British Army Cognitive Test (BARB) Number Distance (Numerical Reasoning) Syllabus

For the close values 47, 48, 51, which pair is closest and which is furthest?

Closest pair: 47 and 48, distance $1$. Furthest pair: 47 and 51, distance $4$. Careful subtraction is essential because the gaps are small.

What is 'recognising number magnitude at a glance' and why does it matter in this sub-test?

It is the skill of instantly ordering numbers by size (smallest to largest) without detailed calculation, letting you quickly spot the extremes that form the widest or narrowest gaps and saving precious seconds.

How does sorting the three numbers first help you answer faster?

Once sorted as $a<b<c$, the structure is fixed: the widest gap is always $(a,c)$, the middle value $b$ is the 'in-between' number, and you only need to compare the two inner gaps $b-a$ and $c-b$ if the closest pair is asked.

If a Number Distance question asks for the number CLOSEST to the others, how do you find it?

Find the value with the smallest total distance to the rest — usually the middle number when values are evenly spread, or the one inside a tight cluster. Sort the numbers and check the inner gaps to confirm.

For 5, 6, 20, which number is closest to the other two?

Either 5 or 6 (both inside the tight cluster). 5 and 6 are distance 1 apart, while 20 sits far away at distances 15 and 14. The 'odd one out' / furthest is 20; the close pair is 5 and 6.

Why is timing critical in the Number Distance sub-test?

BARB sub-tests are strictly timed and adaptive; you must answer as many as possible correctly within the limit. Speed and accuracy together determine your score, so efficient mental arithmetic and pacing are essential.

What pacing principle should you apply if one Number Distance item is taking too long?

Do not dwell. Make your best judgement and move on, because spending too long on one item costs you several easier ones. Maintaining a steady rhythm maximises total correct answers within the time limit.

What is a good self-check before submitting a Number Distance answer?

Re-read whether the question asked for furthest or closest, and confirm you are selecting a NUMBER from the options rather than a distance value. This single check prevents the two most common errors.

Express the rule for the 'odd one out' (furthest) number when three values are given.

The furthest/odd number $x$ maximises the sum of its distances to the other two: $$x = \arg\max_i \big(|n_i - n_j| + |n_i - n_k|\big)$$ In practice it is the smallest or largest value, whichever lies further from the cluster.

Given 9, 11, 12, which is the odd one out (furthest from the others)?

9 is the odd one out: its distances are $|11-9|=2$ and $|12-9|=3$ (total 5), while 11 and 12 are only 1 apart. 9 sits furthest from the tight 11–12 cluster.

How do you quickly compare the two inner gaps for $a<b<c$ to find the closest pair?

Compute $b-a$ and $c-b$. The smaller result is the closest pair. If $b-a < c-b$, the closest pair is $(a,b)$; otherwise it is $(b,c)$.

For 3, 8, 9: use the inner-gap method to find the closest pair.

Inner gaps: $8-3 = 5$ and $9-8 = 1$. Since $1 < 5$, the closest pair is $(8,9)$, and the furthest pair is $(3,9)$ with distance 6.

What mental-maths habit reduces errors when subtracting across a ten (e.g. 53 − 28)?

Bridge the ten: 28 up to 30 is 2, 30 up to 53 is 23, total $2+23 = 25$. Counting up avoids the borrowing mistakes common in column subtraction under time pressure.

Why should you avoid stacked column subtraction during a timed Number Distance test?

Column subtraction with borrowing is slow and error-prone mentally. Counting up or rounding-and-adjusting is faster and less likely to produce mistakes when working at speed without paper.

Define 'range' for a set of three numbers and link it to Number Distance.

The range is the largest value minus the smallest: $\text{range} = \max - \min$. In Number Distance this range is exactly the greatest pairwise distance, identifying the furthest pair.

For 22, 35, 41, compute all three pairwise distances and name the furthest pair.

$|35-22|=13$, $|41-35|=6$, $|41-22|=19$. The furthest pair is 22 and 41 (distance 19), confirming the min–max pair is widest.

What is the key conceptual difference between the 'distance' and the 'number' in this sub-test?

The distance is the gap (a difference like 11), used only as a tool to decide the answer. The number is one of the three given values, which is what you actually choose. Confusing the two is the classic trap.

How can rounding to the nearest ten give a quick magnitude check for 68 and 41?

Round to 70 and 40: estimated gap $\approx 30$. Exact: $68-41 = 27$. The estimate confirms magnitude and ranking quickly, then refine only if two gaps are close.

When two candidate gaps look similar (e.g. distances of 14 and 16), what should you do?

Do not rely on estimation — compute both exactly, since close gaps are where misjudgement happens. The few seconds spent ensures you pick the genuinely larger or smaller gap.

For 100, 102, 130: which number is furthest from the other two and why?

130 is furthest: distances $|130-100|=30$ and $|130-102|=28$, both far greater than the $|102-100|=2$ gap. 130 is the clear outlier above a tight cluster.

Summarise the four-step routine recommended for every Number Distance item.

1) Read whether it asks furthest or closest. 2) Sort the three numbers by size. 3) Compute the relevant gap(s) using fast subtraction. 4) Select the correct NUMBER (not the distance) and move on quickly.

How does the adaptive nature of BARB affect your Number Distance strategy?

Correct answers can lead to harder items and contribute more to your score, so accuracy matters as much as speed. Steady, error-free pacing beats rushing and making careless furthest/closest or distance/number mistakes.

For 14, 19, 21, find the number closest to the other two.

Sort: 14, 19, 21. Inner gaps $19-14 = 5$ and $21-19 = 2$. The tight pair is (19,21), so 19 (or 21) is closest to another value; 14 is the furthest outlier.

Why is it useful to identify the middle number quickly?

The middle number is never part of the furthest (min–max) pair, so in 'furthest pair' tasks you can immediately rule it out as the gap-forming pair, narrowing your decision and saving time.

Give a fast way to compute the distance between 205 and 178.

Bridge: 178 up to 180 is 2, 180 up to 205 is 25, total $2+25 = 27$. So $|205-178| = 27$ without borrowing.

What does it mean to read 'magnitude at a glance' for numbers like 9, 90, 19?

Instantly recognising place value: 90 is by far the largest, 9 the smallest, 19 in between. Spotting that 90 dwarfs the others lets you pick the furthest number almost immediately without subtraction.

For 9, 19, 90, which two numbers are furthest apart?

9 and 90, distance $|90-9| = 81$ — far larger than $|19-9|=10$ or $|90-19|=71$. The min–max pair again forms the widest gap.

What practice routine builds speed for the Number Distance sub-test?

Regular timed drills of three-number difference problems, practising counting-up and round-and-adjust subtraction, and consciously checking the furthest/closest wording each time until the routine becomes automatic.

If you misread 'furthest' as 'closest', what type of answer will you likely give?

You will select the middle/cluster number instead of the extreme outlier (or vice versa) — typically the exact opposite of the intended answer. This is why confirming the wording before answering is essential.

For 60, 64, 95, identify both the closest pair and the furthest pair.

Closest pair: 60 and 64 (distance 4). Furthest pair: 60 and 95 (distance 35). 95 is the outlier; 60 and 64 form the tight cluster.

State the single most important rule to remember for scoring well on Number Distance.

Always answer with the correct NUMBER chosen according to whether the question wants the furthest or closest relationship — never report the distance, and never swap furthest for closest. Speed comes second to getting these two things right.