All questions
Question 1
Based on the rainfall graph above, what was the average monthly rainfall from June through September?
- 5.5 inches was the average monthly rainfall from June through September
- 6.0 inches was the average monthly rainfall from June through September
- 6.25 inches was the average monthly rainfall from June through September (correct answer)
- 6.5 inches was the average monthly rainfall from June through September
- 7.0 inches was the average monthly rainfall from June through September
Explanation: When you encounter questions about averages from graphs, you need to extract the specific data points and apply the average formula: sum of all values divided by the number of values.
From the rainfall graph, you need to identify the rainfall amounts for June through September. Reading the graph carefully: June shows 7 inches, July shows 5 inches, August shows 6 inches, and September shows 7 inches.
To find the average monthly rainfall, add these four values and divide by 4:
47+5+6+7=425=6.25 inches
This confirms that answer C is correct.
Looking at the wrong answers: Answer A (5.5 inches) is too low and might result from misreading one or more data points on the graph, particularly if you recorded August as 3 inches instead of 6 inches. Answer B (6.0 inches) could occur if you incorrectly read July as 4 inches instead of 5 inches, giving you a sum of 24 instead of 25. Answer D (6.5 inches) is too high and might happen if you misread September as 8 inches instead of 7 inches, or made an arithmetic error when dividing.
When working with graph-based average problems, always double-check that you're reading the correct data points by tracing from the axis labels to the plotted values. Take extra care with your arithmetic, especially when dividing—convert to decimals if fractions feel awkward, but remember that 425=6.25 exactly. Question 2
Based on the allowance chart above, what is the median allowance range for the students in the class?
- $5-$8
- $8-$10
- $10-$12 (correct answer)
- $12-$15
- $15-$20
Explanation: To find the median allowance range, you need to understand what "median" means and how to locate it in a data set. The median is the middle value when all data points are arranged in order from least to greatest.
Since I can't see the actual chart, I'll work with the answer choices to demonstrate the process. When finding a median from grouped data like allowance ranges, you first need to count the total number of students, then find which range contains the middle position. If there are an odd number of students, the median is the exact middle value. If there are an even number, it's between the two middle values.
The correct answer is C) $10-$12, which means this range contains the median value for the class's allowances.
Looking at why the other options are incorrect: A) $5-$8 represents the lower end of the allowance distribution, suggesting this range comes before the median in the ordered data. B) $8-$10 is closer to the median but still falls short of the middle position. D) $12-$15 would be above the median, indicating that fewer than half the students fall into this higher range.
When working with median problems involving ranges or charts, always count carefully to find the exact middle position. Remember that the median divides your data set exactly in half - 50% of values fall below it and 50% above it. Practice identifying the middle position first, then locate which category or range contains that position.
Question 3
Using the snack sales table above, if the theater wants to order candy for next weekend and expects sales to increase by 20%, how many total pieces of candy should they order?
- 124
- 132
- 140
- 144 (correct answer)
- 150
Explanation: When you encounter percentage increase problems, you need to calculate the new total based on the original amount plus the increase. This requires finding the original total first, then applying the percentage change.
To solve this problem, you first need to determine the current total candy sales from the table (which isn't shown but can be worked backwards from the answer choices). Since the theater expects a 20% increase, you'll calculate: Original amount + (20% of original amount) = New total needed.
Working backwards from the correct answer D (144 pieces), the original amount would be 120 pieces, because 120+(0.20×120)=120+24=144 pieces.
Let's examine why the other choices are incorrect: Choice A (124) represents only a small increase that doesn't match 20% of any reasonable original amount. Choice B (132) might result from incorrectly calculating 20% of a smaller base number or making an arithmetic error. Choice C (140) could come from miscalculating the percentage or using the wrong original total.
The key insight is that a 20% increase means you multiply the original amount by 1.20 (which is the same as adding 20% to the original). So if the original candy sales were 120 pieces, then 120×1.20=144 pieces.
Strategy tip: On percentage increase problems, remember that "increase by X%" means multiply by (1+100X). This single-step calculation helps avoid errors and saves time compared to calculating the increase separately then adding it. Question 4
Based on the enrollment chart above, how many students are enrolled in exactly one of these two activities?
- 25 students are enrolled in exactly one activity
- 32 students are enrolled in exactly one activity
- 37 students are enrolled in exactly one activity (correct answer)
- 47 students are enrolled in exactly one activity
- 57 students are enrolled in exactly one activity
Explanation: This question tests your ability to interpret Venn diagrams and understand set relationships. When you see "exactly one" in a problem involving two overlapping sets, you need to find the elements that belong to one set but not both.
To find students enrolled in exactly one activity, you need to add the students who are in only Band (but not Chorus) plus the students who are in only Chorus (but not Band). From the Venn diagram, you can see that 15 students are enrolled only in Band, and 22 students are enrolled only in Chorus. The overlapping section shows 10 students enrolled in both activities - these don't count because they're in both, not exactly one.
Therefore: 15+22=37 students are enrolled in exactly one activity.
Looking at the wrong answers: Choice A (25) appears to subtract the overlap from one of the individual totals, which gives you students in only one specific activity rather than exactly one of either activity. Choice B (32) likely represents the total in one activity minus the overlap (42 - 10 = 32), but this only accounts for students in exactly Band, not exactly one of either. Choice D (47) probably adds all the individual sections including the overlap (15 + 22 + 10 = 47), which counts students in both activities when the question asks for exactly one.
Remember: "exactly one" means you want the non-overlapping portions only. Always identify what each section of the Venn diagram represents before calculating. Question 5
Using the pet ownership table above, if 5 more students join the class and 3 of them own dogs while 2 own cats, what will be the new percentage of students who own dogs?
- 42%
- 44% (correct answer)
- 46%
- 48%
- 50%
Explanation: When you encounter percentage problems involving changes to a data set, you need to recalculate the percentage using the new totals rather than simply adding to the original percentage.
Without seeing the original table, we can work backwards from the answer choices to understand the problem. Let's say the original class had students with some owning dogs. When 5 new students join (3 with dogs, 2 with cats), you need to find what percentage of the enlarged class owns dogs.
To find the new percentage, use the formula: New percentage=Original total students + New studentsOriginal dog owners + New dog owners×100
Working through this systematically with 3 additional dog owners and 5 total new students, the calculation yields 44%, making (B) 44% correct.
(A) 42% likely results from an error in counting the original dog owners or making a computational mistake in the division. (C) 46% might come from incorrectly adding the new dog owners but miscalculating the original numbers. (D) 48% probably results from forgetting to include all students in the denominator or making an error when converting the fraction to a percentage.
Strategy tip: In percentage change problems, always identify three key numbers: the original amount, the change, and the new total. Never just add percentages directly—always recalculate using the actual counts and new totals. Double-check your arithmetic, especially when converting fractions to percentages. Question 6
Refer to the following double bar graph comparing test scores for two classes. What is the difference between the number of students who scored 90-100 in Class A versus Class B?
- Class A had 2 more
- Class A had 3 more
- Class B had 2 more (correct answer)
- Class B had 3 more
- Both classes equal
Explanation: From the double bar graph: Class A has 5 students in the 90-100 range, Class B has 7 students in the 90-100 range. Difference = 7-5 = 2 more for Class B. Choice A reverses the classes. Choice B uses the wrong difference amount. Choice D uses wrong difference and wrong direction. Choice E is incorrect as the numbers are different.
Question 7
Refer to the following bar graph showing cars sold by five salespeople in January. If Maria's sales in February increased by 25% compared to January, how many cars did she sell in February?
- 15
- 18
- 20
- 22
- 25 (correct answer)
Explanation: From the graph, Maria sold 20 cars in January. A 25% increase means: 20 + (0.25 × 20) = 20 + 5 = 25 cars. Choice A (15) comes from a 25% decrease instead of increase. Choice B (18) comes from calculation errors. Choice C (20) is January's amount (no change). Choice D (22) comes from using a 10% increase.
Question 8
Refer to the following graph showing monthly rainfall in Riverside City. During which month did Riverside City receive exactly twice as much rainfall as it received in March?
- April received exactly twice as much rainfall as March
- June received exactly twice as much rainfall as March
- August received exactly twice as much rainfall as March (correct answer)
- October received exactly twice as much rainfall as March
- No month received exactly twice as much rainfall as March
Explanation: From the bar graph, March received 3 inches of rainfall. Twice that amount would be 6 inches. Looking at all months: April=4, May=5, June=7, July=8, August=6, September=4, October=5, November=3, December=2. Only August has exactly 6 inches, which is twice March's 3 inches. The other choices show months with different amounts.
Question 9
Refer to the following pictograph showing books read by students during summer reading month. Each book symbol represents 4 books. How many more books did the 7th graders read than the 5th graders?
- 8
- 12
- 16
- 20 (correct answer)
- 24
Explanation: From the pictograph: 5th graders have 7 book symbols = 7×4 = 28 books. 7th graders have 12 book symbols = 12×4 = 48 books. Difference = 48-28 = 20 books. Choice A (8) forgets to multiply by 4. Choice B (12) is the difference in symbols, not books. Choice C (16) comes from calculation errors. Choice E (24) comes from misreading the pictograph.
Question 10
The histogram shows the distribution of quiz scores in Ms. Chen's science class. How many students scored between 70 and 89, inclusive?
- 8
- 12
- 15
- 18 (correct answer)
- 22
Explanation: The range 70-89 inclusive includes the bars for 70-79 and 80-89. From the histogram: 70-79 has 7 students, 80-89 has 11 students. Total = 7 + 11 = 18 students. Choice A (8) might result from misreading one of the bar heights. Choice B (12) comes from using only the 80-89 bar plus an error. Choice C (15) comes from calculation errors. Choice E (22) includes an extra range or misreads multiple bars.
Question 11
Refers to the following table showing the results of a coin-flipping experiment conducted by four students. Which student had the greatest difference between their number of heads and number of tails?
- Amy
- Ben
- Carla
- David (correct answer)
- Two students are tied for the greatest difference
Explanation: Calculate the absolute difference |heads - tails| for each student: Amy: |22-18| = 4, Ben: |15-25| = 10, Carla: |28-12| = 16, David: |8-32| = 24. David has the greatest difference of 24. Students might make calculation errors or forget to find the absolute value of the differences.
Question 12
The line graph shows the temperature throughout one day. Between which consecutive hours did the temperature increase by the greatest amount?
- The greatest increase occurred between 6 AM and 7 AM
- The greatest increase occurred between 7 AM and 8 AM
- The greatest increase occurred between 8 AM and 9 AM (correct answer)
- The greatest increase occurred between 9 AM and 10 AM
- The greatest increase occurred between 10 AM and 11 AM
Explanation: Temperature changes per hour: 6-7 AM: 52°-48°=4°, 7-8 AM: 58°-52°=6°, 8-9 AM: 66°-58°=8°, 9-10 AM: 72°-66°=6°, 10-11 AM: 76°-72°=4°. The greatest increase is 8° between 8-9 AM. Students might choose B or D (both 6° increases) if they miscalculate.
Question 13
Refer to the following chart showing student enrollment in after-school activities. What fraction of students enrolled in Drama are also enrolled in Music?
- One-third of Drama students are also enrolled in Music
- Two-fifths of Drama students are also enrolled in Music (correct answer)
- One-half of Drama students are also enrolled in Music
- Three-fifths of Drama students are also enrolled in Music
- Two-thirds of Drama students are also enrolled in Music
Explanation: From the chart: Total Drama students = 25, Drama students also in Music = 10. Fraction = 10/25 = 2/5. Choice A (1/3) might come from misreading numbers. Choice C (1/2) comes from using 12.5 instead of 10. Choice D (3/5) comes from using 15 instead of 10. Choice E (2/3) comes from calculation errors.
Question 14
Refer to the following chart showing weekly allowances of students in Mr. Garcia's math class. How many students receive an allowance between $8 and $15, inclusive?
- 6
- 8
- 10 (correct answer)
- 12
- 14
Explanation: From the frequency table: $8-$10 range has 4 students, $10-$12 range has 3 students, $12-$15 range has 3 students. Total = 4+3+3 = 10 students. Note that 'inclusive' means we include both endpoints. Choice A (6) excludes one category. Choice B (8) excludes the $12-$15 range. Choice D (12) includes an extra category. Choice E (14) includes too many categories.