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DATA INSIGHTS · GMAT-DI-TADER · DRAFT

Table Analysis: Derived Metrics

Build the concept, interpret evidence, and apply it in a separate assessment pool.

Learn: Evidence and decisions

What a derived metric tells you

A raw count tells you how much; a rate compares that amount with an appropriate base. A store can earn more profit yet retain a smaller fraction of revenue. Before calculating, say what the numerator counts and what the denominator represents.

A repeatable decision method

Read the claim first. Identify the relevant rows, metric, units and restrictions. Choose whether to sort a raw column or calculate a derived value. Test the exact wording, including ties and boundary values. Finally state whether the evidence supports the claim.

Use sorting for the right purpose

Sort a count to find its largest value, or a category to group rows. Sorting revenue does not sort operating margin, and sorting orders does not sort conversion rate. For derived metrics, calculate or compare the required ratios. Do not calculate every cell when a single qualifying counterexample settles the claim.

Read the column definitions first

Confirm what each row represents and whether values are totals, rates, or forecasts. Sorting helps locate extremes, but it does not replace the calculation required by a claim.

Build derived metrics from the table

For operating margin, subtract cost from revenue to get profit, then divide profit by revenue. Compare margins rather than raw profit when the statement asks about margin.

Combine groups with weighted totals

For a combined margin, add profits and divide by the combined revenues. The reliable method is to combine the underlying totals. For two groups, a simple average agrees when the denominators are equal or the two rates are equal; otherwise use the combined totals.

Evaluate each statement independently

For every claim, identify the exact rows and metric, calculate the value, and compare it with the claim. One True answer does not change how another statement is judged.

Successive changes use successive bases

For a multi-period percentage change, compare the final value with the initial value, or multiply the successive growth factors. Do not add percentage changes that use different bases. For a combined group, add its initial and final totals before calculating its percentage change.

A rank does not identify a rate

First decide what each row and column measures. To locate a median, sort the requested quantity. To compare rates, pair every numerator with its own denominator. The row in the middle after sorting counts need not be in the middle after sorting rates.

Learning Objectives

  • Sort a table by the numerical column named in a claim.
  • Compute profit, ratios, and weighted rates from the same rows.
  • Judge each True/False statement separately using its stated period and denominator.

Prerequisite Knowledge

  • Percentages are ratios multiplied by 100.
  • A percentage-point difference subtracts two percentages; a percent change divides the difference by the original value.

Worked Examples

Read a table, compare margins, then combine them

Each row describes one store for the same month. Revenue and operating cost are in thousands of dollars. Which store has the higher operating margin, and what is their combined margin?

Sortable data table. Select a column heading to sort.
Harbor300240
Park10060
  1. Name the requested metric. Margin is the fraction of revenue remaining after operating cost, not the amount of profit.
  2. Compute profit for each row. Sorting revenue alone would not answer the question.
  3. Compare the rates using each store's own revenue.
  4. For the combined margin, add profit and revenue separately.

Conclusion: Park has the higher margin even though Harbor has the greater profit. The combined margin is 25%, closer to Harbor's rate because Harbor contributes more revenue.

Check a conditional claim using a counterexample

Three teams report completed jobs and staff-hours: A has 84 jobs in 60 hours, B has 96 in 80 hours, and C has 65 in 50 hours. Evaluate: Every team completing at least 80 jobs completes at least 1.3 jobs per staff-hour.

Sortable data table. Select a column heading to sort.
A8460
B9680
C6550
  1. First restrict the rows using the condition. Only A and B completed at least 80 jobs.
  2. Calculate productivity only for the qualifying rows.
  3. Compare each qualifying row with the threshold. B fails it.

Conclusion: The statement is false. One qualifying counterexample is enough; C is outside the condition and cannot establish or refute this claim.

Distinguish percentage points from relative change

A department's defect rate falls from 8% to 6%. Find the percentage-point reduction and the relative percentage reduction.

Sortable data table. Select a column heading to sort.
Before8
After6
  1. Subtract the rates for the percentage-point change.
  2. For relative reduction, divide the decrease by the original rate.

Conclusion: The rate falls by two percentage points, which is a 25% reduction relative to its original value. Always identify the requested comparison before calculating.

A maximum may be shared

Plants R, S and T process 120, 180 and 150 units in 8, 12 and 15 hours, respectively. Does S have the uniquely highest hourly output?

Sortable data table. Select a column heading to sort.
R1208
S18012
T15015
  1. Calculate output per hour instead of sorting raw output.
  2. Check whether any other row attains the same maximum.

Conclusion: No. S has the greatest total output, but R and S tie for the highest hourly output. A claim of a unique maximum requires checking ties.

The middle count and the middle rate can belong to different rows

Five delivery hubs report parcels and late parcels for the same week. Identify the median parcel count, then decide whether its hub also has the median late rate.

Sortable data table. Select a column heading to sort.
A1006
B2004
C30015
D40016
E50015
  1. Sort parcel counts. The third of five counts is 300, belonging to C.
  2. Calculate late rates using parcels as each denominator.
  3. Sort the rates separately. The middle rate is 4%, belonging to D.

Conclusion: C has the median count, but D has the median late rate. Keep the complete row together whenever you sort.

Guided Practice: Try, then check

Work through each question on paper before opening its hint or explanation. This learning activity is separate from the scored Practice and Simulation pools.

Guided case: select the denominator and the qualifying rows

A retailer records visits and orders for four channels in one week. Every order is attributed to exactly one channel. Conversion rate is orders divided by visits. Use the sortable table, but calculate a rate when the claim requires one.

Sortable data table. Select a column heading to sort.
A80064
B120084
C50045
D100080
  1. Which channel has the most orders? Does that also establish the highest conversion rate?

    Show hint

    Sort Orders first. Then ask whether the visit counts are equal.

    Check reasoning

    B has the most orders, but the denominators differ. C converts 9% of visits, higher than B's 7%. A and D each convert 8%.

  2. Evaluate: Every channel with at least 800 visits has a conversion rate of at least 8%.

    Show hint

    First select the rows satisfying the visits condition. Check the boundary value too.

    Check reasoning

    A, B and D qualify. B has a 7% conversion rate, so the statement is false. C does not qualify and cannot serve as a counterexample.

  3. Find the combined conversion rate for A and C. Before calculating, predict which two rates it lies between.

    Show hint

    Add orders and visits separately. The combined rate is weighted by visits.

    Check reasoning

    The combined rate is approximately 8.38%, between 8% and 9%. It is closer to A's 8% because A contributes more visits.

Use sorting for raw values, choose the correct denominator for rates, and test only rows satisfying a conditional claim.

Guided challenge: restrictions and an exact budget boundary

A company must choose one supplier for exactly 240 units. All units have the stated price. Freight is charged once per order. A supplier qualifies only if it can deliver within 5 days and total cost is no more than $3,000. Stock and quality are identical.

Sortable data table. Select a column heading to sort.
J11.52405
K12604
L10.83606
M11.81803
  1. Which supplier can you exclude before calculating total costs?

    Show hint

    Both conditions must hold. Use the delivery restriction first.

    Check reasoning

    L takes 6 days and fails the delivery condition. Its lower unit price cannot compensate for that failure.

  2. Which of the remaining suppliers meet the budget? Does J qualify at exactly the limit?

    Show hint

    Multiply unit price by 240, then add freight once. No more than includes equality.

    Check reasoning

    J costs exactly $3,000 and qualifies. K costs $2,940 and qualifies. M costs $3,012 and does not qualify.

  3. Evaluate: Among qualifying suppliers, the lowest unit price also gives the lowest total cost.

    Show hint

    Compare only J and K. Do not ignore the fixed freight charge.

    Check reasoning

    False. J has the lower unit price, but K has the lower total cost. The most useful column depends on the decision being made.

Apply restrictions first, include fixed charges correctly, and treat inclusive boundaries exactly. A low unit price does not guarantee a low total.

Guided case: successive changes and changing bases

The table gives exact quarterly revenue in thousands of dollars for three stores. Evaluate each claim separately. Sorting a revenue column ranks amounts, not percentage growth.

Sortable data table. Select a column heading to sort.
A200250200
B100120132
C300330363
  1. Store A rises by 25% and then falls by 20%. Is its final revenue 5% above its initial revenue?

    Show hint

    The second percentage uses Q2 as its base. Compare Q3 directly with Q1.

    Check reasoning

    No. The increase is $50,000 and the decrease is also $50,000. Revenue returns to $200,000, so the net change is zero.

  2. Does the store with the largest Q3 revenue also have the greatest percentage growth from Q1 to Q3?

    Show hint

    Identify the largest amount, then calculate growth using each store’s own Q1 revenue.

    Check reasoning

    No. C has the largest Q3 revenue, but B has the greatest growth: A 0%, B 32%, and C 21%.

  3. For B and C combined, is Q1-to-Q3 growth the simple average of 32% and 21%?

    Show hint

    Combine the dollar amounts before calculating the rate. The initial revenues are unequal.

    Check reasoning

    No. Combined revenue rises from $400,000 to $495,000, giving 23.75% growth. The simple average, 26.5%, gives both stores equal weight despite their unequal initial revenues.

Choose the base before calculating. Successive rates multiply as growth factors; combined rates use combined totals. Sorting final amounts alone cannot rank growth.

Think Like a GMAT Test-Taker

Sort the relevant column to find a maximum or minimum, then verify the exact derived metric.

Write numerator and denominator before calculating a ratio.

For a combined rate, combine the underlying totals first.

Treat “percentage points” and “percent greater” as different calculations.

Name the measure before sorting; carry the row label with its data.

For an odd number of observations, locate the middle position after sorting the requested measure.

Common Traps

Choosing the row with the largest revenue when the claim asks for the largest margin.

Taking the simple average of margins with different revenue totals.

Calling a 5-percentage-point difference a 5% increase.

The median row in one column need not be the median row in another.

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