Why isn't the answer to TMUA-P2-ARG2-015 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ARG2-015 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ARG2-015?

No — calculators are banned in the TMUA. TMUA-P2-ARG2-015 is set for a no-calculator target of about 270 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ARG2-015?

TMUA-P2-ARG2-015 is Paper P2 · Necessary and sufficient (specification code ARG2), level 3. Drill more of the same topic from this page.

TMUA-P2-ARG2-015 — Paper P2 · Necessary and sufficient · Level 3

P2ARG2Level 3~270s target

Spec: ARG2 · No calculator · ~270s

A driving school states that passing the theory test is necessary but not sufficient for a full licence, because candidates must also pass the practical test. Let

T

be “passes the theory test” and

L

be “holds a full licence”. Dev has passed the theory test but has not taken the practical test. Five verdicts about Dev are offered. Which is valid?

Options

Dev is guaranteed to hold a full licence.
Dev cannot hold a full licence yet, because a necessary condition alone does not guarantee the licence and the practical pass is still missing.
Dev's theory pass must be invalid.
Anyone who passes the practical but not the theory automatically holds a licence.

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 (

L \Rightarrow T

) does not give sufficient (

T \Rightarrow L

); the licence needs the extra practical condition too. Dev satisfies

T

but the sufficient package (

T

plus practical) is incomplete. Trap: treating “necessary” as “sufficient” and concluding the theory pass alone guarantees the licence.

Keep practising

Same topic · same level
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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…
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Open TMUA-P2-ARG1-007 →
More in this topic
P2ARG2Level 3
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Three statements about an integer n are given: A is “ n is a multiple of 3 ”, B is “ n is a multiple of 12 ”, and C is “…
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Open TMUA-P2-ARG2-014 →

Browse more

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Options

Dev is guaranteed to hold a full licence.

Dev cannot hold a full licence yet, because a necessary condition alone does not guarantee the licence and the practical pass is still missing.

Dev's theory pass must be invalid.

Anyone who passes the practical but not the theory automatically holds a licence.

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

Keep practising

Same topic · same 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 →

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 →

TMUA-P2-ARG2-015 — Paper P2 · Necessary and sufficient · Level 3

Options

Keep practising

Master Necessary and sufficient

TMUA-P2-ARG2-015 — Paper P2 · Necessary and sufficient · Level 3

Options

Keep practising

Master Necessary and sufficient