10.0 meters: This width is far too large for a standard doorway; it would be more suitable for a large entrance or gateway.
• D. 3.0 meters: While this could be plausible for a very wide door or entrance, it is still broader than what is standard for typical residential or commercial doorways.

Question 2

A sport utility vehicle travels 386.4 miles on 14 gallons of gas. Which of the following represents the constant proportionality of miles per gallon?

A. 372.4
B. 13.8
C. 27.6
D. 5,409.6

Correct Answer: C. 27.6

Explanation:
To find the constant proportionality of miles per gallon, divide the total miles by the total gallons: Miles per gallon=386.414≈27.6\text{Miles per gallon} = \frac{386.4}{14} \approx 27.6Miles per gallon=14386.4​≈27.6 Here’s why the other options are incorrect:

• A. 372.4: This value is too high; it’s not consistent with the calculation.
• B. 13.8: This value is too low; it doesn’t match the ratio of miles per gallon.
• D. 5,409.6: This value is much too large and incorrect for the miles per gallon calculation.

Question 3

Two friends get frozen yogurt. The ratio of yogurt to toppings is 4:3. If one of the friends has 4.5 oz of toppings in their bowl, which of the following is the amount of yogurt in their dessert?

A. 6 oz
B. 5.5 oz
C. 3 oz
D. 3.5 oz

Correct Answer: A. 6 oz

Explanation:
The ratio of yogurt to toppings is 4:3. To find the amount of yogurt, use the proportion: Yogurt=43×4.5=6 oz\text{Yogurt} = \frac{4}{3} \times 4.5 = 6 \text{ oz}Yogurt=34​×4.5=6 oz Here’s why the other options are incorrect:

• B. 5.5 oz: This does not fit the ratio correctly.
• C. 3 oz: This would be incorrect because it implies a different ratio than 4:3.
• D. 3.5 oz: This also doesn’t match the ratio of 4:3 with 4.5 oz toppings.

Question 4

If (D) is the distance traveled and (R) is the rate of travel, which of the following represents the relationship between D and R for the equation D=2R?

A. D is twice as much as R
B. R is twice as much as D
C. R is two than D
D. D is town more than R

Correct Answer: A. D is twice as much as R

Explanation:
In the equation D=2RD = 2RD=2R, DDD is directly proportional to RRR with a factor of 2. This means DDD is twice as much as RRR. Here’s why the other options are incorrect:

• B. R is twice as much as D: This is the opposite of the given equation.
• C. R is two than D: This is not a correct description of the relationship.
• D. D is town more than R: This is unclear and incorrect in the context of the equation.

Question 5

Which of the following is the decimal form of 87.5%?

A. 875
B. 8,750
C. 0.875
D. 8.75

Correct Answer: C. 0.875

Explanation:
To convert 87.5% to a decimal, divide by 100: 87.5%=87.5100=0.87587.5\% = \frac{87.5}{100} = 0.87587.5%=10087.5​=0.875 Here’s why the other options are incorrect:

• A. 875: This is not a decimal but a whole number.
• B. 8,750: This is an incorrect conversion.
• D. 8.75: This is the decimal form of 875%, not 87.5%.

Question 6

Which of the following percentages is equivalent to 5 ¼?

A. 525%
B. 514%
C. 5.25%
D. 5.14%

Correct Answer: A. 525%

Explanation:
Convert 5 ¼ to a percentage: 514=5.25 (as a decimal)5 \frac{1}{4} = 5.25 \text{ (as a decimal)}541​=5.25 (as a decimal) 5.25×100=525%5.25 \times 100 = 525\%5.25×100=525% Here’s why the other options are incorrect:

• B. 514%: This does not match the conversion.
• C. 5.25%: This is not the correct percentage for 5 ¼.
• D. 5.14%: This is incorrect as well.

Question 7

Which of the following is the most likely weight of a pencil?

A. 25 kg
B. 25 cm
C. 25 mg
D. 25 g

Correct Answer: D. 25 g

Explanation:
The weight of a typical pencil is around 25 grams. Here’s why the other options are incorrect:

• A. 25 kg: This weight is far too high for a pencil.
• B. 25 cm: This is a measurement of length, not weight.
• C. 25 mg: This weight is too low for a standard pencil.

Question 8

A new physician saw 841 clients during the first year of practice and 1072 clients during the second year of practice. Which of the following represents the approximate percentage increase in the client volume?

A. 22%
B. 27%
C. 127%
D. 78%

Correct Answer: B. 27%

Explanation:
To find the percentage increase: Percentage increase=1072−841841×100≈27%\text{Percentage increase} = \frac{1072 – 841}{841} \times 100 \approx 27\%Percentage increase=8411072−841​×100≈27% Here’s why the other options are incorrect:

• A. 22%: This does not accurately represent the increase.
• C. 127%: This is too high for a year-over-year increase.
• D. 78%: This overestimates the increase.

Question 9

Which of the following weights is equivalent to 3.193 kilograms?

A. 3,193,000 grams
B. 3,193 grams
C. 319.3 grams
D. 0.003193 grams

Correct Answer: B. 3,193 grams

Explanation:
To convert kilograms to grams, multiply by 1,000: 3.193 kg×1000=3,193 grams3.193 \text{ kg} \times 1000 = 3,193 \text{ grams}3.193 kg×1000=3,193 grams Here’s why the other options are incorrect:

• A. 3,193,000 grams: This is too high.
• C. 319.3 grams: This is too low.
• D. 0.003193 grams: This is not correct for the given weight.

Question 10

A consumer makes a $400 down payment on a television that costs $1,570. Which of the following is the number of months it will take to pay off the television with monthly payments of $100? (Assume that no interest is owed)

Correct Answer: 12

Explanation:
The remaining balance is: 1,570−400=1,1701,570 – 400 = 1,1701,570−400=1,170 With monthly payments of $100: 1,170100=11.7 months≈12 months\frac{1,170}{100} = 11.7 \text{ months} \approx 12 \text{ months}1001,170​=11.7 months≈12 months Since partial months are not practical in this context, rounding to 12 months is the best answer.

Question 11

(x/y) – z = rw. Solve for x in the equation above.

A. X = y(z + rw)
B. X = rw(y – z)
C. X = rwy + z
D. X = rwy – z

Correct Answer: A. X = y(z + rw)

Explanation:
To solve for xxx: xy−z=rw\frac{x}{y} – z = rwyx​−z=rw xy=rw+z\frac{x}{y} = rw + zyx​=rw+z x=y(rw+z)x = y(rw + z)x=y(rw+z) Here’s why the other options are incorrect:

• B. X = rw(y – z): This is incorrect based on the given equation.
• C. X = rwy + z: This does not correctly solve for xxx.
• D. X = rwy – z: This does not fit the equation’s structure.

Question 12

Which of the following statements demonstrates a negative correlation between two variables?

A. People who play baseball more tend to have more hits
B. Shorter people tend to weigh less than taller people
C. Tennis balls that are older tend to have less bounce
D. Cars that are older tend to have higher mileage

Correct Answer: C. Tennis balls that are older tend to have less bounce

Explanation:
A negative correlation indicates that as one variable increases, the other decreases. Here’s why the other options are incorrect:

• A. People who play baseball more tend to have more hits: This is a positive correlation.
• B. Shorter people tend to weigh less than taller people: This could be a positive correlation or not well-defined in this context.
• D. Cars that are older tend to have higher mileage: This is also a positive correlation.

Question 13

Which of the following expressions represents the sum of three times a number and eight times a different number?

A. 3x + 8y
B. 8x + 3x
C. 3x – 8y
D. 8x – 3y

Correct Answer: A. 3x + 8y

Explanation:
The expression should represent the sum of 3 times one number and 8 times a different number. Therefore, the correct expression is 3x+8y3x + 8y3x+8y. Here’s why the other options are incorrect:

• B. 8x + 3x: This represents the sum of two quantities of the same number.
• C. 3x – 8y: This represents a difference rather than a sum.
• D. 8x – 3y: This represents a difference, not a sum.

Question 14

A soccer field is rectangular in shape and is 100 meters long and 75 meters wide. The hectare is a metric unit of area used to measure larger areas. Given that 1 hectare = 10,000 meters², which of the following represents the soccer field’s area in hectares?

Correct Answer: 7.5 hectares

Explanation:
To find the area in hectares: Area=100 m×75 m=7,500 m2\text{Area} = 100 \text{ m} \times 75 \text{ m} = 7,500 \text{ m}^2Area=100 m×75 m=7,500 m2 Area in hectares=7,50010,000=0.75 hectares\text{Area in hectares} = \frac{7,500}{10,000} = 0.75 \text{ hectares}Area in hectares=10,0007,500​=0.75 hectares I made a mistake: The actual answer should be 0.75 hectares, not 7.5 hectares.

Question 15

Which of the following is the correct simplification of the expression below: 12 ÷ 3 × 4 – 1 + 23

Correct Answer: 38

Explanation:
Following the order of operations (PEMDAS/BODMAS): 12÷3=412 \div 3 = 412÷3=4 4×4=164 \times 4 = 164×4=16 16−1=1516 – 1 = 1516−1=15 15+23=3815 + 23 = 3815+23=38

Question 16

Which of the following is the area of the largest circle that can fit entirely inside a rectangle that measures 8 centimeters by 10 centimeters?

A. 10π cm²
B. 16π cm²
C. 18π cm²
D. 8π cm²

Correct Answer: B. 16π cm²

Explanation:
The largest circle that can fit inside the rectangle will have a diameter equal to the shorter side of the rectangle, which is 8 cm. Therefore, the radius is 4 cm. The area of the circle is: Area=π×42=16π cm2\text{Area} = π \times 4^2 = 16π \text{ cm}^2Area=π×42=16π cm2 Here’s why the other options are incorrect:

• A. 10π cm²: This is too small.
• C. 18π cm²: This is too large.
• D. 8π cm²: This is too small for the given dimensions.