PSLE Before-and-After Questions, Shown Working (incl. Helen and Ivan)

Q: Are these solutions reliable?

Each solution was worked independently then checked against the verified GPA key: the official marking scheme where one exists, and a handwritten key for 2021. Both examples agreed on every answer. Mrs Eileen Toh signs off the mathematics.

PSLE before-and-after questions, shown working.

The short version

A before-and-after question shows two moments with a change in between, and it rewards one disciplined move: find the quantity that stays constant, a total, a difference, or something that simply does not move, then compare across that constant rather than the surface numbers. Below are two worked examples, including the Helen and Ivan coins question, each solved cleanly and checked against the verified GPA key.

Figures from GPA's tagged index of 709 PSLE questions, 664-basis, with the MOE Specimen reported separately · every solution worked independently then checked against the verified GPA key · Mrs Eileen Toh signs off the mathematics · last reviewed 22 Jun 2026

Before-and-after questions are real, but rarer than the worry around them suggests.

When we tagged and counted across the fourteen years, before-and-after sat at 17 questions, fewer than the anxiety suggests. They are worth understanding well, because they all reward the same single move: find the quantity that stays constant, then compare across that. Learn that one habit and a whole category stops being a surprise.

A constant total

Two people share the same total, so a gain for one is a matching loss for the other.

A constant difference

When both change by the same amount, the gap between them holds steady throughout.

A quantity that does not move

One quantity is untouched by the change, so it anchors the before and the after on one scale.

These figures describe past papers, not a forecast of the next one. Source: GPA's tagged index of 709 PSLE questions, 664-basis, with the MOE Specimen reported separately.

Find the constant, then compare across it.

Every before-and-after question hides one quantity that the change does not touch. The work is to identify what is held constant, whether that is a total, a difference, or a quantity that simply does not change, and then compare across that constant rather than across the surface numbers the story happens to put side by side.

In change problems specifically, the same instinct applies: track the quantity that does not move. Once you have named it, the before-amounts, the change, and the after-amounts can all be placed on one scale, and the single fact the question gives you fixes everything else. That is the whole method, and the two examples below show it twice.

2021 · Paper 2 · Q15 the Helen and Ivan coins question

The same number of coins, swapped

The question

Helen and Ivan have the same total number of coins. Helen has a number of fifty-cent coins and 64 twenty-cent coins. The total mass of her coins is 1.134 kg. Ivan has a number of fifty-cent coins and 104 twenty-cent coins. (a) Who has more money, and how much more? (b) Each fifty-cent coin is 2.7 g heavier than each twenty-cent coin. What is the total mass of Ivan's coins in kg?

We reproduce this one because it made national news — the famous “Helen and Ivan” coins question, covered by Mothership. For other questions our pages point you to your Ten-Year Series instead.

Video: a Genius Plus Academy teacher solving PSLE 2021 Paper 2 Question 15, the Helen and Ivan coins question

Teacher video · 2021 P2 Q15

The lock

The two children share the same total number of coins, and that is the constant. The comparison that matters is the swap between coin types, not the raw masses.

The key

Hold the constant (the same number of coins), then read the difference as a set of swaps.

Worked steps

Same total number of coins, and Ivan has $104 - 64 = 40$ more twenty-cent coins, so Helen has 40 more fifty-cent coins than Ivan.
(a) Helen has more money: $40 \times \$0.50 - 40 \times \$0.20 = 20 - 8 = \$12$ more.
(b) Swapping a fifty-cent coin for a twenty-cent coin reduces mass by 2.7 g; Ivan's collection is Helen's with 40 such swaps: $40 \times 2.7 = 108$ g $= 0.108$ kg lighter.
Ivan's coins $= 1.134 - 0.108 = 1.026$ kg.

Answer: (a) Helen, by $12. (b) 1.026 kg.

What makes it click. The constant, the same number of coins, turns the whole problem into 40 swaps. Compare across the constant, not across the surface numbers.

Independently solved, matches the GPA handwritten key. Open the full worked solution →

2018 · Paper 2 · Q14 before, change, after

Ann's beads, before and after

Where to find it

This is a worded PSLE question, so we don’t reproduce it here. Find it in your Ten-Year Series (TYS) or the official paper — 2018 Paper 2, Q14, parts (a) and (b) (the before-and-after coloured-beads question) — then follow our worked solution below.

The lock

Two moments, before and after, with a change in between. The blue beads are the quantity to anchor in units; the after-ratio is read against the after-amounts, not the before-amounts.

The key

Let the blue beads before be a clean number of units, track the change, then read the after-ratio.

Worked steps

(a) $40\% = \frac{40}{100} = \frac{2}{5}$.
(b) Let blue before $= 5$u; she used 2u (the 40%), leaving 3u.
After, red left : blue left $=$ 1 : 3, so red left $=$ 1u, and red before $= 1\text{u} + 45$.
Total before: $(1\text{u} + 45) + 5\text{u} = 285$, so $6\text{u} = 240$ and u $= 40$.
Beads left $= 1\text{u} + 3\text{u} = 4\text{u} = 160$.

Answer: (a) 2/5. (b) 160 beads.

What makes it click. Naming the blue beads as 5 units lets the before-amounts, the change, and the after-ratio all live on one scale, so the single total of 285 fixes the unit.

Independently solved, matches the GPA marking-scheme key. Open the full worked solution →

Comparing the wrong two quantities.

In change and equal-total problems, children tend to subtract the two figures that happen to be adjacent in the story, rather than the two the question actually relates. In the Helen and Ivan question, the tempting move is to compare the raw masses; in Ann's beads, it is to read the after-ratio against the before-amounts. Both lead the same way: a confident subtraction of the wrong pair.

The fix is the same move that opens every one of these: find the quantity the question holds constant, and compare across that. Once the constant is named, the right pair to compare is no longer a guess, it is forced by the structure.

Questions parents ask

What is the Helen and Ivan PSLE question?

It is a commonly searched before-and-after question from PSLE 2021 Paper 2 Q15. Helen and Ivan have the same total number of coins, mixing fifty-cent and twenty-cent coins, and the task is to compare their money and the mass of Ivan's coins. The constant is the equal number of coins, which turns the problem into a set of 40 swaps. We solve it in full above.

How common are before-and-after questions in the PSLE?

They are real, but rarer than the worry around them suggests. Across the fourteen years we counted, before-and-after sat at 17 questions in our tagged index. They are worth understanding well because they all reward the same single move. This is analysis of past papers, not a forecast of the next one.

What is the one move that solves them?

Find the quantity that stays constant, a total, a difference, or a quantity that simply does not change, then compare across that constant rather than the surface numbers. In change problems, track the quantity that does not move. Once the constant is named, the right pair to compare is forced by the structure.

Are these solutions reliable?

Each solution here was worked independently and then checked against the verified GPA key: the official marking scheme where one exists, and a handwritten key for 2021. Both examples agreed on every answer. Mrs Eileen Toh signs off the mathematics. You can browse more in our worked-solutions library.

PSLE before-and-after questions, shown working.

Before-and-after questions are real, but rarer than the worry around them suggests.

Find the constant, then compare across it.

The same number of coins, swapped

Ann's beads, before and after

Comparing the wrong two quantities.

The 10 PSLE Question Types, cheat sheet

This trains finding the constant before comparing.

Keep reading

Questions parents ask

See how your child reads the change.