Numerosity

What you see

The top of the screen shows an expression written left to right: some numbers and operators are printed, and some are dashed blanks. After the equals sign sits the target, a whole number. Below is the Tray: number tiles and, at higher levels, operator tiles (+, −, ×, ÷).

• One blank is selected at a time. Choosing a tray tile drops it into the selected blank if the kinds match; otherwise it goes into the next empty blank of its kind. The selection then moves on to the next empty blank. Choosing the tile in the selected blank again takes it back.
• Choose a blank to select it, or move between blanks with the Left and Right arrow keys. Clear (Backspace) takes the tile in the selected blank back to the tray.
• Typing a number places the unused tile with that value, wherever it sits in the tray. A digit that could start a longer number on the tray waits briefly for the next digit. The keys + - * / place operator tiles, and x also gives ×.
• Each tile can be used once. A placed tile is greyed out in the tray.
• Standard precedence applies: × and ÷ are worked first, left to right, then + and −, left to right. There are no brackets.
• Division must come out exact. A fill that would divide 7 by 2 does not produce a value at all, so it can never match the target.

Once every blank is filled, the line under the board shows what the expression really makes, for example 8 × 3 − 7 = 17, or why it makes nothing, for example 7 ÷ 2 does not divide exactly. If the expression does not equal the target, the = before the target becomes ≠. You can still take tiles back. Nothing is scored until you press Check answer (or Enter); the target box then turns green or red.

The tray always contains every tile a correct answer needs, plus decoys. A number decoy is a near miss of a true tile: one or two above or below it, or, for true values from 13 to 98, the same digits reversed (14 becomes 41). Occasionally it is just a random number in range. A number decoy never has the same value as a tile the answer needs. An operator decoy is an operator from the set in use at that level that none of the operator blanks needs, so it never duplicates a true operator (two decoys can be the same operator). At levels with operator blanks every second decoy is an operator: 2 number decoys and 1 operator decoy at levels 5 to 7, 2 of each at levels 8 and 9, and 1 of each at level 10.

At levels 1 and 2 any fill that reaches the target is accepted. From level 3 the generator only keeps trials with exactly one working fill, counting two tiles with the same value as the same choice. Numbers run from 1 (or 2) up to a ceiling between 9 and 19 depending on the level, and targets stay within 999 either side of zero. In practice mode there is no countdown; a clock counts up in the side rail, and a session starts at level 3.

What it measures

Despite its name, Numerosity is a test of exact symbolic arithmetic under constraints, not of estimating quantities. On our profile it feeds two places. In Reasoning it is the Numerical reasoning facet, carrying 7 percent of that dimension. In Planning it sits under Keeping options open, carrying 14 percent of that dimension, because with several blanks and single-use tiles, an early careless placement can make the rest impossible. Internally the game is weighted 60 percent numerical reasoning, 20 percent quantitative comparison and 20 percent working memory.

Three strands of research explain what the task draws on.

Working memory. Holding partial results while you compute the next step is a working memory job; DeStefano and LeFevre reviewed the evidence on how mental arithmetic loads working memory. That load is why multi-blank levels feel disproportionately harder than single-blank ones: each blank adds a value you must hold while testing the others.

Order of operations. Precedence is a convention, not a law of nature, and it is easy to slip back into reading left to right under pressure. Numerosity fixes the rule: 2 + 3 × 4 is 14, never 20. Our Number Builder game deliberately works left to right instead, so the contrast is worth keeping straight.

Number sense. The name comes from the approximate number system, the intuitive sense of magnitude that lets you tell at a glance that 30 dots are more than 20 without counting. Halberda, Mazzocco and Feigenson found that the precision of this sense in 14-year-olds correlated with their past maths achievement scores, going all the way back to kindergarten. The precision is described by a Weber fraction: the smaller the ratio difference you can reliably detect, the sharper your number sense. Halberda and Feigenson showed that this precision keeps improving through childhood and reaches adult levels surprisingly late.

You can try a quick estimation exercise here:

Practice drillSign in to try it

How it is scored here

The evaluator substitutes your tiles into the expression and evaluates it with standard precedence.

• It hits the target: Correct, whatever fill you used.
• It misses: Partly correct, with credit capped at half (Incorrect if the credit is zero). The evaluator finds the valid solution that agrees with your fill in the most blanks and gives you 50 percent times the share of blanks that agree. With four blanks and two matching, that is 25 percent. With no blanks matching, it is zero.

Difficulty adapts after each trial: a Correct answer moves you up one level, a Partly correct one keeps you at the same level, and an Incorrect one (zero credit) moves you down. Your 0–100 Numerosity score is centred so that 50 means what the difficulty you work at predicts. Accuracy carries most of the weight; time matters a little (15 percent of the weight). A score appears after at least four trials, and recent sessions count for more. The session report headline is Blanks filled as in a correct solution: across your trials, the share of blanks you filled in agreement with a valid solution.

Where you will meet it

Filling blanks in an equation is one of the most common numerical formats in game-based aptitude tests, and Indian candidates meet it in campus rounds.

Aon describes digitChallenge as measuring your ability to solve basic arithmetic using mental calculation, with difficulty that rises as you answer correctly and falls when you answer wrongly. Numerosity is a close cousin rather than a copy. It adds decoy tiles and operator blanks, uses division, and fixes the order of operations. Those extras make it a slightly broader workout: if you are comfortable at level 7 and above here, a digits-only keypad format should feel familiar.

The method

1. Split the expression into terms

   Under precedence, an expression is a sum and difference of terms, where each term is a run of numbers joined by × or ÷. In _ × 3 − _ = 19, the terms are (blank × 3) and (blank). Work at the level of terms first, individual tiles second.

2. Move everything known to one side

   If a term is fully known, subtract it from (or add it to) the target. What remains is the value the unknown terms must produce together.

3. Estimate before you calculate

   Ask how big things are. If the known numbers are small and the target is large, a × must be doing the work. If the target is smaller than a printed number, a − or ÷ must be pulling it down.

4. Fill the most constrained blank first

   An operator blank next to ÷ is limited by divisibility. A blank multiplied by a printed number must make a multiple of it. Start where the fewest tiles could fit, which keeps the other tiles available for later blanks.

5. Screen the decoys

   For each candidate tile, check its neighbours in the tray. If 8 and 7 are both there, only one can be right; test the arithmetic, not the look. Reversed digits (14 and 41) are a hint that one of them is a decoy.

6. Verify, then check

   Recompute the whole expression under precedence once. When the line under the board shows the target and the sign reads =, press Check answer.

Worked example 1

Use the trial shown at the top of this lesson: _ × 3 − _ = 19, with tiles 7, 5, 8 and 6.

Show the solution

Terms. The expression is (first blank × 3) minus (second blank). So 3 × first − second = 19, which means 3 × first = 19 + second.

Estimate. 3 × first must be more than 19, so the first blank is at least 7. The candidates in the tray are 7 and 8.

• First blank 7: 21 − second = 19, so the second blank is 2. There is no 2. Rejected.
• First blank 8: 24 − second = 19, so the second blank is 5. There is a 5. Accepted.

Answer: 8 × 3 − 5 = 19. The decoys were 7 (one below 8) and 6 (one above 5), exactly the near-miss pattern the game uses.

Worked example 2

Show the solution

Most constrained first. The operator blank sits between 12 and 4, and the tray offers ÷, × and −. Try each against the target of 7.

• 12 × 4 = 48. Then 48 + blank = 7 needs a negative number. Rejected.
• 12 − 4 + blank = 7 means 8 + blank = 7. Also needs a negative. Rejected.
• 12 ÷ 4 = 3. Then 3 + blank = 7, so the blank is 4. There is a 4 in the tray. Accepted.

Answer: 12 ÷ 4 + 4 = 7. The size check did the work here: the target is much smaller than 12, so the operator had to shrink 12 a lot, and only ÷ does that.

Worked example 3

Show the solution

Estimate. The target 21 is not far above 9, so 9 is unlikely to be multiplied. That points to 9 + (something) = 21, with the something built from the number blank and 3.

Move the known part. 21 − 9 = 12. So the rest, (number, operator, 3), must make 12 as a single term. With × that is number × 3 = 12, so the number is 4. There is a 4. With ÷ it would be number ÷ 3 = 12, so 36, which is not in the tray.

Check the whole expression under precedence: 9 + 4 × 3 = 9 + 12 = 21. Answer: +, 4, ×.

A quick search confirms the estimate. 9 × 4 ÷ 3 = 12 and 9 + 6 + 3 = 18. Anything starting 9 × followed by + or − lands at 33 or more, and anything starting 9 − stays well below 21. Exactly one fill works.

Tips and traps

Levelling up

The jumps come at level 3 (multiplication, and exactly one answer), level 5 (division, and the first operator blank), level 6 (four numbers), and level 8 (two operator blanks). Operator blanks are the biggest change, because they multiply the options and because the operator you choose decides how precedence groups the rest.

• With two operator blanks, list which operator pairs are even possible from the tray before choosing numbers. Often only two or three pairs survive a size check.
• At four numbers, mark the terms explicitly. A × placed in the middle binds its neighbours into one term and changes what everything else must do.
• Keep your options open. If two blanks both want the same tile, fill the one with no alternative first.

1. Week 1
   • Three sessions of 12 to 15 trials, saying the terms aloud before placing any tile
   • Before each answer, estimate whether the target needs a × or a ÷
   • Note every left-to-right error you catch and rework it
2. Week 2
   • Three sessions aiming for level 5 and above
   • On operator-blank trials, list the possible operators before choosing numbers
   • Pair with one Number Builder session to contrast left-to-right evaluation with standard precedence
3. Week 3
   • Three sessions holding level 7 or above
   • Aim to press Check answer the first time the expression is complete, with no tiles taken back
   • Practise mental multiplication tables up to 19 × 9 for five minutes a day

Check yourself

5 practice questions

1. 4 + _ × 2 = 20. The tray holds 6, 8 and 9. Which tile goes in the blank?
2. Why can 15 ÷ 4 never appear in a correct Numerosity answer?
3. A level 8 trial has four blanks. Your fill misses the target, but two of your four tiles agree with the one valid solution. What do you score?

and 2 more

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Sources

1. Aon. Practice Tasks: Deductive Numeracy (digitChallenge). PDF
2. Aon. Prepare for your online assessment: Numeracy (digitChallenge). aon.com
3. DeStefano, D., & LeFevre, J.-A. (2004). The role of working memory in mental arithmetic. European Journal of Cognitive Psychology, 16(3), 353–386. doi.org
4. Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668. PubMed
5. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the number sense: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457–1465. PubMed
6. Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. PubMed
7. PrepInsta. Capgemini Exceller game-based aptitude test questions (candidate-reported). prepinsta.com

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