Why isn't the answer to TMUA-P2-ARG2-006 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ARG2-006 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ARG2-006?

No — calculators are banned in the TMUA. TMUA-P2-ARG2-006 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ARG2-006?

TMUA-P2-ARG2-006 is Paper P2 · Necessary and sufficient (specification code ARG2), level 2. Drill more of the same topic from this page.

TMUA-P2-ARG2-006 — Paper P2 · Necessary and sufficient · Level 2

P2ARG2Level 2~210s target

Spec: ARG2 · No calculator · ~210s

An airline states that holding a valid passport is necessary but not sufficient for boarding an international flight, because passengers must also hold a valid boarding pass and pass security screening without any prohibited items in their luggage. Let

P

be “holds a valid passport” and

B

be “boards the flight”. Amara satisfies

P

but has not yet obtained a boarding pass. Which conclusion about Amara follows from the airline's statement?

Options

Amara is guaranteed to be able to board.
Amara cannot board yet, because a necessary condition alone does not guarantee boarding and she lacks the boarding pass.
Amara's passport must be invalid.
Anyone with a boarding pass but no passport can board.
Passports are irrelevant to boarding.

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: necessary-vs-sufficient-swap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Necessary (

\text{board} \Rightarrow \text{passport}

) does not give sufficient (

\text{passport} \Rightarrow \text{board}

); boarding needs the extra conditions too. Trap: treating “necessary” as “sufficient” and concluding the passport alone guarantees boarding.

Keep practising

Same topic · same level
P2ARG2Level 2
TMUA-P2-ARG2-003
Let P be “ n is a multiple of 4 ” and Q be “ n is even”, for an integer n. How is P related to Q?
Necessary and sufficient
Open TMUA-P2-ARG2-003 →
Same trap: necessary-vs-sufficient-swap
P2ARG1Level 2
TMUA-P2-ARG1-007
The notice reads: “A number n is prime greater than 2 only if n is odd.” If P is “ n is prime greater than 2 ” and Q is…
Statements and connectives
Open TMUA-P2-ARG1-007 →
Step up a level
P2ARG2Level 3
TMUA-P2-ARG2-008
A puzzle book gives two clues about three statements A, B and C concerning a hidden integer: clue one says that A is suf…
Necessary and sufficient
Open TMUA-P2-ARG2-008 →

Browse more

Loading…

Options

Amara is guaranteed to be able to board.

Amara cannot board yet, because a necessary condition alone does not guarantee boarding and she lacks the boarding pass.

Amara's passport must be invalid.

Anyone with a boarding pass but no passport can board.

Passports are irrelevant to boarding.

Letters only — the answer key is hidden. Work it out, then check the solution below.

Keep practising

Same topic · same level

P2ARG2Level 2

TMUA-P2-ARG2-003

Let P be “ n is a multiple of 4 ” and Q be “ n is even”, for an integer n. How is P related to Q?

Necessary and sufficient

Open TMUA-P2-ARG2-003 →

Same trap: necessary-vs-sufficient-swap

P2ARG1Level 2

TMUA-P2-ARG1-007

The notice reads: “A number n is prime greater than 2 only if n is odd.” If P is “ n is prime greater than 2 ” and Q is…

Statements and connectives

Open TMUA-P2-ARG1-007 →

Step up a level

P2ARG2Level 3

TMUA-P2-ARG2-008

A puzzle book gives two clues about three statements A, B and C concerning a hidden integer: clue one says that A is suf…

Necessary and sufficient

Open TMUA-P2-ARG2-008 →

TMUA-P2-ARG2-006 — Paper P2 · Necessary and sufficient · Level 2

Options

Keep practising

Master Necessary and sufficient

TMUA-P2-ARG2-006 — Paper P2 · Necessary and sufficient · Level 2

Options

Keep practising

Master Necessary and sufficient