Data and Percentage

11 students, 2 jumps each — the longer jump counts. Student 6 turned a modest 4.6m into a 5.7m second jump. Student 9 peaked at 5.5m on their first attempt. One slip in the ranking and you'll call the wrong 5th place.

Table-reading and ranking questions appear regularly at the easier end of NSW Selective TS — they reward students who read the scoring rule carefully and process every row systematically before ranking.

The examiner tests whether students can apply a simple rule (take the maximum of two values), process all rows without skipping, and correctly sort a list — especially when the best attempt is the first one (a common trap).

A table gives two values per student (two attempts, two scores, two measurements). The 'result' is the larger (or smaller) value. Students calculate each result, rank all students, and identify who is in a specific position. Options include students near the target rank to test careful reading.

Five made-up coins in Oceantown: azzes, bayos, cotts, duits and enits. Four conversion rates are given. How many of the smallest coin fit into the largest? Chain the multiplications one step at a time.

Chained unit conversion questions appear regularly on NSW Selective TS Mathematical Problem Solving. The values always chain neatly — each step is a single multiplication. The trap is skipping a step or multiplying in the wrong direction.

The examiner tests whether students can (a) read each conversion in the correct direction (bigger unit = more of the smaller), (b) chain four multiplications without error, and (c) avoid the trap of stopping too early (after only three steps, you get 16 — option A — which is wrong).

A fictional currency (or measurement) system gives a chain of conversions from smallest to largest unit. Students must find how many of the smallest unit fit into the largest by multiplying step by step.

60 legs in a dog park, 8 owners — some with 1 dog, some with 2. No one tells you how many of each, but two simple equations crack it. The secret: every extra dog adds exactly 4 legs.

Leg-count word problems with two unknowns appear regularly in NSW Selective TS at medium difficulty — they are disguised simultaneous equations that reward students who can translate a story into algebra.

The examiner tests whether students can set up two equations from a word problem (one for totals, one for leg counts), solve them, and verify the answer — rather than guessing or trial-and-error through all four options.

A scene describes two groups of people/animals, each contributing a different number of legs. The total count and total legs are given. Students form a system of two equations (count + legs) to find how many are in each group.

A zoo has snakes (0 legs), horses (4 legs), and eagles (2 legs). Nine animals, 10 legs total — what is the highest possible number of snakes? The trick: maximising one type means minimising the others, and you can only try a handful of combinations.

Maximise/minimise questions with simultaneous constraints appear regularly on NSW Selective TS Mathematical Problem Solving. They are distinct from standard equation questions because students must not only satisfy the equations but also optimise — choosing values that push one variable as high (or as low) as possible.

The examiner checks whether students can (a) convert the word problem into two equations, (b) recognise that maximising snakes means minimising horses + eagles, (c) apply the constraint that each animal type must appear at least once, and (d) test valid combinations starting from the minimum rather than guessing from the answer options.

Three quantities are linked by two linear equations (total count and total legs/cost/weight). One quantity contributes zero to the second equation (snakes have no legs), making it the easiest to maximise. Students must find valid whole-number solutions and then identify which gives the largest (or smallest) value of the target quantity.

Three piles of tokens — 2-point, 5-point, 10-point — all with the same count. Two piles together make 96. Which two? The answer must give a whole number of tokens, so only one pairing works.

Equal-count pile problems requiring systematic case testing appear regularly in NSW Selective TS Mathematical Problem Solving. The key constraint (n must be a whole number) eliminates all but one case, giving a unique answer. Recognising this constraint is the main skill being tested.

The examiner tests whether students can (a) represent pile totals algebraically (2n, 5n, 10n), (b) systematically test all three possible pairs of piles against the sum constraint, (c) reject pairs where n is not a whole number, and (d) calculate the remaining pile's total using the valid n.

Three groups each have n items worth different amounts. The combined total of two groups is given. Students test all three pairs, reject those giving non-integer n, and find the remaining group's total.

21 people vote on 5 movies. Kate says the winner needs at least 5 votes. Samira says 11 votes is a guaranteed win. To check Kate, you need to prove it's impossible for all movies to get 4 or fewer votes — a classic pigeonhole argument.

Voting minimum/majority problems appear in NSW Selective TS Mathematical Problem Solving. They test two complementary skills: proving the minimum winning vote count (Kate — pigeonhole) and proving a majority vote guarantees a win (Samira — majority). Questions ask whose reasoning is correct.

The examiner tests whether students can (a) prove Kate's claim by contradiction (5 movies × 4 max votes = 20 < 21, so winner needs ≥ 5), and (b) verify Samira's claim by checking 11 votes leaves only 10 for all others combined, making 11 unbeatable.

A vote-counting scenario gives total voters and number of options. Two people make claims — one about the minimum required to win, one about a vote count that guarantees winning. Both claims are correct and must be verified by arithmetic reasoning.

Data questions often start with a table: read every row carefully, then do one clear calculation — no guessing from the options.

Chart- and table-reading items appear regularly on Selective TS; many wrong answers come from misreading a single cell or skipping a row.

The examiner checks that you can extract the right numbers from a table and combine them accurately — separating “read the data” from “do the maths.”

A table lists values by category (e.g. books borrowed per month). You find a total, difference, or average using only the figures given.

Harder data items chain several steps: group sizes, fractions or ratios, then different percentages on different totals.

Multi-step survey problems sit in the harder third of Selective mocks — distractors are often the result of stopping one step early.

You must infer a missing group size, apply unlike fractions to each group, find supporters vs non-supporters, then apply two percentages to the correct bases and add only the final categories asked for.

A population is split across districts with different support rates; one district’s size is “the remainder.” Two follow-up percentages apply to different subgroups.

To guarantee a prize, your target student must be able to score high enough that even the best possible opponent score cannot beat them — and a tie doesn't count as winning.

Guarantee/minimum score questions appear in the harder half of Selective TS papers and combine table reading with reverse-calculation — a reliable source of marks once you know the method.

The examiner tests whether you can identify the one student who can mathematically guarantee the prize, find their worst-case rival, and calculate the exact minimum score needed — not forgetting the tie rule.

A table shows scores for multiple students across two completed tests. A third test is upcoming. A prize goes to the highest total; ties mean nobody wins. One student is flagged as able to guarantee the prize — find the minimum score they need in the final test.

A six-digit bike lock code. The middle two digits are the product of the first two. The last two are double the middle two. The first digit is 7 and all six digits are different. Only one value of the second digit makes everything work.

Digit constraint puzzles — where you must find unknown digits satisfying multiplication or doubling rules plus an all-different constraint — appear regularly in NSW Selective TS Mathematical Problem Solving.

The examiner checks whether students can (a) correctly interpret 'two-digit number formed by the middle two digits' as a two-digit positional number (not a sum), (b) set up the relationships as equations, (c) narrow the candidate range for the unknown digit, and (d) systematically test each candidate until all constraints are satisfied.

A multi-digit code is described using multiplication, doubling, or other arithmetic relationships between groups of digits. An all-different constraint eliminates most candidates. Students test each feasible value of the key unknown digit and identify the unique valid solution.