Grade 11 · Reading & language

Read necessary and sufficient conditions

Interpret the direction and limits of conditional statements without assuming their converses.

8 authored questions + worked example

Worked example

The workshop rule says, “A visitor may use the cutting station only if the safety briefing has been completed.” The rule does not say that completing the briefing guarantees a turn.

Which statement follows from the rule?

Answer & why

Answer: Anyone permitted to use the station must have completed the briefing.

“Only if” makes the briefing a necessary condition for permitted use. The final sentence explicitly rules out treating it as a guarantee.

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All questions

All 8 authored questions for this skill.

Question 1

A sensor cannot be installed unless it passes both checks. Passing both checks makes installation possible, but available space is also considered.

Which statement follows?

  1. Available space is the only requirement.
  2. A sensor failing either check cannot be installed.
  3. Passing one check is enough for installation.
  4. Passing both checks always guarantees installation.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: A sensor failing either check cannot be installed.

“Both” requires each check. Failing either means the required condition is not met; space prevents reading the condition as a guarantee.

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Question 2

Only measurements that include units may be entered in the comparison table. The editor will choose which eligible measurements are useful.

Which conclusion is supported?

  1. Measurements without units are always preferred.
  2. Every measurement with units must be entered.
  3. Every measurement entered in the table must include units.
  4. The editor must enter every available measurement.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: Every measurement entered in the table must include units.

Units are necessary for entry, while the second sentence preserves selection among eligible measurements.

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Question 3

The workshop rule says, “A visitor may use the cutting station only if the safety briefing has been completed.” The rule does not say that completing the briefing guarantees a turn.

Which statement follows from the rule?

  1. The station can never be used.
  2. Anyone permitted to use the station must have completed the briefing.
  3. Every person who completes the briefing is guaranteed an immediate turn.
  4. No briefing is needed to use the station.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: Anyone permitted to use the station must have completed the briefing.

“Only if” makes the briefing a necessary condition for permitted use. The final sentence explicitly rules out treating it as a guarantee.

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Question 4

The sorting instruction states, “If a book has a red label, place it on shelf R.” It gives no instruction saying that shelf R contains only red-labeled books.

Which conclusion is supported?

  1. Every book on shelf R must have a red label.
  2. Every book without a red label must be discarded.
  3. Every red-labeled book belongs on shelf R under this instruction.
  4. No red-labeled book belongs on shelf R.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: Every red-labeled book belongs on shelf R under this instruction.

The instruction moves from a red label to shelf R. Reversing that direction would add a rule the passage does not give.

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Question 5

The notice says the outdoor rehearsal will proceed if no lightning is reported. If lightning is reported, the organizers will announce a decision after a safety review.

Which condition guarantees rehearsal under the stated notice?

  1. No lightning is reported.
  2. The passage gives no condition for rehearsal.
  3. Lightning is reported and no decision has been announced.
  4. Any report of lightning guarantees immediate rehearsal.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: No lightning is reported.

The first sentence directly guarantees rehearsal when no lightning is reported. The other situation requires a later decision.

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Question 6

The display policy says, “A model will be displayed only when all three reviewers approve it.” It does not promise that every approved model will be selected for display.

Which conclusion follows?

  1. No displayed model can have approval.
  2. A displayed model must have approval from all three reviewers.
  3. One reviewer’s approval guarantees display.
  4. All approved models must be displayed.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: A displayed model must have approval from all three reviewers.

Approval by all three is required for display. It is not stated to be sufficient for selection.

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Question 7

Every proposal that reduces access must include an alternative route. The document does not require every proposal to reduce access.

Which statement is supported?

  1. No proposal can include an alternative route.
  2. Any proposal with an alternative route must reduce access.
  3. All proposals reduce access.
  4. A proposal that reduces access needs an alternative route.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: A proposal that reduces access needs an alternative route.

The requirement applies to the specified proposals. Neither its converse nor a claim about all proposals is stated.

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Question 8

A request is eligible for review if it arrives by Friday. Reviewers may still decline it after examining the evidence.

What does timely arrival establish?

  1. It proves every late request is accepted.
  2. It guarantees acceptance.
  3. It establishes eligibility for review, not guaranteed acceptance.
  4. It means the evidence will never be examined.
A hint

Track the direction of the condition. A requirement for an outcome does not automatically guarantee that outcome; a sufficient condition need not be the only route.

Answer & why

Answer: It establishes eligibility for review, not guaranteed acceptance.

The first sentence grants review eligibility; the second explicitly separates eligibility from acceptance.

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