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6. Grouping, Data Sufficiency and Critical Reasoning

CSS GSA — Paper 7, Part-II, Section VII, Sub-topic 6 (Grouping, Data Sufficiency and Critical Reasoning)

Past Paper Weightage

  • Moderate — data sufficiency and critical reasoning are less frequent than arrangement puzzles, but predictable in format once the shortcut is known.

Grouping/Selection Puzzles — Shortcut Method

  • Trick: Most grouping questions reduce to a straightforward combination formula
nCr=n!r!(n−r)!{}^nC_r = \frac{n!}{r!(n-r)!}

once you correctly identify the eligible pool size (n) and the number to choose (r) — the hard part is usually just applying any "exclude/include specific person" condition to shrink the pool BEFORE applying the formula.

  • Step order: (1) Apply any forced inclusions/exclusions to adjust the pool and the remaining slots to fill; (2) THEN apply the combination formula to what's left.

Worked Example (Grouping)

  • A committee of 3 must be chosen from 4 men and 3 women. How many valid committees exclude a specific man, X?
    • Step 1: Since X must be excluded, remove him from the pool: pool shrinks from 7 to 6 people (3 remaining men + 3 women).
    • Step 2: We still need to choose 3 from these 6, with no other restriction — apply ⁶C₃.
    • Step 3: Calculate: ⁶C₃ = 6!/(3!×3!) = (6×5×4)/(3×2×1) = 120/6 = 20 valid committees.

Data Sufficiency — Shortcut Method

  • Trick: Test EACH statement completely separately first (never combine them on your first pass). Ask only: "does this statement alone pin down ONE unique answer?" — not "what is the answer."
  • Standard 5-option shortcut labels: (A) Statement 1 alone is sufficient, Statement 2 is not; (B) Statement 2 alone is sufficient, Statement 1 is not; (C) Both together are needed (neither alone suffices); (D) Either alone is sufficient; (E) Even both together are insufficient.

Worked Example (Data Sufficiency)

  • "What is the value of x?" Statement 1: x + 5 = 12. Statement 2: x is a positive integer.
    • Step 1: Test Statement 1 alone: x+5=12 → x=7, one unique value — sufficient alone.
    • Step 2: Test Statement 2 alone: "x is a positive integer" fits infinitely many values — not sufficient alone.
    • Step 3: Since Statement 1 alone works but Statement 2 alone doesn't, the answer matches label (A).

Critical Reasoning — Shortcut Method

  • Trick: First identify the argument's conclusion and its supporting evidence separately. To weaken: find an option that breaks the link between evidence and conclusion (usually by suggesting an alternative cause). To strengthen: find an option that reinforces that the evidence really does cause/support the conclusion.
  • Ignore any answer choice that is simply true-but-irrelevant to the specific logical link in the argument — a very common wrong-answer trap.

Worked Example (Critical Reasoning)

  • Argument: "Sales of umbrellas rose sharply this month, so it must have rained more than usual." Which most weakens this?
    • Step 1: Identify conclusion ("it rained more") and evidence ("umbrella sales rose").
    • Step 2: Look for an alternative explanation for the sales rise unrelated to rainfall — "A major umbrella retailer ran a 50%-off promotion this month" does exactly this.
    • Step 3: This option breaks the assumed evidence→conclusion link, so it most weakens the argument.

MCQ Traps

  • In data sufficiency, don't solve for the actual numeric answer unless asked — only determine whether a unique answer CAN be found
  • In critical reasoning, an answer that is merely "related to the topic" but doesn't address the specific logical gap is a distractor, not the correct choice

Self-Test Questions

  1. From 5 men and 4 women, how many 4-person committees have exactly 2 men and 2 women? Show the combination steps.
  2. "What is y?" Statement 1: 2y − 3 = 11. Statement 2: y is even. Determine sufficiency using the shortcut labels.
  3. Argument: "Students who study in groups score higher on exams, so group study causes better exam performance." Which statement most weakens this argument?

Past-Paper MCQs (FPSC)

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The FPSC MCQ papers you shared (2024 and 2025) had no direct grouping, data-sufficiency or critical-reasoning question.

Past-Paper Questions with Answers (FPSC)

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No descriptive question asked for pure data-sufficiency or critical reasoning. The data-interpretation questions below (reading a table and a pie chart) are the closest. Answers are worked out by me.

  • CSS 2016 Q11(a): A distributor's stores by distance from the godown: up to 10 km: 3; 11–20: 15; 21–30: 26; 31–40: 20; 41–50: 16. (i) How many stores? (ii) most common distance? (iii) stores 35 km or more? (iv) percentage 31 km or more? (5)
    1. (i) Total stores = 3 + 15 + 26 + 20 + 16 = 80
    2. (ii) Most common distance (largest group) = 21–30 km (26 stores)
    3. (iii) Stores 35 km or more: the 41–50 km group gives 16 for certain; the 31–40 km group (20 stores) cannot be split from the table, so a spread-out estimate gives about 12 more, ≈ 28 in all (state the assumption)
    4. (iv) 31 km or more = 20 + 16 = 36 stores = 36 ÷ 80 = 45%
  • CSS 2018 Q7: Pie chart of a family's monthly spending: Food 15%, Travel 10%, Childcare 15%, Rent 26%, Local tax 10%, Utilities 8%, Other ?%. (5 each)
    1. (A) Other = 100 − (15 + 10 + 15 + 26 + 10 + 8) = 100 − 84 = 16%
    2. (B) Utilities + rent + food = 8 + 26 + 15 = 49%, about one half
    3. (C) Utilities Rs. 11,600 = 8%, so total = 11,600 ÷ 0.08 = Rs. 145,000
    4. (D) 'Other' is split savings : entertainment : luxury = 3 : 4 : 1. On Rs. 24,000, other = 16% = Rs. 3,840; savings = 3/8 × 3,840 = Rs. 1,440 a month

CSS Exam Perspective

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  • How this is tested: reading tables and charts (2016, 2018)
  • Tip: read titles and units first; check that percentages add to 100% and counts to the total