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GMAT Data Insights Practice Questions with Answers & Detailed Explanations

This practice set has been created specifically to help you prepare for the GMAT Data Insights section. The questions are original and designed to reflect the style, reasoning, and problem-solving skills tested on the current GMAT. These questions are made for practice and learning purposes only and are not taken from, adapted from any official GMAT source.

You'll find balanced practice across all five Data Insights question types: Data Sufficiency, Multi-Source Reasoning, Table Analysis, Graphics Interpretation, and Two-Part Analysis. The questions draw on a wide range of quantitative concepts, including arithmetic, algebra, ratios, percentages, rates, statistics, probability, inequalities, weighted averages, and business data interpretation.

Coverage Map

Question Type Questions in this set Main skills practiced
Data Sufficiency 1-8 Data adequacy, algebra, number properties, inequalities, probability
Table Analysis 9-16 Sorting, ratios, percentages, rates, totals, business metrics
Graphics Interpretation 17-24 Charts, trends, percent change, indexed data, break-even analysis
Two-Part Analysis 25-32 Linked decisions, equations, mixtures, rates, probability, inequalities
Multi-Source Reasoning 33-40 Using multiple sources, criteria testing, consistency, business calculations

Practice Questions with Detailed Solutions

Data Sufficiency

Question 1 - Percent change and reverse calculation

A product was sold at a discount. What was the original list price of the product?

(1) The selling price after a 20% discount was $96.

(2) The discount was $24.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: D

Explanation:

Statement (1): If the item sold for 80% of the original price, then 0.80 × original = 96, so the original price is uniquely determined as 120. Sufficient. Statement (2): If the discount was 20% of the original price and that discount was $24, then 0.20 × original = 24, so the original price is uniquely determined as 120. Sufficient. Each statement alone gives one exact original price.

Tip: For percent questions, translate the sentence into an equation with the original amount as x. A statement is sufficient if it leads to one value, not merely an estimate.

Question 2 - Weighted average

A class has boys and girls. What is the average score of the entire class?

(1) The boys averaged 78 and the girls averaged 84.

(2) There are 12 boys and 18 girls in the class.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: C

Explanation:

Statement (1) gives the two group averages but not the group sizes, so the overall weighted average cannot be found. Statement (2) gives the group sizes but not the scores. Together, use weighted average: (12×78 + 18×84)⁄(12+18), which gives one value. Thus together sufficient, neither alone sufficient.

Tip: Weighted averages require both group values and weights. If either the numbers or the averages are missing, the whole average usually cannot be fixed.

Question 3 - Number properties

Is integer n divisible by 6?

(1) n is divisible by 3.

(2) n is even.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: C

Explanation:

To be divisible by 6, an integer must be divisible by both 2 and 3. Statement (1) gives divisibility by 3 but not by 2, so n could be 9 or 12. Not sufficient. Statement (2) gives evenness but not divisibility by 3, so n could be 8 or 12. Not sufficient. Together, n is even and divisible by 3, so n is divisible by 6.

Tip: Break composite divisibility into prime factors. For 6, check 2 and 3; for 12, check 3 and 4; for 15, check 3 and 5.

Question 4 - Linear equation

What is the value of x + y?

(1) 2x + 2y = 18.

(2) x - y = 5.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: A

Explanation:

Statement (1) simplifies to x + y = 9, exactly what is asked. Sufficient. Statement (2) gives only the difference, not the sum. For example, x=5,y=0 gives sum 5, while x=6,y=1 gives sum 7. Not sufficient.

Tip: Do not solve for variables unless necessary. If the question asks for x+y, any equation that directly gives x+y may be enough.

Question 5 - Rates and work

Machine A and Machine B together produce 600 parts. How many parts did Machine A produce?

(1) Machine A produced 40% more parts than Machine B.

(2) Machine B produced 250 parts.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: D

Explanation:

Statement (1): Let B=b, then A=1.4b and A+B=600. This gives one value for A. Sufficient. Statement (2): Since total production is 600 and B=250, A=350. Sufficient. Each statement alone gives a unique answer.

Tip: When a total is in the stem, a ratio or one part often fixes the other part. Always use information from the question stem.

Question 6 - Median with a small set

The five numbers a, 7, 9, 12, and 15 are arranged in increasing order. What is the median?

(1) a < 7.

(2) a = 10.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: A

Explanation:

The stem says the numbers are arranged in increasing order as written, so a is first and the middle number is 9. Statement (1) is consistent with that and confirms a is before 7, so the median is 9. Sufficient. Statement (2) conflicts with the order in the stem because if a=10, the list as written would not be increasing. On GMAT-style problems, statements should be considered with the stem; this inconsistency means the statement cannot produce a valid unique median under the given condition. Not sufficient.

Tip: Read ordering language carefully. In DS, the stem conditions are always active; do not ignore them when testing a statement.

Question 7 - Inequalities

Is x greater than 10?

(1) x > 8.

(2) x < 12.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: E

Explanation:

Statement (1) allows x=9 and x=11, so the answer could be no or yes. Statement (2) allows x=9 and x=11, so the answer could be no or yes. Together, 8 < x < 12, and x could still be 9 or 11. The answer is not fixed.

Tip: For yes/no DS questions, sufficient means the answer is always yes or always no. Mixed yes/no cases are insufficient.

Question 8 - Probability basics

A box contains only red and blue markers. If one marker is selected at random, what is the probability it is red?

(1) There are 18 markers in the box.

(2) The ratio of red markers to blue markers is 2 to 7.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C. Both statements together are sufficient, but neither statement alone is sufficient.
D. Each statement alone is sufficient.
E. Statements (1) and (2) together are not sufficient.

Answer: B

Explanation:

Statement (1) gives the total but not how many are red. Not sufficient. Statement (2) gives the fraction red as 2⁄(2+7)=2⁄9, regardless of the total. Sufficient.

Tip: For probability with two categories, a ratio can be enough because probability is favorable/total, not necessarily a count. Table Analysis

Table Analysis

Question 9 - Sortable table: sales productivity

The table shows monthly performance for five sales representatives.

RepLeadsSalesRevenue ($000)Hours
Asha802096160
Ben651378130
Chen9027108180
Divya751899150
Eli701484140

For each statement, determine whether it is True or False.

A. The representative with the highest conversion rate also generated the highest revenue.
B. Exactly two representatives generated at least $6,000 in revenue per sale.
C. Chen had the highest revenue per hour.

Answer: A) True, B) True, C) False

Explanation:

Conversion rates are Sales⁄Leads: Asha 25%, Ben 20%, Chen 30%, Divya 24%, and Eli 20%. Chen has the highest conversion rate and also the highest revenue, so statement 1 is True. Revenue per sale is Revenue⁄Sales: Asha $4,800, Ben $6,000, Chen $4,000, Divya $5,500, and Eli $6,000. Exactly Ben and Eli are at least $6,000 per sale, so statement 2 is True. Revenue per hour is Revenue⁄Hours: Asha, Ben, Chen, and Eli each generate $600 per hour, while Divya generates $660 per hour; therefore statement 3 is False.

Tip: Create new columns in your scratch work: rate, ratio, or difference. Do not rely on the largest raw number when the statement asks for efficiency.

Question 10 - Employee training hours

Use the table to evaluate training completion.

TeamEmployeesAvg HoursCompleted Module (%)Cost per Employee ($)
Alpha241175420
Beta30980360
Gamma181367500
Delta281070390
Epsilon201285450

For each statement, determine whether it is True or False.

A. Beta had the greatest number of employees who completed the module.
B. Gamma had the highest total training cost.
C. Epsilon had the highest average hours and highest completion percentage.

Answer: A) True, B) False, C) False

Explanation:

Completed counts: Alpha 18, Beta 24, Gamma about 12.06, Delta 19.6, Epsilon 17; Beta is greatest. Total cost equals employees times cost: Alpha 10,080; Beta 10,800; Gamma 9,000; Delta 10,920; Epsilon 9,000, so Gamma is not highest. Epsilon has the highest completion rate, but Gamma has the highest average hours, so the last statement is false.

Tip: When percentages are applied to different bases, convert to counts before comparing.

Question 11 - Inventory turnover

The table shows inventory and sales for five stores.

StoreOpening Inv.Closing Inv.COGSSales
P120100440600
Q90110500690
R150130560760
S80120480640
T100100450585

For each statement, determine whether it is True or False.

A. Store Q had the highest gross margin percentage.
B. Store S had the highest inventory turnover, using COGS divided by average inventory.
C. Store T had the same opening and closing inventory.

Answer: A) True, B) False, C) True

Explanation:

Gross margin percentage = (Sales − COGS) ⁄ Sales. The percentages are P 26.7%, Q 27.5%, R 26.3%, S 25.0%, and T 23.1%, so statement 1 is True. Inventory turnover = COGS ⁄ average inventory. The turnovers are P 4.0, Q 5.0, R 4.0, S 4.8, and T 4.5, so Q, not S, has the highest turnover; statement 2 is False. Store T has opening inventory 100 and closing inventory 100, so statement 3 is True.

Tip: Be careful: a plausible answer may come from eyeballing. Compute the exact ratio for the top contenders.

Question 12 - Subscription plan analysis

A streaming company tracks five plans.

PlanMonthly PriceSubscribersChurn %Support Tickets
Basic8120006420
Plus1290004360
Family1865003310
Student670005175
Premium2240002220

For each statement, determine whether it is True or False.

A. Premium has the lowest churn rate but not the lowest number of churned subscribers.
B. Family generates more monthly revenue than Plus.
C. Student has the fewest support tickets per 1,000 subscribers.

Answer: A) False, B) True, C) True

Explanation:

Churned subscribers are Basic 720, Plus 360, Family 195, Student 350, and Premium 80. Premium has the lowest churn rate and also the lowest number of churned subscribers, so statement 1 is False. Monthly revenue is price times subscribers: Family $117,000 and Plus $108,000, so statement 2 is True. Support tickets per 1,000 subscribers are Basic 35, Plus 40, Family about 47.7, Student 25, and Premium 55, so statement 3 is True.

Tip: For rate statements, check whether the question asks about a rate or an actual count. The lowest percentage may or may not give the lowest number.

Question 13 - Profit by region

The table summarizes regional results.

RegionUnits SoldPrice per UnitVariable Cost per UnitFixed Cost ($000)
North9000321860
South7500352055
East8200301750
West6800402265
Central7200341945

For each statement, determine whether it is True or False.

A. West has the highest contribution margin per unit.
B. North has the highest total contribution before fixed costs.
C. Central has the highest operating profit.

Answer: A) True, B) True, C) False

Explanation:

Contribution per unit: North 14, South 15, East 13, West 18, Central 15; West is highest. Total contribution: North 126k, South 112.5k, East 106.6k, West 122.4k, Central 108k; North is highest. Operating profit subtracts fixed cost: North 66k, South 57.5k, East 56.6k, West 57.4k, Central 63k; North is highest, not Central.

Tip: Separate contribution margin from operating profit. Fixed costs do not affect contribution per unit, but they do affect final profit.

Question 14 - Order fulfillment

The table shows order data by warehouse.

WarehouseOrdersLate OrdersReturned OrdersAvg Ship Cost ($)
A120084367.5
B95057198.2
C110066447.1
D80048169.0
E100050307.8

For each statement, determine whether it is True or False.

A. Warehouse E has the lowest late-order rate.
B. Warehouse C has the highest return rate.
C. Warehouse A has the lowest total shipping cost.

Answer: A) True, B) True, C) False

Explanation:

Late rates: A 7%, B 6%, C 6%, D 6%, E 5%; E is lowest. Return rates: A 3%, B 2%, C 4%, D 2%, E 3%; C is highest. Total shipping cost: A 1200×7.5=9000; B 7790; C 7810; D 7200; E 7800, so D is lowest, not A.

Tip: Rates require division; totals require multiplication. GMAT tables often test whether you confuse the two.

Question 15 - Market research survey

A survey reports preference by age group.

Age GroupRespondentsPrefer Product XPrefer Product YNo Preference
18-24160725632
25-342201106644
35-44180817227
45-54140566321
55+100354520

For each statement, determine whether it is True or False.

A. The 25-34 group has the largest number and the largest percentage preferring Product X.
B. The 45-54 group is the only group in which Product Y is preferred by more respondents than Product X.
C. Overall, exactly half of all respondents prefer Product X.

Answer: A) True, B) False, C) False

Explanation:

Counts for X are highest for 25-34 at 110. Percentages for X: 45%, 50%, 45%, 40%, 35%; 25-34 is also highest. Product Y exceeds X in 45-54 and 55+, so it is not the only group. Total respondents = 800; Product X total = 354, not 400, so not exactly half.

Tip: For “largest number and largest percentage,” verify both; large groups can dominate counts but not percentages.

Question 16 - Project portfolio

The table lists project budgets and returns.

ProjectInitial Cost ($000)Expected Annual Cash Flow ($000)Risk ScoreDuration (years)
A3009534
B45012025
C2508043
D50016054
E35010035

For each statement, determine whether it is True or False.

A. Project C has the shortest payback period.
B. Project B has the lowest risk score.
C. Project D has the greatest total expected cash flow over its duration.

Answer: A) True, B) True, C) True

Explanation:

Payback = initial cost ⁄ annual cash flow. A is about 3.16 years, B is 3.75 years, C is 3.125 years, D is 3.125 years, and E is 3.5 years. Since C is tied for the shortest payback period, statement 1 is True. Project B has the lowest risk score, so statement 2 is True. Total expected cash flow equals annual cash flow times duration: A 380, B 600, C 240, D 640, and E 500 thousand dollars; D is greatest, so statement 3 is True.

Tip: Pay attention to words such as greatest, unique, exactly, at least, and more than. Ties can change the truth of a statement. Graphics Interpretation

Graphics Interpretation

Question 17 - Line graph: margin trend

Refer to the line graph showing revenue and cost for Northstar Apps.


Complete the statements using the most accurate choices.

A. The months with the greatest profit were _____.
B. From January to June, revenue increased by approximately _____.

Answer: A) May and June; B) 50%

Explanation:

Profit is revenue minus cost. The monthly profits are 40, 45, 40, 50, 54, and 54 thousand dollars. May and June tie for greatest profit, so the most accurate answer is May and June. Revenue increased from 120 to 180, an increase of 60 on a base of 120, or 50%.

Tip: Always calculate the value represented by the graph if the question asks for margin, gap, or change. Do not simply look for the highest line.

Question 18 - Scatter plot: demand relationship

Refer to the scatter plot of drink price and weekly units sold.


Complete the statements using the most accurate choices.

A. The relationship between price and units sold is best described as _____.
B. When the average price rose from $10 to $14, weekly units sold decreased by _____.

Answer: A) Negative; B) 100 units

Explanation:

As price increases, units sold generally decreases, so the relationship is negative. At $10, units sold are 360. At $14, units sold are 260. The decrease is 100 units.

Tip: For scatter plots, describe direction first: positive, negative, or no clear relationship. Then use exact plotted values for calculations.

Question 19 - Bar chart: contribution estimate

Refer to the chart of margin per unit and monthly volume.


Complete the statements using the most accurate choices.

A. The product with the greatest estimated monthly contribution is _____.
B. Product D has a higher margin than Product B by _____.

Answer: A) C; C) $6

Explanation:

Monthly contribution equals margin per unit times units sold. A: 18×12,000=216,000; B: 24×8,000=192,000; C: 15×16,000=240,000; D: 30×6,000=180,000; E: 21×10,000=210,000. Product C is greatest, not A. Product D margin exceeds B by 30−24=$6.

Tip: When a chart shows two variables, the best business metric may be their product, not either variable alone.

Question 20 - Histogram: delivery time

Refer to the histogram of delivery times for 60 orders.


Complete the statements using the most accurate choices.

A. The modal delivery-time interval is _____.
B. The percentage of orders delivered in less than 6 days is approximately _____.

Answer: A) 4-6 days; B) 72%

Explanation:

The tallest bar is the 4-6 day interval with 21 orders, so it is the modal interval. Less than 6 days includes 0-2, 2-4, and 4-6: 8+14+21=43 orders. 43⁄60 = 71.7%, approximately 72%.

Tip: In histograms, bars represent intervals, not exact values. Add all relevant intervals for cumulative questions.

Question 21 - Stacked bar: channel mix

Refer to the stacked bar chart of sales channel mix by region.


Complete the statements using the most accurate choices.

A. The region with the greatest online share is _____.
B. The difference between East and South online shares is ____ percentage points.

Answer: A) North; B) 3

Explanation:

Online shares are North 48%, South 38%, West 44%, and East 35%. North is highest. The difference between East and South is 38 - 35 = 3 percentage points.

Tip: Percentage point difference is subtraction of percentages. Percent change would divide by a base.

Question 22 - Indexed revenue table

A company indexed revenue to 100 in Year 1. Year 2 index = 115, Year 3 index = 138, Year 4 index = 131.

Complete the statements using the most accurate choices.

A. From Year 1 to Year 3, revenue increased by _____.
B. From Year 3 to Year 4, revenue changed by approximately _____.

Answer: A) 38%; B) decreased by 5.1%

Explanation:

An index of 138 means revenue is 38% higher than the Year 1 base. From Year 3 to Year 4, the change is (131−138)⁄138 = −7⁄138 = about −5.1%, so revenue decreased by about 5.1%.

Tip: Index questions usually use the base year as 100. For changes between two non-base years, divide by the earlier year, not by 100.

Question 23 - Break-even chart in words

A vendor has fixed costs of $12,000, price per unit of $50, and variable cost per unit of $30.

Complete the statements using the most accurate choices.

A. The break-even number of units is _____.
B. At 900 units, profit is _____.

Answer: A) 600 units; B) $6,000

Explanation:

Contribution per unit is price minus variable cost = 50 − 30 = 20. Break-even units = fixed cost ⁄ contribution per unit = 12,000⁄20 = 600. At 900 units, profit = 900×20 − 12,000 = 18,000 − 12,000 = 6,000.

Tip: For break-even, memorize: fixed cost divided by contribution margin per unit.

Question 24 - Pie-style market shares from data

A market has four brands with shares: A 32%, B 28%, C 25%, and D 15%. Total market sales are $80 million.

Complete the statements using the most accurate choices.

A. The dollar sales of Brand C are _____.
B. Brands A and B together exceed Brand C by _____ percentage points.

Answer: A) $20 million; B) 35

Explanation:

Brand C sales are 25% of 80 million = 20 million. A+B = 32%+28%=60%; 60%-25%=35 percentage points.

Tip: Pie-chart questions often ask either for the part amount or for a difference in share. Decide whether to multiply by the total or subtract percentages. Multi-Source Reasoning

Two-Part Analysis

Question 25. Simultaneous equations

A store sold notebooks and pens. Notebooks cost $4 each and pens cost $1.50 each. A customer bought 20 items for $50. Select the number of notebooks and the number of pens.

Select one answer in each column.

Option Notebooks Pens
8
9
10
11
12

Answer: 8 notebooks; 12 pens

Explanation:

Let n be notebooks and p be pens. The total-item equation is n + p = 20. The total-cost equation is 4n + 1.50p = 50. Substitute p = 20 − n: 4n + 1.50(20 − n) = 50, so 4n + 30 − 1.5n = 50, 2.5n = 20, and n = 8. Therefore p = 12.

Tip: For two-part equations, set up both conditions. Check that the selected pair satisfies every condition, not just one.

Question 26. Discount and tax

An item is discounted by 25% and then taxed at 8%. The final price is $81. Select the list price and the tax amount.

Select one answer in each column.

Option List Price Tax Amount
$90
$96
$100
$108
$120
$6

Answer: List price = $100; Tax Amount = $6

Explanation:

After a 25% discount, the customer pays 75% of list price before tax. Tax is 8% of the discounted price, so final price = list price × 0.75 × 1.08 = list price × 0.81. If final is 81, list price is 100. Discounted price is 75, so tax is 0.08×75=6.

Tip: Apply percent changes in order. A discount followed by tax is multiplication by 0.75 and then 1.08, not by adding -25% and +8%.

Question 27. Mixture

How many liters of 20% acid solution and 50% acid solution should be mixed to make 30 liters of 38% acid solution?

Select one answer in each column.

Option 20% Solution 50% Solution
10
12
15
18
20

Answer: 12 liters; 18 liters

Explanation:

Let x be liters of 20% solution and y be liters of 50% solution. x+y=30. Acid equation: .20x+.50y=.38(30)=11.4. Substitute x=30−y: 6−.20y+.50y=11.4, so .30y=5.4 and y=18; x=12.

Tip: For mixtures, write one equation for total amount and one for pure ingredient amount.

Question 28. Rate trade-off

A consultant can complete a report in 6 hours and an analyst can complete it in 10 hours. If they work together for some time and then the consultant works alone for 2 hours, the report is completed. Select the total hours the analyst worked and total hours the consultant worked.

Select one answer in each column.

Option Analyst Hours Consultant Hours
2
2.5
3
4
4.5

Answer: 2.5 hours; 4.5 hours

Explanation:

Let t be the time they work together. Analyst works t hours; consultant works t+2 hours. Work completed: t⁄10 + (t+2)⁄6 = 1. Multiply by 30: 3t + 5t + 10 = 30, so 8t=20 and t=2.5. Then analyst 2.5 and consultant 4.5. Correct pair: 2.5; 4.5, which requires 4.5 as option.

Tip: Use work fractions: time/rate-time. If someone works longer, reflect that in the numerator.

Question 29. Profit target

A retailer sells a product for $75. Variable cost is $45, and fixed cost is $18,000. Select the units that break even and the units needed for $12,000 profit.

Select one answer in each column.

Option Break-even Units Units for $12,000 Profit
400
500
600
800
1,000

Answer: 600; 1,000

Explanation:

Contribution per unit = 75−45=30. Break-even units = 18,000⁄30=600. For $12,000 profit, contribution must cover fixed cost plus target profit: 18,000+12,000=30,000. 30,000⁄30=1,000.

Tip: Target-profit questions are break-even questions with desired profit added to fixed cost.

Question 30. Mean and total

The average of x, y, and z is 18. The average of x and y is 15. Select z and x+y.

Select one answer in each column.

Option z x + y
30
36
42
45
54
24

Answer: 24; 30

Explanation:

Total x+y+z = 3×18 = 54. Since the average of x and y is 15, x+y = 30. Therefore z = 54−30 = 24. Correct pair: z=24 and x+y=30.

Tip: Convert averages to totals immediately. Totals combine more easily than averages.

Question 31. Probability with replacement

A bag contains 3 green, 2 yellow, and 5 black tokens. One token is drawn, replaced, and another token is drawn. Select the probability that both tokens are green and the probability that at least one is black.

Select one answer in each column.

Option Both Green At Least One Black
3⁄10
9⁄100
1⁄4
1⁄2
3⁄4

Answer: 9⁄100; 3⁄4

Explanation:

Because the token is replaced, draws are independent. P(both green)=(3⁄10)(3⁄10)=9⁄100. P(at least one black)=1-P(no black). No black means green or yellow, probability 5⁄10 each draw, so no black=(1⁄2)²=1⁄4. Therefore at least one black=3⁄4.

Tip: For “at least one,” consider the complement. It is often faster and less error-prone.

Question 32. Inequality interval

For which values of x is 3x − 5 < 16 and 2x + 1 ≥ 9? Select the lower bound and upper bound of the solution interval.

Select one answer in each column.

Option Lower Bound Included Upper Bound Not Included
2
4
5
7
9

Answer: 4; 7

Explanation:

Solve each inequality. 3x−5<16 gives 3x<21, so x<7. 2x+1≥9 gives 2x≥8, so x≥4. Together, 4 ≤ x < 7. Lower bound included is 4; upper bound not included is 7.

Tip: When combining inequalities, draw a number line. Check open vs. closed endpoints carefully.

Multi-Source Reasoning

Question 33 - Expansion decision

Which region satisfies both expansion criteria?

Source 1 - Manager memo: A retailer will expand only if a region has projected revenue of at least $2.0 million and payback period below 3 years.

Source 2 - Finance table: Region North: investment $900k, annual cash flow $360k, projected revenue $2.4m. Region South: investment $750k, annual cash flow $250k, projected revenue $2.1m. Region West: investment $1.2m, annual cash flow $500k, projected revenue $1.9m.

A. North only
B. South only
C. West only
D. North and West

Answer: A

Explanation:

Payback = investment ⁄ annual cash flow. North: 900⁄360 = 2.5 years and revenue 2.4m, so it qualifies. South: 750⁄250 = 3.0 years, not below 3, so it fails. West: 1200⁄500 = 2.4 years but revenue is only 1.9m, so it fails.

Tip: In MSR, underline each criterion and test candidates one by one. Do not stop after only one condition.

Question 34 - Supplier selection

Which supplier is acceptable?

Source 1 - Policy: A supplier is acceptable if defect rate is below 2.5%, on-time rate is at least 94%, and unit cost is no more than $18.

Source 2 - Supplier data: A: defect 2.1%, on-time 95%, cost $19. B: defect 2.4%, on-time 94%, cost $18. C: defect 1.8%, on-time 92%, cost $17. D: defect 2.6%, on-time 97%, cost $16.

A. A
B. B
C. C
D. D

Answer: B

Explanation:

Supplier B meets all three conditions exactly or better: defect 2.4% below 2.5%, on-time 94% at least 94%, cost 18 no more than 18. A fails cost, C fails on-time rate, and D fails defect rate.

Tip: Watch inclusive language: “at least” and “no more than” include equality; “below” does not.

Question 35 - Campaign ROI

Which campaign or campaigns were successful?

Source 1 - Formula: ROI = (incremental profit − campaign cost) ⁄ campaign cost. A campaign is successful if ROI is at least 25%.

Source 2 - Data: Email: incremental profit $45k, cost $30k. Search: profit $70k, cost $60k. Social: profit $55k, cost $40k.

A. Email only
B. Social only
C. Email and Social
D. Search and Social

Answer: C

Explanation:

Email ROI=(45−30)/30=50%. Search ROI=(70−60)/60=16.7%. Social ROI=(55−40)/40=37.5%. Email and Social meet or exceed 25%; Search does not.

Tip: Use the formula exactly as given. A large profit does not guarantee a high ROI if cost is also large.

Question 36 - Hiring plan

How many additional analysts should be hired for next quarter?

Source 1 - Staffing rule: A team must add one analyst for every additional 120 client accounts beyond 600 accounts. Round up partial requirements.

Source 2 - Forecast: Current accounts: 610. Forecast accounts next quarter: 925. Current analysts: 3.

A. 1
B. 2
C. 3
D. 4

Answer: C

Explanation:

Additional accounts beyond 600 next quarter = 925 − 600 = 325. One analyst is needed for every 120 accounts, and partial requirements are rounded up: 325⁄120 = 2.71, so 3 analysts are required. The question asks how many additional analysts should be hired; since the rule is about analysts needed beyond 600, the answer is 3.

Tip: Round-up rules are common in staffing/capacity problems. If any fraction of a unit is needed, round to the next whole unit.

Question 37 - Capacity and bottleneck

What is the maximum number of units the plant can produce per day?

Source 1 - Production notes: Each unit requires 4 minutes on Machine X and 6 minutes on Machine Y. The plant operates 8 hours per day.

Source 2 - Availability: Machine X has 2 machines available. Machine Y has 3 machines available. Demand is 250 units per day.

A. 160
B. 240
C. 250
D. 320

Answer: B

Explanation:

Daily minutes available: Machine X has 2×8×60=960 minutes, so capacity is 960⁄4=240 units. Machine Y has 3×8×60=1440 minutes, so capacity is 1440⁄6=240 units. The plant maximum is the smaller bottleneck capacity: 240 units.

Tip: For multi-step production, capacity is limited by the bottleneck, the minimum capacity among required resources.

Question 38 - Customer lifetime value

Which segment has the greatest lifetime value?

Source 1 - Model: Lifetime value = monthly gross profit × expected months retained − acquisition cost.

Source 2 - Segment data: Segment Small: monthly profit $35, retained 18 months, acquisition cost $220. Segment Mid: monthly profit $60, retained 14 months, acquisition cost $360. Segment Enterprise: monthly profit $140, retained 8 months, acquisition cost $650.

A. Small
B. Mid
C. Enterprise
D. Small and Mid tie

Answer: B

Explanation:

Small LTV = 35×18 − 220 = 410. Mid LTV = 60×14 − 360 = 480. Enterprise LTV = 140×8 − 650 = 470. Mid is greatest.

Tip: Multiply before subtracting fixed acquisition cost. Then compare final value, not monthly profit alone.

Question 39 - Pricing experiment

Was the price increase successful?

Source 1 - Test design: A price increase is considered successful if total revenue rises and unit sales fall by no more than 10%.

Source 2 - Results: Old price $20, old units 5,000. New price $23, new units 4,600.

A. Yes, because both criteria were met.
B. Yes, because revenue rose even though unit loss exceeded 10%.
C. No, because revenue fell.
D. No, because units fell by more than 10%.

Answer: A

Explanation:

Old revenue = 20×5000 = 100,000. New revenue = 23×4600 = 105,800, so revenue rose. Unit loss = 400 units on a base of 5,000, or 8%, which is no more than 10%. Both criteria are met.

Tip: Use the original value as the base when calculating percent decrease.

Question 40 - Data discrepancy

Which conclusion is best supported?

Source 1 - Operations report: The company shipped 12,000 orders in May, and 96% were delivered on time.

Source 2 - Customer service report: In May, customers filed 620 late-delivery complaints. Each late order can generate at most one late-delivery complaint.

A. The two reports are consistent because 4% of 12,000 is 480, which is less than 620.
B. The reports cannot both be accurate under the stated complaint rule.
C. At least 620 orders were delivered on time.
D. Exactly 480 customers filed complaints.

Answer: B

Explanation:

If 96% were on time, then 4% were late. 4% of 12,000 is 480 late orders. Since each late order can generate at most one late-delivery complaint, complaints cannot exceed late orders. But the customer service report shows 620 complaints. Therefore the reports cannot both be accurate.

Tip: MSR often asks about consistency. Convert percentages into counts and compare with stated limits.