Back to the on-screen lesson ·
Distinguish independent from dependent tasks and select one supported response in each column.
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.
Distinguish independent from dependent tasks and select one supported response in each column.
Read conditional statements precisely and keep ratios, percentages and units distinct. A fraction compares a part with a named whole; an implication states a relationship rather than its converse. Before combining quantities, check that they refer to the same population and time period. If an arithmetic operation is uncertain, use the linked mathematics lesson to repair it before adding a timer. The purpose of this lesson is to decide what follows from supplied information, not to test outside knowledge of the scenario.
| Term | What it means |
|---|---|
| Coupled targets | Two requested values constrained by a shared relationship. |
| Feasible pair | Two choices satisfying every original condition together. |
| Necessary condition | Something that must hold, but need not alone guarantee the result. |
A two-part question asks for two answers from a common set of alternatives. The parts may be mathematical, verbal or a mixture. Their shared display does not tell you whether they can be solved independently: read the conditions to determine the dependency. In a system of equations, choosing the first variable constrains the second. In a verbal question asking for a fact that establishes a policy's success and another that rules it out, both decisions refer to the same definition but play different logical roles.
Name the columns in your own words before examining the alternatives. Short headings can omit conditions stated in the stem. If the task asks for an initial amount and an increase, selecting the final amount in the second column may satisfy familiar arithmetic while answering the wrong question. Keep units beside each target. The two parts need not have different answers unless the task says so; the same alternative can satisfy both columns. Conversely, two individually plausible choices may form an incompatible pair.
The entire item is correct only when both selections satisfy the supplied conditions. Solve the relationship, choose each component, then substitute the pair into every original condition. This last check catches swapped roles, sign errors and choices that fit only one equation. For verbal pairs, test each selected statement against its assigned role and ensure that no outside assumption supplies the missing link. Do not award yourself half a successful item merely because one part is familiar.
Another way: steps
Distinguish independent from dependent tasks and select one supported response in each column.
Suppose two small packages and one large package contain seventy units, while one small and two large contain eighty. Let x and y be their sizes. The equations are 2x+y=70 and x+2y=80. Subtracting gives y-x=10. Substituting y=x+10 yields 3x=60, so x=20 and y=30. Check both original totals: forty plus thirty is seventy, and twenty plus sixty is eighty. Selecting twenty for the large size and thirty for the small size would use the same two numbers but violate the column meanings. The pair, its order and the units are all part of the answer.
A short common option list can make testing pairs faster than unrestricted algebra, especially when integer or order constraints eliminate many combinations. Begin with the most restrictive relationship. If one value must exceed the other by ten, identify option pairs with that difference before checking a total. Avoid testing all pairs blindly. If the same option is allowed twice, include equal pairs when the conditions permit them. When an answer set contains negatives or fractions, do not discard them merely because the context usually uses positive integers; instead read the explicit domain and ask whether such a value makes sense under that domain.
Suppose a proposal is eligible exactly when it reduces delay and stays within budget. If delay reduction is given, learning that it stays within budget completes a sufficient case for eligibility. Learning that it exceeds budget rules eligibility out. A memorable name or the fate of another proposal does neither. The phrase 'only if' by itself states a necessary condition, not a complete guarantee; 'if and only if' or 'exactly when' supplies both directions. For a two-part task about support and opposition, compare each fact's effect on the same target. A fact about the general topic may be irrelevant to both columns.
After solving, reread the complete stem with both chosen values or propositions inserted. Check whether totals, ratios, time units and inclusive boundaries still hold. If the task asks for a minimum and maximum, verify feasibility at both endpoints and exclude values beyond them. If it asks for cause and effect, do not swap an observation with an explanation. If it asks for two facts jointly sufficient, neither may settle the question alone, but together they must do so. A mental check of one convenient condition is not enough when the pair is constrained by several. Use each condition once as an independent verification rather than repeating the same rearranged equation.
Suppose a mixture must contain equal volumes of a ten-percent concentrate solution and a forty-percent concentrate solution, producing thirty liters altogether. Each component volume is fifteen liters, and the final concentration is twenty-five percent. A two-column response can therefore require selecting the same number in both columns. Eliminating equal selections merely because the screen displays two columns would remove the correct pair before any mathematics was done. Test the stem, not an imagined interface convention.
For a boundary task, suppose x and y are nonnegative integers, x+y=20, and 2x+3y is at most 46. Replacing x by 20-y gives 40+y at most 46, so y ranges from zero through six. The minimum and maximum targets are zero and six. Both endpoints are feasible: their companion x values are twenty and fourteen. A value of seven fails the cost limit, while a negative value fails the domain. This check establishes both feasibility and exclusion. It is stronger than finding two pairs that happen to work. Distinguish an endpoint proof from a sample calculation whenever the columns ask for a minimum, maximum, least or greatest value.
Two-part reasoning appears when a planner chooses a quantity and a price, a rate and a duration, or an enabling condition and a blocking condition. The variables can trade off: a higher rate with a shorter duration may produce the same output. A feasible answer must meet the stated constraints, not simply improve one appealing feature. In a policy case, first translate the eligibility rule into a logical condition, then evaluate the proposed evidence without assuming facts about implementation that were never supplied.
During practice, write the two target labels and the dependency between them before opening the options. Solve or eliminate pairs systematically, then check the final pair against the original wording. If only one part was wrong, identify whether its error was independent or propagated from the first choice. Rework the pair after a study gap with changed conditions so that remembering two numbers does not replace reasoning. The response controls permit a choice in each column; they do not imply that the choices must be different or that solving either one alone completes the item.
Do not infer a result from an attractive label or the order of displayed alternatives. A complete answer must preserve every stated restriction and the scope of the requested conclusion. When a tempting response is wrong, identify the exact missing dependency or violated condition; merely saying that it feels too strong does not explain the error.
Read the target and its restrictions
For deliveries, case 1, two package sizes are sold. A small package has x units and a large package has y units. Two small packages plus one large contain 70 units. One small plus two large contain 80 units. Find each package size.
Distinguish independent from dependent tasks and select one supported response in each column.
Derive the deciding relationship
Subtract the equations to get y-x=10; then 3x+10=70, so x=20. With x=20, y=70-2(20)=30. The pair satisfies both equations.
Subtract the equations to get y-x=10; then 3x+10=70, so x=20. With x=20, y=70-2(20)=30. The pair satisfies both equations.
Compare competing responses
Subtract the equations to get y-x=10; then 3x+10=70, so x=20. Subtract the equations to get y-x=10; then 3x+10=70, so x=20. Subtract the equations to get y-x=10; then 3x+10=70, so x=20. Subtract the equations to get y-x=10; then 3x+10=70, so x=20. With x=20, y=70-2(20)=30. The pair satisfies both equations. With x=20, y=70-2(20)=30. The pair satisfies both equations. With x=20, y=70-2(20)=30. The pair satisfies both equations. With x=20, y=70-2(20)=30. The pair satisfies both equations.
Subtract the equations to get y-x=10; then 3x+10=70, so x=20. With x=20, y=70-2(20)=30. The pair satisfies both equations.
Select and verify the complete response
Units in the small package: 20; Units in the large package: 30
Subtract the equations to get y-x=10; then 3x+10=70, so x=20. With x=20, y=70-2(20)=30. The pair satisfies both equations.
Read the target and its restrictions
For support tickets, case 1, revenue is 138 credits and cost is 92 credits. Select profit and profit as a percentage of cost.
Distinguish independent from dependent tasks and select one supported response in each column.
Derive the deciding relationship
Profit is 138-92=46. (46)/(92) times 100=50 percent. The base is cost, not revenue.
Profit is 138-92=46. (46)/(92) times 100=50 percent. The base is cost, not revenue.
Check the information boundary
Solve coupled numerical targets together
Suppose two small packages and one large package contain seventy units, while one small and two large contain eighty. Let x and y be their sizes. The equations are 2x+y=70 and x+2y=80. Subtracting gives y-x=10. Substituting y=x+10 yields 3x=60, so x=20 and y=30. Check both original totals: forty plus thirty is seventy, and twenty plus sixty is eighty. Selecting twenty for the large size and thirty for the small size would use the same two numbers but violate the column meanings. The pair, its order and the units are all part of the answer.
Compare competing responses
Profit is 138-92=46. Profit is 138-92=46. Profit is 138-92=46. Profit is 138-92=46. (46)/(92) times 100=50 percent. The base is cost, not revenue. (46)/(92) times 100=50 percent. The base is cost, not revenue. (46)/(92) times 100=50 percent. The base is cost, not revenue. (46)/(92) times 100=50 percent. The base is cost, not revenue.
Profit is 138-92=46. (46)/(92) times 100=50 percent. The base is cost, not revenue.
Select and verify the complete response
Profit in credits: 46; Profit as a percentage of cost: 50
Profit is 138-92=46. (46)/(92) times 100=50 percent. The base is cost, not revenue.
Read the target and its restrictions
A warehouse picks plan, version 1, aims to shorten delays without increasing total cost. Its trial reduced delay, but the report gives no cost data. Select what remains necessary to establish the stated goal and what would demonstrate failure of that goal.
Distinguish independent from dependent tasks and select one supported response in each column.
Derive the deciding relationship
Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Check the information boundary
Decide when enumeration is efficient
A short common option list can make testing pairs faster than unrestricted algebra, especially when integer or order constraints eliminate many combinations. Begin with the most restrictive relationship. If one value must exceed the other by ten, identify option pairs with that difference before checking a total. Avoid testing all pairs blindly. If the same option is allowed twice, include equal pairs when the conditions permit them. When an answer set contains negatives or fractions, do not discard them merely because the context usually uses positive integers; instead read the explicit domain and ask whether such a value makes sense under that domain.
Compare competing responses
Delay reduction is established; the no-cost-increase condition remains unverified. Delay reduction is established; the no-cost-increase condition remains unverified. Delay reduction is established; the no-cost-increase condition remains unverified. Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell. An increase in total cost violates the conjunction defining success even if delay fell. An increase in total cost violates the conjunction defining success even if delay fell. An increase in total cost violates the conjunction defining success even if delay fell.
Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Select and verify the complete response
Needed to establish the goal: Total cost did not increase.; Demonstrates failure of the stated goal: Total cost increased.
Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Verify the target under the original conditions
Needed to establish the goal: Total cost did not increase.; Demonstrates failure of the stated goal: Total cost increased.
Distinguish independent from dependent tasks and select one supported response in each column. Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Read the target and its restrictions
A warehouse picks plan, version 1, aims to shorten delays without increasing total cost. Its trial reduced delay, but the report gives no cost data. Select what remains necessary to establish the stated goal and what would demonstrate failure of that goal.
Distinguish independent from dependent tasks and select one supported response in each column.
Derive the deciding relationship
Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Delay reduction is established; the no-cost-increase condition remains unverified. An increase in total cost violates the conjunction defining success even if delay fell.
Check the information boundary
Answer every part using the supplied sources. All parts must be correct.
For deliveries, case 1, two package sizes are sold. A small package has x units and a large package has y units. Two small packages plus one large contain 70 units. One small plus two large contain 80 units. Find each package size.
Answer every part using the supplied sources. All parts must be correct.
For repair orders, case 1, machine A completes a job alone in 21 hours and machine B in 31 hours. Each operates at a constant rate. Select the fraction of one job completed by each machine in one hour.
Answer every part using the supplied sources. All parts must be correct.
For support tickets, case 1, revenue is 138 credits and cost is 92 credits. Select profit and profit as a percentage of cost.
Answer every part using the supplied sources. All parts must be correct.
For training seats, case 1, nonnegative integers x and y satisfy x+y=24 and 2x+3y is at most 54. Select the minimum and maximum possible y.
Answer every part using the supplied sources. All parts must be correct.
Policy review for parts inspected, case 1: a proposal is eligible only if it reduces delay and stays within budget. Proposal P reduces delay, but no budget information has been supplied. Select one fact that establishes eligibility and one that rules it out. For this question the two conditions together are sufficient as well as necessary.
Answer every part using the supplied sources. All parts must be correct.
An analyst attributes a fall in subscriptions delays to a new reminder system in trial 1. The claim concerns the reminder's causal effect. Select evidence that strengthens and evidence that weakens this attribution. Treat each candidate as true.
Answer every part using the supplied sources. All parts must be correct.
In appointments review 1, every approved proposal has an audited budget. Some audited proposals were rejected. Select a statement that must be true and one that must be false.
Answer every part using the supplied sources. All parts must be correct.
A warehouse picks plan, version 1, aims to shorten delays without increasing total cost. Its trial reduced delay, but the report gives no cost data. Select what remains necessary to establish the stated goal and what would demonstrate failure of that goal.
Answer every part using the supplied sources. All parts must be correct.
In reservations audit 1, one report counts work completed in April and another counts work billed in April. Their totals differ. Evaluate each candidate as a hypothetical additional condition, separately. Select one that can reconcile the difference and one that would require equal totals.
Answer every part using the supplied sources. All parts must be correct.
For deliveries, case 2, two package sizes are sold. A small package has x units and a large package has y units. Two small packages plus one large contain 79 units. One small plus two large contain 89 units. Find each package size.
Answer every part using the supplied sources. All parts must be correct.
A 44-liter mixture for library loans, case 1, combines a 10-percent solution and a 40-percent solution to produce a 25-percent solution. Volumes add. Select the liters of each starting solution.
Answer three reserved questions without hints. These cases are separate from lesson practice.
Answer every part using the supplied sources. All parts must be correct.
A 50-liter mixture for library loans, case 2, combines a 10-percent solution and a 40-percent solution to produce a 25-percent solution. Volumes add. Select the liters of each starting solution.
Answer every part using the supplied sources. All parts must be correct.
For support tickets, case 2, revenue is 156 credits and cost is 104 credits. Select profit and profit as a percentage of cost.
Answer every part using the supplied sources. All parts must be correct.
For repair orders, case 2, machine A completes a job alone in 24 hours and machine B in 34 hours. Each operates at a constant rate. Select the fraction of one job completed by each machine in one hour.
After a study gap, recover the method without notes, then solve a different case. Identify the exact condition that decides the answer before comparing feedback.
15. Complete the final evidence check, step 3
Decide when enumeration is efficient
A short common option list can make testing pairs faster than unrestricted algebra, especially when integer or order constraints eliminate many combinations. Begin with the most restrictive relationship. If one value must exceed the other by ten, identify option pairs with that difference before checking a total. Avoid testing all pairs blindly. If the same option is allowed twice, include equal pairs when the conditions permit them. When an answer set contains negatives or fractions, do not discard them merely because the context usually uses positive integers; instead read the explicit domain and ask whether such a value makes sense under that domain.