Why isn't the answer to TMUA-P2-PRF5-013 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-PRF5-013 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-PRF5-013?

No — calculators are banned in the TMUA. TMUA-P2-PRF5-013 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-PRF5-013?

TMUA-P2-PRF5-013 is Paper P2 · Following proofs (specification code PRF5), level 3. Drill more of the same topic from this page.

TMUA-P2-PRF5-013 — Paper P2 · Following proofs · Level 3

P2PRF5Level 3~270s target

Spec: PRF5 · No calculator · ~270s

Let

P

be “

n

is a multiple of

48

”,

Q

be “

n

is a multiple of

24

”, and

R

be “

n

is a multiple of

8

”. It is shown that

P \Rightarrow Q

and

Q \Rightarrow R

. Which verdict about

P

and

R

is correct?

Options

$P$ and $R$ are equivalent.
$R$ implies $P$ .
No chain links $P$ to $R$ .
$P$ implies $R$ by chaining ( $n = 48k = 8(6k)$ ), but $R$ does not imply $P$ : e.g. $n = 8$ is a multiple of $8$ but not of $48$ .

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: chain-transitivity, single-counterexample. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Transitivity yields

P \Rightarrow R

with explicit witness

n = 8(6k)

. The converse fails by the single counterexample

n = 8

. Trap: assuming chains reverse (upgrading divisibility by

8

to divisibility by

48

), or refusing to chain linked implications at all.

Keep practising

Same topic · same level
P2PRF5Level 3
TMUA-P2-PRF5-005
A revision guide prints a short proof without a theorem statement: suppose x and y are rational, write x = a/b and y = c…
Following proofs
Open TMUA-P2-PRF5-005 →
Same trap: single-counterexample
P2ARG1Level 3
TMUA-P2-ARG1-009
A textbook exercise states the following facts about positive integers, where P is “ n is divisible by 6 ” and Q is “ n…
Statements and connectives
Open TMUA-P2-ARG1-009 →
More in this topic
P2PRF5Level 3
TMUA-P2-PRF5-011
Three statements P, Q, R satisfy P ⇒ Q, Q ⇒ R and R ⇒ P. A study group offers five verdicts about the trio. Which is cor…
Following proofs
Open TMUA-P2-PRF5-011 →

Browse more

Loading…

Options

P

and

R

are equivalent.

R

implies

P

No chain links

P

R

P

implies

R

by chaining (

n = 48k = 8(6k)

), but

R

does not imply

P

: e.g.

n = 8

is a multiple of

8

but not of

48

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

Keep practising

Same topic · same level

P2PRF5Level 3

TMUA-P2-PRF5-005

A revision guide prints a short proof without a theorem statement: suppose x and y are rational, write x = a/b and y = c…

Following proofs

Open TMUA-P2-PRF5-005 →

Same trap: single-counterexample

P2ARG1Level 3

TMUA-P2-ARG1-009

A textbook exercise states the following facts about positive integers, where P is “ n is divisible by 6 ” and Q is “ n…

Statements and connectives

Open TMUA-P2-ARG1-009 →

TMUA-P2-PRF5-013 — Paper P2 · Following proofs · Level 3

Options

Keep practising

Master Following proofs

TMUA-P2-PRF5-013 — Paper P2 · Following proofs · Level 3

Options

Keep practising

Master Following proofs