Why isn't the answer to TMUA-P1-MNUM-031 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MNUM-031 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MNUM-031?

No — calculators are banned in the TMUA. TMUA-P1-MNUM-031 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MNUM-031?

TMUA-P1-MNUM-031 is Paper P1 · Number (specification code M-Num), level 3. Drill more of the same topic from this page.

TMUA-P1-MNUM-031 — Paper P1 · Number · Level 3

P1M-NumLevel 3~240s target

Spec: M-Num · No calculator · ~240s

Two numbers are in the ratio

5:7

. Adding

6

to each gives numbers in the ratio

3:4

. What is the smaller of the original numbers?

Options

$42$
$24$
$36$
$18$
$30$

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: mratio-algebra, combined-ratio. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Write the numbers as

5k

and

7k

\frac{5k + 6}{7k + 6} = \frac{3}{4}

, so

20k + 24 = 21k + 18

and

k = 6

. The smaller original is

5 \times 6 = 30

.
Trap:

42

solves for

k

correctly but reports the larger number.

Keep practising

Same topic · same level
P1M-NumLevel 3
TMUA-P1-MNUM-011
4000 is invested. It grows by 5\% in year one, then falls by 5\% in year two. What is its final value?
Number
Open TMUA-P1-MNUM-011 →
Same trap: combined-ratio
P1M-NumLevel 3
TMUA-P1-MNUM-012
A:B = 2:3 and B:C = 4:5. A total of 350 counters is shared in the ratio A:B:C. How many does B receive?
Number
Open TMUA-P1-MNUM-012 →
More in this topic
P1M-NumLevel 3
TMUA-P1-MNUM-022
What is the larger solution of 2x^2 - 7x + 3 = 0?
Number
Open TMUA-P1-MNUM-022 →

Browse more

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Keep practising

Same topic · same level

P1M-NumLevel 3

TMUA-P1-MNUM-011

4000 is invested. It grows by 5\% in year one, then falls by 5\% in year two. What is its final value?

Number

Open TMUA-P1-MNUM-011 →

Same trap: combined-ratio

P1M-NumLevel 3

TMUA-P1-MNUM-012

A:B = 2:3 and B:C = 4:5. A total of 350 counters is shared in the ratio A:B:C. How many does B receive?

Number

Open TMUA-P1-MNUM-012 →

TMUA-P1-MNUM-031 — Paper P1 · Number · Level 3

Options

Keep practising

Master Number

TMUA-P1-MNUM-031 — Paper P1 · Number · Level 3

Options

Keep practising

Master Number