Why isn't the answer to TMUA-P1-MNUM-045 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MNUM-045 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MNUM-045?

No — calculators are banned in the TMUA. TMUA-P1-MNUM-045 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-045?

TMUA-P1-MNUM-045 is Paper P1 · Number (specification code M-Num), level 3. Drill more of the same topic from this page.

TMUA-P1-MNUM-045 — Paper P1 · Number · Level 3

P1M-NumLevel 3~180s target

Spec: M-Num · No calculator · ~180s

What is the remainder when

5^{50}

is divided by

6

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

Modulo

6

5 \equiv -1

, so

5^{50} \equiv (-1)^{50} = 1

. The remainder is

1

.
Trap:

5

answers with the base instead of reducing it modulo

6

Keep practising

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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?
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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: modular-cycle

P1M-NumLevel 2

TMUA-P1-MNUM-013

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

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Open TMUA-P1-MNUM-013 →

TMUA-P1-MNUM-045 — Paper P1 · Number · Level 3

Options

Keep practising

Master Number

TMUA-P1-MNUM-045 — Paper P1 · Number · Level 3

Options

Keep practising

Master Number