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

Number Distance (Numerical Reasoning) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Number Distance (Numerical Reasoning) in British Army Cognitive Test (BARB), not a summary of it.

1. 1

   Number Distance Fundamentals

   3 topics

   • Format of the Number Distance sub-test
     • Three numbers presented on screen
     • Identifying which two numbers are furthest apart
     • Identifying which two numbers are closest together
   • Calculating numerical distance
     • Absolute difference between two values
     • Comparing the three possible pair distances
   • Selecting the correct number, not the distance
     • Reporting the value rather than the gap
2. 2

   Mental Arithmetic for Distance Problems

   3 topics

   • Fast subtraction strategies
     • Counting up from the smaller number
     • Rounding then adjusting
   • Comparing multiple differences quickly
     • Eliminating the obvious non-extreme pair
   • Handling close-together values
     • Distinguishing small gaps accurately
3. 3

   Number Sense and Accuracy

   3 topics

   • Recognising number magnitude at a glance
     • Place-value awareness for two and three digit numbers
   • Avoiding the furthest/closest swap error
     • Re-reading the question prompt each item
   • Timed practice and pacing
     • Building speed without sacrificing precision

Number Distance (Numerical Reasoning) flashcards for British Army Cognitive Test (BARB)

24 of 51 cards from the Number Distance (Numerical Reasoning) deck — real questions with worked answers.

1. What does the BARB (British Army Recruit Battery) assess, and where does the Number Distance sub-test fit?

   The BARB is a computerised psychometric test used by the British Army to assess cognitive aptitude and predict trainability. Number Distance is one of its sub-tests, measuring numerical reasoning by asking you to judge the gaps (distances) between numbers.

2. What is the basic format of a Number Distance question?

   You are shown a row of three numbers. You must identify which two are furthest apart (or closest together) and then select the number that is left over (the odd one out), not the size of the gap itself.

3. In Number Distance, what is the 'numerical distance' between two numbers?

   The absolute difference between them: for numbers $a$ and $b$ the distance is $|a-b|$. It is always a positive value regardless of order.

4. Write the formula for the distance between two numbers $a$ and $b$.

   $$d = |a - b|$$ The absolute value ensures the distance is non-negative.

5. Why is the distance defined using absolute value rather than simple subtraction?

   Because distance has no direction; $|a-b| = |b-a|$. Whether you subtract the larger from the smaller or vice versa, the magnitude of the gap is the same positive number.

6. The single most common mistake in Number Distance is answering the gap value. What should you actually select?

   You must select the third number (the one not involved in the largest or smallest pair), NOT the numerical distance itself. The distance is only used to decide which pair to pick.

7. A typical Number Distance question asks: 'Which number is furthest from the other two?' Restate what this is really asking.

   Find the number whose distances to both of the others are greatest overall, i.e. the outlier/extreme value, then select that number as your answer.

8. Given the three numbers 4, 7, 15, which two are furthest apart and what is that distance?

   The furthest pair is 4 and 15, with distance $|15-4| = 11$.

9. For the numbers 4, 7, 15, which two are closest together and what is the distance?

   The closest pair is 4 and 7, with distance $|7-4| = 3$.

10. Explain the 'furthest/closest swap error' in Number Distance.

    It is reading the question as asking for the closest pair when it actually asks for the furthest pair (or vice versa), then selecting the wrong number. Always re-read whether the question wants the largest or smallest gap before answering.

11. What is a reliable process for solving a 'which is furthest' Number Distance item with three numbers?

    1) Identify the smallest and largest of the three. 2) Their gap is the largest distance. 3) Decide which question is being asked. 4) For 'furthest from the others', select the extreme number; for the pair task, select the number NOT in the furthest pair.

12. For numbers $a < b < c$, which pair always has the greatest distance?

    The pair $(a, c)$ — the smallest and the largest — always has the greatest distance, equal to $c - a$, because the range spans the full set.

13. For three ordered numbers $a < b < c$, what are the three pairwise distances?

    $$|b-a|,\quad |c-b|,\quad |c-a|$$ where $c-a$ is always the largest because $(c-a)=(b-a)+(c-b)$.

14. Why does the gap between the smallest and largest equal the sum of the two inner gaps?

    For $a<b<c$, $(c-a) = (b-a) + (c-b)$. The total span is the sum of the two consecutive gaps, so the outer pair is necessarily the widest.

15. Describe a fast subtraction strategy for finding the distance between 38 and 52.

    Count up from the smaller to the larger in convenient jumps: 38 to 40 is 2, 40 to 52 is 12, total $2+12 = 14$. This 'bridging through a round number' avoids borrowing.

16. What fast mental strategy helps subtract numbers like 71 and 46 quickly?

    Round and adjust: $71 - 46$. Treat as $71 - 50 = 21$, then add back the 4 you over-subtracted: $21 + 4 = 25$. So $71-46 = 25$.

17. How can you use 'complements to round numbers' to speed up distance calculations?

    Bridge through the nearest ten or hundred. For $|83-67|$: 67 up to 70 is 3, 70 up to 83 is 13, so distance $= 3+13 = 16$. Splitting at the round number removes borrowing.

18. When comparing multiple differences quickly, what shortcut avoids computing every exact distance?

    Compare the most extreme candidates first. The smallest and largest numbers usually form the widest gap, so you can often confirm the answer by checking that pair rather than calculating all three differences exactly.

19. For 12, 14, 30, identify the number that is furthest from the other two.

    30 is furthest: its distances are $|30-12|=18$ and $|30-14|=16$, both far larger than the $|14-12|=2$ gap between the other two.

20. What does 'handling close-together values' refer to in Number Distance, and why is it tricky?

    It refers to items where two or all three numbers are numerically near each other (e.g. 47, 48, 51). Small gaps are easy to misjudge at a glance, so you must subtract carefully rather than estimate.

21. 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.

22. 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.

23. 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.

24. 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.

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