Why isn't the answer to TMUA-P1-MNUM-043 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MNUM-043 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MNUM-043?

No — calculators are banned in the TMUA. TMUA-P1-MNUM-043 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-P1-MNUM-043?

TMUA-P1-MNUM-043 is Paper P1 · Number (specification code M-Num), level 2. Drill more of the same topic from this page.

TMUA-P1-MNUM-043 — Paper P1 · Number · Level 2

P1M-NumLevel 2~180s target

Spec: M-Num · No calculator · ~180s

What is the remainder when

3^{20}

is divided by

7

Options

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: mnum-modular, modular-cycle. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Powers of

3

cycle mod

7

: since

3^6 = 729 = 7 \times 104 + 1

, we have

3^{18} \equiv 1

, so

3^{20} = 3^{18} \cdot 3^2 \equiv 9 \equiv 2 \pmod 7

. The remainder is

2

.
Trap:

1

spots the cycle but forgets the leftover

3^2

factor.

Keep practising

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Step up a level
P1M-NumLevel 3
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Keep practising

Same topic · same level

P1M-NumLevel 2

TMUA-P1-MNUM-005

What is the lowest common multiple (LCM) of 12, 18 and 20?

Number

Open TMUA-P1-MNUM-005 →

Same trap: modular-cycle

P1M-NumLevel 2

TMUA-P1-MNUM-013

What is the remainder when 2^10 is divided by 7?

Number

Open TMUA-P1-MNUM-013 →

Step up a 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 →

TMUA-P1-MNUM-043 — Paper P1 · Number · Level 2

Options

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Master Number

TMUA-P1-MNUM-043 — Paper P1 · Number · Level 2

Options

Keep practising

Master Number