Why isn't the answer to TMUA-P2-PRF5-009 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-PRF5-009 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-PRF5-009?

No — calculators are banned in the TMUA. TMUA-P2-PRF5-009 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-PRF5-009?

TMUA-P2-PRF5-009 is Paper P2 · Following proofs (specification code PRF5), level 2. Drill more of the same topic from this page.

TMUA-P2-PRF5-009 — Paper P2 · Following proofs · Level 2

P2PRF5Level 2~180s target

Spec: PRF5 · No calculator · ~180s

It is given that

p > q

and

q > r

, where

p

q

r

are real numbers. Which conclusion follows by chaining the inequalities?

Options

$r > p$ .
$p > r$ : adding the two given inequalities (or transitivity of $>$ ) gives $p > r$ .
$p = r$ .
Nothing follows without knowing the actual values.

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. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The relation

>

is transitive:

p > q > r

collapses to

p > r

(equivalently, adding

p > q

and

q > r

gives

p + q > q + r

, so

p > r

). Trap: reversing the chain or treating two linked comparisons as uncombinable.

Keep practising

Same topic · same level
P2PRF5Level 2
TMUA-P2-PRF5-002
A proof that the square of an odd integer is odd reads: (1) Write n = 2k + 1. (2) Then n^2 = 4k^2 + 4k + 1. (3)??? (4) H…
Following proofs
Open TMUA-P2-PRF5-002 →
Same trap: chain-transitivity
P2PRF5Level 1
TMUA-P2-PRF5-006
It is known that statement A implies statement B, and statement B implies statement C. Which conclusion follows by chain…
Following proofs
Open TMUA-P2-PRF5-006 →
Step up a 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 →

Browse more

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Keep practising

Same topic · same level

P2PRF5Level 2

TMUA-P2-PRF5-002

A proof that the square of an odd integer is odd reads: (1) Write n = 2k + 1. (2) Then n^2 = 4k^2 + 4k + 1. (3)??? (4) H…

Following proofs

Open TMUA-P2-PRF5-002 →

Same trap: chain-transitivity

P2PRF5Level 1

TMUA-P2-PRF5-006

It is known that statement A implies statement B, and statement B implies statement C. Which conclusion follows by chain…

Following proofs

Open TMUA-P2-PRF5-006 →

Step up a 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 →

TMUA-P2-PRF5-009 — Paper P2 · Following proofs · Level 2

Options

Keep practising

Master Following proofs

TMUA-P2-PRF5-009 — Paper P2 · Following proofs · Level 2

Options

Keep practising

Master Following proofs