PSLE Gaps and Differences Questions, Shown Working

Q: How often do gaps-and-differences questions appear in the PSLE?

In GPA's tagged index, gaps-and-differences questions appear 21 times across the fourteen years we counted. They are real but rarer than the worry suggests, turning up here and there rather than in every paper. This is honest analysis of past papers, not a forecast.

Q: What is the method for these questions?

Make a list and be systematic. When items come in fixed pack sizes, round up to whole packs, reason about quantity and value together, and test combinations against every constraint until one fits. A short, honest list does the work; there is no clever formula to memorise.

Q: What is the most common mistake?

Dividing, seeing a decimal, and being unsure whether to round. When items are sold only in whole boxes, the counts must be multiples of the box size, so you round up to whole boxes, then test combinations against the constraints. Rounding the wrong way is where marks slip.

Q: Is the worked solution reliable?

Yes. The worked example was solved independently and then checked against the verified GPA marking-scheme key, and the two agree on every answer. Mrs Eileen Toh signs off the mathematics. The full set is in the worked-solutions library.

PSLE gaps and differences questions, shown working.

The short version

A gaps-and-differences question gives you items in fixed pack sizes and a target gap, then asks for the combination that fits. The reliable method is to make a list and be systematic: when items come in fixed packs, round up to whole packs, reason about quantity and value together, and test combinations against every constraint until one fits. It rewards a short, honest list, not a clever formula.

Based on GPA's tagged index of 709 PSLE questions, with frequency figures from the 664 questions in the 14 papers actually sat 2012 to 2025 and 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

The word-problem types parents lose sleep over are real, but rarer than the worry suggests.

Gaps-and-differences questions appear 21 times across the fourteen years we counted. They turn up here and there rather than every single paper, and when they do, they reward systematic listing, not a clever formula. A child who knows the habit, round up to whole packs and test combinations against every constraint, meets a question that is steady and checkable rather than scary.

Make a list

Write the possibilities down in order. A short, honest list beats trying to guess a formula.

Round up to whole packs

When items come in fixed pack sizes, the counts must be multiples of the pack size, so round up.

Test against every constraint

Use quantity-and-value reasoning, then keep the one combination that satisfies all the conditions.

Figures from GPA's tagged index of 709 PSLE questions, on the 664-question basis from the 14 papers actually sat, with the MOE Specimen reported separately. This is honest analysis of past papers, not a forecast of the next one.

Make a list, be systematic, and let the constraints do the deciding.

These questions hand you items in fixed pack sizes, a difference to hit, and sometimes a total to stay under. There is no shortcut formula waiting to be remembered. The method is to be patient and orderly: make a list of the sensible possibilities, then test each one against every constraint until exactly one survives.

Two reflexes carry almost every question of this kind:

Round up to whole packs

When something is sold in boxes of seven, you cannot buy a part of a box. The counts must be multiples of the pack size, so when a division leaves a remainder, you round up to the next whole pack.

Reason about quantity and value

Hold two ideas at once: how many items each combination gives, and how much it costs. The right answer is the combination that hits the required gap and obeys every other condition.

Written down in order, the work is calm and self-checking. You are not hunting for a trick; you are eliminating possibilities until the question answers itself.

2018 · Paper 2 · Q17 buy in fixed boxes Gaps & Differences

The candles that only come in boxes

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, Q17, parts (a) and (b) (the buying-in-fixed-boxes question) — then follow our worked solution below.

Video: a Genius Plus Academy teacher solving PSLE 2018 Paper 2 Question 17

Teacher video · 2018 P2 Q17

The lock

A child divides 19 by 7, gets a decimal, and is unsure whether to round. You can only buy whole boxes, so the counts must be multiples of 7 and 5, and part (b) has exactly one combination that fits both conditions.

The key

Round up to whole boxes, then list box-combinations against the constraints. A short, honest list beats a clever formula.

Worked steps

(a) 3 long candles need 1 box ($3.20). 19 short candles need $19 \div 7 = 2$ remainder 5, so 3 boxes (21 candles, $2.50 each). Least cost $= 3.20 + 3 \times 2.50 = 10.70$.
(b) Long come in 5s, short in 7s. We need $5L - 7S = 21$ with total $5L + 7S < 50$.
Listing: $L = 7$ boxes gives 35 long; $S = 2$ boxes gives 14 short. Then $35 - 14 = 21$ and $35 + 14 = 49 < 50$. This is the one combination under 50.
Cost $= 7 \times 3.20 + 2 \times 2.50 = 22.40 + 5.00 = 27.40$.

Answer: (a) $10.70. (b) $27.40.

What makes it click. "Sold only in boxes" is the whole instruction: round up to whole boxes, then test box-counts against both conditions until one fits.

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

Dividing, then being unsure whether to round.

The mark slips away at one moment: a child divides, sees a decimal, and freezes. Nineteen short candles divided by seven is two and a bit, and the question is whether that "bit" rounds up or down. The instruction "sold only in boxes" decides it. When items are sold only in whole boxes, the counts must be multiples of the box size, so you round up to whole boxes, never down, because a part-box does not exist.

Once the counts are whole boxes, the second half of the trap disappears too. You stop searching for a formula and simply test combinations against the constraints: the required difference, and any limit on the total. List the box-counts in order, check each against every condition, and keep the one that fits. Calm and orderly beats clever here every time.

Questions parents ask

How often do gaps-and-differences questions appear in the PSLE?

In GPA's tagged index, gaps-and-differences questions appear 21 times across the fourteen years we counted. They are real but rarer than the worry suggests, turning up here and there rather than in every paper. This is honest analysis of past papers, not a forecast of the next one.

What is the method for these questions?

Make a list and be systematic. When items come in fixed pack sizes, round up to whole packs, reason about quantity and value together, and test combinations against every constraint until one fits. A short, honest list does the work; there is no clever formula to memorise.

What is the most common mistake?

Dividing, seeing a decimal, and being unsure whether to round. When items are sold only in whole boxes, the counts must be multiples of the box size, so you round up to whole boxes, then test combinations against the constraints. Rounding the wrong way, or guessing a formula, is where marks slip.

Is the worked solution reliable?

Yes. The worked example was solved independently and then checked against the verified GPA marking-scheme key, and the two agree on every answer. Mrs Eileen Toh signs off the mathematics. You can browse the full set in our worked-solutions library.

PSLE gaps and differences questions, shown working.

The word-problem types parents lose sleep over are real, but rarer than the worry suggests.

Make a list, be systematic, and let the constraints do the deciding.

The candles that only come in boxes

Dividing, then being unsure whether to round.

The 10 PSLE Question Types, cheat sheet

This trains systematic listing against a constraint.

Keep reading

Questions parents ask

See how your child reads a question like this.