electronicity.space

USS · Paper II

Data & reasoning

Data handling, averages, series, and the puzzle questions.

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What the paper asks

Five questions. Number and letter series, averages, median and mode, coding, odd-one-out and simple logic puzzles. There is little to learn here and a lot to practise — speed comes from having met the pattern before, not from being cleverer on the day.

Number series — check the gaps first
  • Write the differences underneath. If they are constant, it is a simple step.
  • If the differences themselves form a pattern, use that. 3, 6, 11, 18, 27 → gaps 3, 5, 7, 9 → next gap 11 → 38.
  • If the numbers grow fast, test multiplying: 5, 10, 20, 40 → ×2 → 80.
  • Recognise the standard families on sight — squares, cubes, primes and Fibonacci.
FamilySequence
Squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Cubes1, 8, 27, 64, 125
Primes2, 3, 5, 7, 11, 13, 17, 19
Fibonacci1, 1, 2, 3, 5, 8, 13, 21 — each is the sum of the two before
Triangular1, 3, 6, 10, 15, 21
Averages, median, mode, range
  • Mean = total ÷ count. And total = mean × count — the reverse is asked just as often.
  • Median = the middle value once ordered. With an even count, the mean of the middle two.
  • Mode = the value that appears most often.
  • Range = largest − smallest. It measures spread, not size.
  • Order the numbers before finding a median. Skipping that step is the usual error.
Coding and letter series
  • The commonest code is A = 1 … Z = 26. Learn the anchors: E = 5, J = 10, O = 15, T = 20, Z = 26.
  • Read the letters in the order given, not alphabetically. CAB is 3, 1, 2 → 312.
  • For letter series, count the gaps in the alphabet. Z, X, V, T skips one each time, so R comes next.
  • Reverse-alphabet codes (A = 26, Z = 1) appear too — check the first letter against both.
Logic and everyday problems
  • Chained comparisons: A > B and B > C gives A > B > C, so C is smallest.
  • Days of the week: divide by 7 and use the remainder. 10 days on from Wednesday → remainder 3 → Saturday.
  • Inverse proportion: twice as many workers, half the time.
  • When the answer must be a whole object, round down. ₹63 buys 12 pencils at ₹5, not 12.6.
  • Clock angles: each hour mark is 30° apart.
Odd one out
  • Look for the property three of them share. Squares, cubes, primes, multiples, or a category.
  • 8, 27, 36, 64 — three are cubes; 36 is a square but not a cube.
  • 9, 16, 24, 25 — three are squares; 24 is not.
  • If numbers do not reveal it, try the category: table, chair, bench, bread.
Worked through

What comes next: 2, 6, 12, 20, 30, ___ ?

  1. Gaps: 4, 6, 8, 10 — rising by 2 each time.
  2. Next gap is 12.
  3. 30 + 12 = 42. (The terms are also 1×2, 2×3, 3×4, 4×5, 5×6, then 6×7.)

In a class of 40, 60% are girls. How many boys?

  1. Girls 60%, so boys 40%.
  2. 40% of 40 = 16.
  3. Check: 24 girls + 16 boys = 40.

If 5 workers finish a job in 10 days, how long for 10 workers?

  1. More workers means less time — inverse proportion.
  2. Total work = 5 × 10 = 50 worker-days.
  3. 50 ÷ 10 workers = 5 days.
Where the marks go

These are the mistakes, not the rules — each one is something a student who knows the topic still does under time pressure.

  1. Assuming a constant gap after checking only the first step. 5, 10, 20 is doubling, not +5.
  2. Finding the median without ordering the numbers first.
  3. Treating workers-and-days as direct proportion. More workers means fewer days.
  4. Rounding a whole-object answer upward.
  5. Coding letters alphabetically rather than in the order they appear in the word.
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