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Paper IPaper I · General Mental Ability

Exam Strategy and Shortcuts

Time management, when to skip, negative-marking maths, calculation speed tricks, and a consolidated formula cheat sheet

CAPF wiki•5 min read•13 sections
At a glance
PaperPaper ISubjectGMASyllabusGeneral Mental Ability: logical reasoning, quantitative aptitude including numerical ability, and data interpretationImportanceHigh
GMAStrategyTime ManagementNegative MarkingSpeed MathsCheat SheetPaper 1

The General Mental Ability questions in Paper I are scoring and learnable, so the difference between candidates is usually time management and guessing discipline, not knowledge. This note covers how to spend your minutes, when to guess under negative marking, fast mental-maths tricks, and a one-page formula recall for the whole module.

Negative-marking maths

CAPF Paper I uses objective MCQs with negative marking, typically one third of a question's mark deducted for a wrong answer (verify the current pattern in the official notification each year through Index).

Situation Expected value of a guess Verdict
Blind guess, 4 options (1/4)(+1) + (3/4)(-1/3) = 1/4 - 1/4 = 0 Neutral; guessing neither helps nor hurts on average
Eliminate 1 option (3 left) (1/3)(+1) + (2/3)(-1/3) = 1/3 - 2/9 = 1/9 Positive; worth guessing
Eliminate 2 options (2 left) (1/2)(+1) + (1/2)(-1/3) = 1/2 - 1/6 = 1/3 Strongly worth guessing

Rule of thumb: if you can rule out even one option, the expected value of guessing turns positive, so guess. With no idea at all and a one-third penalty, a blind guess is break-even, so use judgement and avoid it under time pressure.

Time management

  • Do an easy first pass: in the first sweep, solve only the questions you can finish quickly and mark the rest. Never let a single hard sum eat three minutes early on.
  • Aim for a rough pace; if the GMA block holds about 50 to 60 questions, budget under one minute each, leaving a buffer for the second pass and the bubble check.
  • Reasoning and data interpretation tend to be faster per mark than long quantitative word problems; clear them first to bank marks.
  • Reserve the last few minutes to transfer any pending answers and to revisit only questions where you eliminated one or two options.

When to skip

  • Skip if the topic is one you have not drilled and the question is computation-heavy; the time cost is too high.
  • Skip a DI set only if the chart units are confusing; otherwise DI sub-questions reuse one reading, so they are efficient.
  • Do not skip series, analogy, coding, mirror and water image, or direction questions; these are fast and high-yield.
  • Mark and move on rather than abandoning; come back in the second pass with a fresh eye.

Calculation speed tricks

Trick How
Multiply by 5 Multiply by 10, then halve (47 times 5 = 470/2 = 235)
Multiply by 25 Multiply by 100, then divide by 4
Multiply by 11 (2-digit) Add the two digits, place between them (34 times 11: 3_(3+4)_4 = 374)
Square ending in 5 n5 squared = n(n+1) then append 25 (352 = 3 times 4 = 12, so 1225)
Percent swap x% of y = y% of × (8% of 50 = 50% of 8 = 4)
Fraction equivalents Use 1/8 = 12.5%, 1/6 = 16.66%, etc. (see percentage ratio and average)
Approximate then refine For wide-apart options, estimate to the nearest round figure first

Consolidated formula cheat sheet

Topic Key formula
LCM and HCF LCM times HCF = product of the two numbers
Sum 1 to n n(n+1)/2
Percentage change (change / original) times 100
Successive change a%, b% a + b + (ab/100)
Ratio division one part = total / (sum of ratio terms)
Average sum / count
Average speed (equal distance) 2ab/(a+b)
Alligation cheaper : dearer = (D - M) : (M - C)
Distance speed times time
km/h to m/s times 5/18
Boat (still water) (downstream + upstream)/2
Work together (two) ab/(a+b)
Profit percent (profit/CP) times 100
SP from profit% CP times (1 + p/100)
Same SP, plus and minus x% net loss = x2/100 percent
Simple Interest PRT/100
Compound Amount P times (1 + R/100)T
CI minus SI (2 years) P times (R/100)2
Pie chart 1% = 3.6°
Ranking in a line N = (rank from one end) + (rank from other end) - 1
Mirror image left-right flip
Water image top-bottom flip
Paper folding holes double per fold, symmetric about each fold line

Worked decision examples

Example 1: Should you guess?

You have a 4-option question and can confidently rule out two options. Should you guess from the remaining two?

Expected value = (1/2)(+1) + (1/2)(-1/3) = 1/2 - 1/6 = 1/3, which is positive. Yes, guess.

Example 2: Speed multiplication

Compute 64 times 25 quickly.

64 times 100 = 6400, then divide by 4 = 1600.

Example 3: Percent swap

Find 16% of 25.

Swap to 25% of 16 = a quarter of 16 = 4.

Example 4: Square ending in 5

Compute 45 squared.

n = 4, so n(n+1) = 4 times 5 = 20, append 25, giving 2025.

Practice questions

  1. A question has 4 options. You can eliminate one. Is guessing worthwhile?
  2. Compute 84 times 5 using the times-10-then-halve trick.
  3. Compute 53 times 11 mentally.
  4. Find 4% of 75 using the percent-swap trick.
  5. Compute 65 squared using the ending-in-5 rule.
  6. Under a one-third penalty, what is the expected value of a blind 4-option guess?
  7. You have 8 minutes left and 6 questions, two of which are long DI computations. Which should you attempt first and why?
  8. Compute 240 times 25.
  9. Convert the fraction 3/8 to a percentage from memory.
  10. You rule out three of four options. Should you mark the remaining one?

Answer key

Reveal the answer key and full worked solutions
  1. Yes; eliminating even one option makes the expected value positive (1/9 here).
  2. 840 / 2 = 420.
  3. 5_(5+3)_3 = 583.
  4. 75% of 4 = 3.
  5. 6 times 7 = 42, append 25, so 4225.
  6. (1/4)(+1) + (3/4)(-1/3) = 1/4 - 1/4 = 0 (break-even).
  7. Attempt the four shorter questions first to bank marks fast; the two long DI sums risk eating the whole 8 minutes.
  8. 240 times 100 = 24000, divide by 4 = 6000.
  9. 3/8 = 37.5%.
  10. Yes; with only one option left it is effectively a known answer, expected value strongly positive.

See also

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