Back to the on-screen lesson ·
Combine tabular records with definitions and policies to select a supported quantitative or logical conclusion.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Combine tabular records with definitions and policies to select a supported quantitative or logical conclusion.
Combine tabular records with definitions and policies to select a supported quantitative or logical conclusion.
| Term | What it means |
|---|---|
| Join key | The shared identifier that lets values from separate sources describe the same case. |
| Denominator | The population or base relative to which a rate or proportion is measured. |
| Feasible option | An option satisfying every stated constraint, including boundary conditions. |
| Threshold | The boundary at which a rule changes, with eligibility determined by whether equality is included. |
A table does not interpret itself. Before calculating, identify what one row represents, which unit each column uses, what period the values cover, and whether categories overlap. Read the accompanying policy source before deciding that two totals should agree. Active subscriptions on the last day of a month and accounts visiting during that month are different populations. An account may belong to either, both or neither set. Their numerical difference is not automatically a count of inactive users. The first task in a multi-source problem is therefore semantic reconciliation: determine whether the quantities are commensurable before choosing an arithmetic operation.
Another way: steps
Definition source to value source to constraint check to comparison: match identifiers, reconstruct totals, apply every threshold, then compare eligible options. For two groups, combine event counts over combined eligible counts; do not average percentages without checking their weights.
A combined rate uses the combined numerator divided by the combined denominator. Averaging subgroup rates gives the same answer only under appropriate weighting conditions. Two branches with different numbers of jobs should not contribute equally merely because each occupies one table row. Similarly, a reduction in resource use may require weighting by baseline consumption rather than by the number of households. Write the definition in words before inserting values. Rework rate means jobs requiring rework divided by completed jobs. Productivity means output divided by the stated input. A rise in output alone does not prove a rise in productivity if the required staff time grew even faster.
A proposal with the greatest apparent benefit may be infeasible. List the budget, required number of selections, threshold rules and timing dependencies before ranking alternatives. If exactly two projects are required, one attractive project is not a permitted answer. If purity must reach a cutoff and yield must exceed another, good performance on one dimension cannot compensate for failure on the other. Distinguish inclusive from strict boundaries: at least permits equality, while above does not. In a scheduling question, tasks that start together do not have their durations added unless the dependency rules make them sequential. A decision model is complete only when all supplied constraints are represented.
Comparing purchase prices alone can conceal differences in fixed fees, marginal charges, coverage limits or operating periods. Express each alternative as a total-cost function of the same activity level. Locate a crossover by solving equality, then test which side makes the desired option cheaper. If the quantity must be an integer, distinguish the boundary from the first qualifying count. A price conversion also needs a common quantity basis: total contract price and price per unit are different targets. Convert each per-unit amount in the correct direction, then compare. A lower total price can coexist with a higher unit cost when quantities differ.
Inventory and accounting problems often require signs more than sophisticated mathematics. Opening stock plus receipts minus shipments plus usable customer returns gives closing stock, provided the sources exclude other movements. The word return does not determine a sign by itself: a return from a customer and a return to a supplier move inventory in opposite directions. For defect categories, a rejected unit with both defects should be counted once if rejection is defined by either defect. Subtract the overlap when forming the union. Keep a small reconciliation table of disjoint categories or signed movements; it can reveal a wrong sign or double count that a long calculation hides.
Sometimes the correct conclusion is that the given sources do not determine the requested result. Do not invent an overlap between sets, an interview success rate, or a rule connecting a necessary condition to approval. A hiring screen can eliminate ineligible candidates without guaranteeing a job to everyone who passes. A comparison of total counts may leave rates unknown, while a rate comparison may leave final counts unknown. Identify exactly what additional fact would close the gap, then check whether any source supplies it. When answering, preserve the difference between a numerical consequence of the definitions and a causal story that the same numbers merely suggest.
A table and a policy note may use different labels for related quantities. Before combining them, identify the common key: project, month, customer group or product code. Row order is not a reliable key. Check whether a cost is per unit, per order or per period, and whether a reported total includes a fixed fee. For a shipping decision, a table might show transit days while a note supplies handling days and a deadline. Delivery time then includes both components unless the definitions say otherwise. Do not substitute the smallest transit figure for the earliest arrival without joining the handling rule. Missing information is itself relevant. If two sources report the numbers of subscribers and visitors but do not describe overlap, adding them cannot establish the number of distinct people. State the possible overlap or its bounds instead of silently assuming the groups are disjoint.
An aggregate percentage must weight each group by the population relevant to that percentage. Suppose one team completes 40 orders with a ten percent rework rate and another completes 160 orders with a five percent rate. The rework counts are four and eight; the combined rate is twelve out of two hundred, or six percent. The unweighted average of the two rates is seven and a half percent, which describes neither the actual order mix nor its total rework. If the question instead asks for the average team rate, equal weighting might be appropriate. Read the target carefully. The same issue affects utilization, renewal and defect percentages. Check whether the denominator is eligible accounts, all accounts, shipped units or inspected units. Even a correctly calculated percentage can answer the wrong question when its denominator changes across sources. Sorting a table helps locate values but does not resolve incompatible definitions.
Words such as at least, more than and no later than determine whether equality qualifies. A discount available for orders over six thousand units excludes an order of exactly six thousand; if only whole units are allowed, the first eligible quantity is six thousand and one. Preserve this distinction when a question asks for the threshold itself rather than the first eligible order. For multiple constraints, test each candidate against all conditions before ranking it by cost or benefit. The cheapest option is not the best feasible option if it misses a deadline or violates a capacity limit. Conversely, a feasible option is not necessarily optimal. Separate filtering from comparison. With two activities sharing a resource, add their simultaneous demand, not their independently reported capacities. With sequential stages, the slowest required stage may limit throughput. These structural choices come before arithmetic and often explain the most plausible distractor.
After each data problem, identify the source that supplied the answer's definition and the source that supplied its values. If an incorrect option was a genuine intermediate result, label the quantity it actually measured. For a weighting error, rebuild numerator and denominator from counts. For a policy error, write a feasible and an infeasible example around the boundary. Use the on-screen source controls to revisit definitions instead of relying on memory of the first table. A calculator can help execute the arithmetic, but it cannot decide whether an arrival interval starts at ordering or dispatch, whether a threshold includes equality, or whether two populations overlap.
A supplier quotes 900 credits plus 40 for shipping with two handling days and three transit days. Another quotes 940 including shipping with one handling day and three transit days. If arrival must occur within four days, the first supplier fails the deadline even though its total price is also 940. The second is feasible. This decision requires the price table, shipping note and deadline together; reading only the base-price column produces the wrong ranking. A source checklist makes the missing component visible before calculation.
Read numerator and denominator
Branch Harbor completed 120 jobs with 6 reworks; Branch Ridge completed 30 jobs with 6 reworks. A rework is counted once per job.
The policy defines a job-level rate, so the branches must contribute according to their completed jobs rather than as two equal rows.
Aggregate matching quantities
Total reworks are 12 and total completed jobs are 150.
Both numerators and denominators describe the same period and unit. No overlap between branch job lists is indicated.
Calculate the combined rate
The combined rework rate is 12/150=8%.
The simple mean of 5% and 20% would be 12.5%, but it would overrepresent the smaller branch.
Check the rate bounds
The combined rate lies between 5% and 20% and closer to 5%.
The larger branch handles four times as many jobs, so the weighted result should sit closer to its rate. This gives a structural check beyond arithmetic.
Write comparable cost functions
Plan M costs 90 credits plus 6 per visit; Plan N costs 210 credits plus 3 per visit.
Both expressions cover the same period and include all listed costs, so they can be compared at a common visit count n.
Find the tie
90+6n=210+3n gives n=40.
The equality identifies the crossover. It does not itself establish that either plan is strictly cheaper at the boundary.
Determine the direction
For n>40, N is cheaper because its variable cost grows more slowly.
Testing n=50 gives costs 390 and 360, confirming which side of the boundary favors N.
Answer with the required form
The threshold is 40 visits; the least whole-number count giving a strict saving is 41.
Both numbers can be meaningful, but the question's wording decides which one to select. Confusing a boundary with a qualifying integer is a target error.
Check the threshold boundary
Substitute the break-even quantity into both cost formulas before choosing the cheaper side.
Equal costs at the boundary do not establish that either supplier is strictly cheaper there; the question's inequality determines eligibility.
Identify the two sets
A studio lists 300 active paid accounts on September 30 and 280 distinct visiting accounts during September.
The first set is defined by status on one date; the second by activity over a period. These are not automatically nested populations.
Read the policy qualifications
An account can visit and then cancel before month-end; an active account can make no visit.
Each source explicitly allows accounts that belong only to one of the two sets.
Test simple subtraction
The difference of 20 does not establish exactly 20 active nonvisitors.
If 30 visitors canceled and the overlap is 250, there would instead be 50 active nonvisitors while both totals still match.
State the missing information
The overlap, or a condition fixing it, is needed to determine active nonvisitors.
Two compatible scenarios with different answers establish insufficiency. They do not imply that either source is inaccurate.
Construct two compatible overlaps
If all 280 visitors remain active, there are 20 active nonvisitors. If only 250 remain active, there are 50.
Both models satisfy the reported totals and policy, so the difference of the totals cannot uniquely determine active nonvisitors.
Locate the missing field
A count of visiting accounts still active on September 30 would fix the overlap.
Subtracting that intersection from the 300 active accounts would then answer the question without assuming that visitors never cancel.
Assign signs from direction
A workshop starts with 75 units, receives 40, ships 62, and returns 8 defective units to its supplier.
Supplier returns leave the workshop, unlike usable customer returns.
Reconcile the stock
75+40-62-8=45 units.
Every movement is counted once with the sign determined by its effect on stock.
Check the physical interpretation
What is the combined rework rate?
A repair firm compares two branches' completed jobs.
| Branch | Jobs | Rework jobs |
|---|---|---|
| Elm | 80 | 4 |
| Pine | 20 | 3 |
A job requiring rework is counted once. The firm reports its combined rework rate using all completed jobs.
Above how many pages per month is A strictly cheaper than B?
A printer compares two supply contracts.
| Contract | Monthly fixed fee | Cost per page |
|---|---|---|
| A | 180 | 0.03 |
| B | 60 | 0.05 |
Fees and page charges are the only costs. Page counts are whole numbers, and both contracts provide equivalent output.
What is closing usable stock?
A wholesaler reconciles inventory movements.
| Entry | Units |
|---|---|
| Opening stock | 140 |
| Receipts | 95 |
| Customer shipments | 170 |
| Customer returns | 12 |
Returned units are usable and reenter stock. No other movements occurred.
How did productivity change?
A service company evaluates a pilot.
| Period | Completed requests | Total staff hours |
|---|---|---|
| Before | 360 | 120 |
| Pilot | 450 | 180 |
Productivity means completed requests per staff hour. Completion counts and staff hours refer to the same periods.
Which permitted pair has the greatest expected annual savings?
A fund compares investment proposals.
| Proposal | Cost | Expected annual savings |
|---|---|---|
| J | 300 | 90 |
| K | 240 | 72 |
| L | 150 | 60 |
Choose exactly two proposals. Total cost cannot exceed 400. Savings add, and all figures use the same monetary unit.
Which conclusion is justified?
An analyst compares membership data from two sources.
| Source | Reported members |
|---|---|
| Billing ledger | 420 |
| Access log | 390 |
The ledger counts accounts with an active paid subscription on June 30. The log counts distinct accounts that entered at least once during June. Paid accounts may have no visits, and June visitors may have canceled before June 30.
Which packages were on time?
A fulfillment manager reviews promised delivery dates.
| Package | Order day | Dispatch day | Arrival day |
|---|---|---|---|
| R | 1 | 3 | 6 |
| S | 2 | 2 | 6 |
| T | 4 | 5 | 8 |
A delivery is on time if arrival is no later than four days after the order day. Dates are consecutive calendar days; dispatch time is included.
What percentage of inspected units is rejected?
A quality team records two categories of defects.
| Measure | Units |
|---|---|
| Inspected | 200 |
| Surface defect | 28 |
| Seal defect | 19 |
| Both defects | 7 |
Each unit appears at most once in each category. A unit is rejected if it has either defect.
For which annual repair counts is Plus strictly cheaper?
An equipment team compares annual maintenance options.
| Option | Annual fee | Covered repairs |
|---|---|---|
| Basic | 120 | 0 |
| Plus | 300 | 3 |
Each uncovered repair costs 90. Plus covers the first three repairs completely; any later repairs cost 90 each. Basic covers none.
What is the final order charge?
A retailer calculates an order's revenue.
| Item | Quantity | List price |
|---|---|---|
| Desk | 3 | 200 |
| Chair | 4 | 75 |
A 10% discount applies to desks only. Delivery adds a flat 45 to the order. Ignore tax.
What is the total-use reduction?
A water authority compares conservation reports.
| District | Households | Mean monthly use before | Mean monthly use after |
|---|---|---|---|
| Hill | 100 | 40 | 32 |
| Valley | 300 | 20 | 18 |
Household counts are unchanged. All use figures are in the same unit. Compute the percentage reduction in total use across both districts.
Three fresh reserved problems. Choose your method without hints; explanations follow your response.
Which batches are accepted?
A laboratory compares batches that meet different acceptance criteria.
| Batch | Purity percent | Yield percent |
|---|---|---|
| A | 98 | 70 |
| B | 96 | 85 |
| C | 99 | 78 |
Acceptance requires purity at least 97% and yield above 75%. Both conditions are mandatory.
How did total revenue change from the first month to the second?
An online store reconciles two monthly indicators.
| Month | Orders | Mean order value |
|---|---|---|
| First | 240 | 50 |
| Second | 300 | 44 |
Revenue equals orders times mean order value. No refunds or additional revenue occur.
What is total renewal revenue?
A subscription service applies a renewal offer.
| Tier | Accounts | Monthly fee |
|---|---|---|
| Standard | 80 | 15 |
| Premium | 20 | 30 |
All accounts renew for one month. Standard receives a 20% fee reduction; Premium receives none. No account changes tier.
Explain the decisive restriction or inference in your own notes, then answer three new reserved questions without hints. Review and classify errors before trying a different problem after a study gap.
17. Follow a different inventory flow, step 3
Units entering total 115; units leaving total 70.
Their difference reproduces the closing stock without relying on the first expression's order.