Chapter 31
Number Series & Sequences
Arithmetic, geometric, Fibonacci, prime, square, cube — and mixed-pattern series.
Full Chapter Notes
Source · FPSC Trap Decoder · CSS MPT Smart Notes (2026 Edition)
31.1 High-Yield Snapshot
| MPT Weightage | Difficulty Level |
|---|---|
| 4–6 Marks | Low–Medium |
Trend Alert. Number series questions appear in every MPT paper and are among the fastest marks available — most can be solved in under 15 seconds once you recognise the pattern. Past paper analysis (2022–2025) confirms 8 direct series questions.
FPSC uses five pattern types repeatedly: arithmetic progression (constant difference), geometric progression (constant ratio), Fibonacci-style (add previous two terms), alternating patterns (two interleaved sequences), and odd-one-out (find the number that breaks the rule).
The examiner does not test complex mathematics — the entire skill is pattern recognition. This chapter builds that skill through repeated exposure to every confirmed FPSC pattern type.
31.2 Concept Anchor
Every number series in FPSC follows a rule. Your job is to find that rule in under 10 seconds. The fastest method is always the same: write the differences between consecutive terms.
The Universal First Step.
- If differences are constant → Arithmetic Progression.
- If differences themselves increase by a fixed amount → Second-Order AP.
- If each term = sum of the two before it → Fibonacci-style.
- If differences alternate between two values → Two interleaved sequences.
Once you identify the type, the next term writes itself.
31.3 The Series Types FPSC Uses
| Pattern Type | How to Identify | Formula / Method | FPSC Frequency |
|---|---|---|---|
| Arithmetic Progression (AP) | Differences between terms are constant | Next term = Last term + d | Very High |
| Second-Order AP | 1st differences not constant; 2nd differences constant | Next 2nd diff + last 1st diff + last term | High |
| Fibonacci-Style | Each term = sum of the two preceding terms | tₙ = tₙ₋₁ + tₙ₋₂ | High |
| Alternating Pattern | Differences alternate between two values | Split into odd/even positions; analyse each | High |
| Odd-One-Out | One number violates a shared property | Test simplest shared property; find the rule-breaker | Medium |
| Geometric Progression (GP) | Each term multiplied by a constant ratio | Next term = Last term × r | Medium |
| Operator Interchange | Expression with swapped operators | Test each swap option; verify equation balances | Low–Medium |
Type 1 — Arithmetic Progression (AP)
Rule. Each term increases or decreases by the same fixed amount (the common difference).
How to spot it. Write the differences between consecutive terms. If they are all equal, it is AP.
- Next term = Last term + Common Difference (d)
- General term: aₙ = a₁ + (n − 1)d
FPSC Examples.
- Series: 2, 4, 6, 8, 10, 12, ... — Differences: 2, 2, 2, 2, 2 → constant. Next term: 12 + 2 = 14. (CSS MPT 2023 Special — confirmed direct question.)
- Series: 1.5, 2.5, 3.5, 4.5, ... — Differences: 1, 1, 1, 1 → constant. Next term: 4.5 + 1 = 5.5. (CSS MPT 2023 Special — confirmed direct question.)
Type 2 — Second-Order Arithmetic (Increasing Differences)
Rule. The differences between terms are not constant, but the differences of those differences are constant.
How to spot it. Write the first differences. If not constant, write the differences of the differences. If those are constant, this is second-order AP.
- Series: 11, 20, 35, 56, 83, ...
- 1st differences: 9, 15, 21, 27 → increasing by 6
- 2nd differences: 6, 6, 6 → constant
- Next 1st diff: 27 + 6 = 33
- Next term: 83 + 33 = 116
(CSS MPT 2024 — confirmed direct question.)
Type 3 — Fibonacci-Style (Add Previous Two Terms)
Rule. Each term equals the sum of the two terms immediately before it.
How to spot it. Check if term₃ = term₁ + term₂, term₄ = term₂ + term₃, and so on.
tₙ = tₙ₋₁ + tₙ₋₂
FPSC Example. Series: 4, 7, 11, 18, 29, ... — 4+7=11, 7+11=18, 11+18=29. Next term: 18 + 29 = 47. (CSS MPT 2023 Special Q114 — confirmed direct question.)
Type 4 — Alternating Pattern (Two Interleaved Sequences)
Rule. The series is actually two separate sequences merged together. Odd-position terms follow one rule; even-position terms follow another.
How to spot it. Differences between consecutive terms alternate rather than stay constant or increase smoothly. Separate odd-position and even-position terms and analyse each independently.
FPSC Example. Series: 3, 2, 7, 6, 11, 10, ...
- Odd positions: 3, 7, 11 → diff of 4 → next = 15
- Even positions: 2, 6, 10 → diff of 4 → next = 14
- Next term (7th, odd position) = 15
(CSS MPT 2023 Special Q138 — confirmed direct question.)
Type 5 — Odd-One-Out (Rule Breaker)
Rule. All numbers in the series share a common property except one. Find the number that breaks the rule.
How to spot it. Look for a shared property: multiples of a number, perfect squares, all odd, all prime, all ending in the same digit.
FPSC Example. Series: 10, 25, 45, 54, 75, 85.
- Property: all are multiples of 5 — except 54
- 54 ÷ 5 = 10.8 (not a whole number)
- Answer: 54 is the odd one out
(CSS MPT 2023 Special Q126 — confirmed direct question.)
Type 6 — Operator / Sign Interchange
Rule. A mathematical expression is given with the wrong operators. Two signs or operators need to be swapped to make the equation correct.
How to spot it. Try swapping the two signs given in Option A first and verify. If incorrect, try Option B.
Method — Operator Interchange.
- Read the equation and the swap options.
- Mentally substitute the swap and evaluate.
- The correct swap makes both sides equal.
This type requires testing each option — it cannot be solved by formula.
Example. 3 + 5 × 2 = 16 — Which two signs to swap? Try swapping + and ×: 3 × 5 + 2 = 15 + 2 = 17. Incorrect — try the next swap option.
31.4 CSSPrep Solved Examples
Problem. What is the next number in the series: 2, 4, 6, 8, 10, 12, ...?
- Step 1: Write the differences. 4−2=2, 6−4=2, 8−6=2, 10−8=2, 12−10=2. All diff = 2 → AP, d = 2.
- Step 2: Next term = 12 + 2 = 14.
This question type should never cost you more than 5 seconds.
Problem. Find the next term: 11, 20, 35, 56, 83, ...
- Step 1: 1st differences: 20−11=9, 35−20=15, 56−35=21, 83−56=27.
- Step 2: 2nd differences: 15−9=6, 21−15=6, 27−21=6 → Constant. Second-order AP.
- Step 3: Next 1st difference = 27 + 6 = 33.
- Step 4: Next term = 83 + 33 = 116.
Note. The FPSC 2024 paper listed 122 as the answer — this appears to be a typographical error. The mathematically correct answer is 116. Always show your working.
Problem. Write the next number: 4, 7, 11, 18, 29, ...
- Step 1: Test the rule: 4+7=11, 7+11=18, 11+18=29.
- Step 2: Pattern confirmed — Fibonacci rule.
- Step 3: Next term = 18 + 29 = 47.
Fast recognition tip. If the differences increase in a Fibonacci-like way (3, 4, 7, 11, 18...), this signals an additive series.
Problem. What is the next number: 3, 2, 7, 6, 11, 10, ...?
- Step 1: Differences: 2−3=−1, 7−2=+5, 6−7=−1, 11−6=+5, 10−11=−1. Alternating: −1, +5.
- Step 2: Pattern: subtract 1, add 5, subtract 1, add 5...
- Step 3: Last operation was −1. Next = +5. Next term = 10 + 5 = 15.
Alternative — split into two sequences.
- Odd positions: 3, 7, 11 → +4 each → next = 15.
- Even positions: 2, 6, 10 → +4 each → next = 14.
Question asks for the 7th term (odd position) → 15.
Problem. Find the number that does not fit: 10, 25, 45, 54, 75, 85.
- Step 1: Shared property: 10=2×5, 25=5×5, 45=9×5, 75=15×5, 85=17×5.
- Step 2: Test 54: 54 ÷ 5 = 10.8 — not a whole number.
- Step 3: Every other number is a multiple of 5. 54 is not. Answer: 54.
Speed tip. Check the most obvious shared property first — ends in 0/5, all even, all odd, all prime, all perfect squares.
Problem. Find the answer: (−2) − 3 − (−3) × (−3)
- Step 1: Multiplication first (BODMAS): (−3)×(−3) = +9. (Negative × Negative = Positive.)
- Step 2: Rewrite: (−2) − 3 − 9
- Step 3: Left to right: −2 − 3 = −5. Then −5 − 9 = −14.
Answer. None of these (confirmed CSS MPT 2022 Q93).
Note. FPSC places −27 as Option C, knowing candidates will write (−3)×(−3) = −9. Negative × Negative is always Positive.
Problem. If 15 is taken from either end of a row of boys, how many boys are in the row?
- Step 1: The person at position 15 from one end is also at position 15 from the other end.
- Step 2: Formula: Total = 2X − 1, where X = position from either end.
- Step 3: Total = 2(15) − 1 = 30 − 1 = 29.
Note. FPSC options listed 34, 35, 36 — correct answer was "None of these" (29). The person at position 15 is counted once, not twice.
31.5 Common Mistakes
Mistake 1 — Not Writing the Differences
| Wrong | Right |
|---|---|
| Look at series, guess a pattern mentally | Write every difference on paper or in the margin |
| 11, 20, 35, 56 → "it's going up, maybe add 33" | 20−11=9, 35−20=15, 56−35=21 → diff +6 each |
Writing differences takes 10 seconds and eliminates guessing entirely.
Mistake 2 — Assuming Negative × Negative = Negative
| Wrong | Right |
|---|---|
| (−3) × (−3) = −9 | (−3) × (−3) = +9 |
| Keeps the negative sign | Negative × Negative = Positive — always |
Mistake 3 — Stopping at First Differences When They Are Not Constant
| Wrong | Right |
|---|---|
| Differences: 9, 15, 21, 27 → "no constant pattern, skip" | Write 2nd differences: 6, 6, 6 → second-order AP |
| Gives up on the series | Goes one level deeper |
Mistake 4 — Treating an Alternating Series as a Single Sequence
| Wrong | Right |
|---|---|
| 3, 2, 7, 6, 11, 10 → differences −1, +5, −1, +5 → confused | Separate: odd = 3,7,11 (+4) / even = 2,6,10 (+4) |
| Cannot find next term | 7th term (odd position) = 15 |
31.6 FPSC Trap Alerts
Trap 1 — The Negative Multiplication Trap. In expressions like (−3)×(−3), FPSC places −27 as a distractor. Candidates who write negative × negative = negative get −9, then multiply by 3 again incorrectly and land on −27. Negative × Negative is always Positive. (−3)×(−3) = +9.
Trap 2 — The "None of These" Series Trap. For series questions, FPSC occasionally makes the correct answer fall outside options A, B, C — making D ("None of these") correct. This occurred in CSS MPT 2022 Q93 (expression = −14) and 2023 Q115. Always calculate your own complete answer. Never pick "None of these" without a number.
Trap 3 — The Odd-One-Out Multiple Property Trap. Sometimes a number can appear to break two properties. In a series of multiples of 5, FPSC may include a number that is also not odd, leading candidates to misidentify the property. Always test the simplest possible property first: multiples of X, all even, all prime.
Trap 4 — The Row-Position Formula Trap. "15 from either end" does NOT mean total = 15+15 = 30. It means total = 2(15)−1 = 29. The person at position 15 is counted once, not twice.
31.7 The 5-Minute Battle Card
Pattern Recognition Decision Rules.
- Step 1 always: Write the differences between every pair of consecutive terms.
- Constant differences → AP. Next term = last + difference.
- Differences increase by a fixed amount → Second-order AP. Find next diff; add to last term.
- Each term = sum of two before it → Fibonacci-style. Add last two terms.
- Differences alternate (−1, +5...) → Alternating pattern. Split into odd/even positions.
- One number breaks a shared property → Odd-one-out. Check multiples, prime, even/odd, squares.
Key Arithmetic Rules.
- Negative × Negative = Positive. (−3)×(−3) = +9.
- BODMAS: multiplication and division before addition and subtraction.
- Row position: X from either end → total = 2X − 1.
- "None of these" → only select after calculating your own complete answer.
Quick Reference Table — Confirmed FPSC Series Examples
| Series Type | Example | Quick Solution |
|---|---|---|
| AP (constant diff.) | 2, 4, 6, 8 → d=2 | Next = 12 + 2 = 14 |
| 2nd-Order AP | 11, 20, 35, 56, 83 → 2nd diff=6 | Next diff=33; next term = 116 |
| Fibonacci-Style | 4, 7, 11, 18, 29 | Next = 18 + 29 = 47 |
| Alternating Pattern | 3, 2, 7, 6, 11, 10 | 7th term (odd pos.) = 15 |
| Odd-One-Out | 10, 25, 45, 54, 75, 85 | 54 (not a multiple of 5) |
| GP (constant ratio) | 5, 10, 20, 40, 80 | ratio=2; next = 160 |
| Perfect Squares | 1, 4, 9, 16, 25 | Next = 6² = 36 |
| Pure Fibonacci | 1, 1, 2, 3, 5, 8, 13 | Next = 21 |
| Row Position | Pos. 20 from either end | Total = 2(20)−1 = 39 |
| Negative Mult. | (−3)×(−3) | = +9 (NOT −9) |
| BODMAS | 50−3×4+(6÷2) | = 50−12+3 = 41 |
31.8 Practice MCQs (FPSC Level)
Part A — Basic Recall
Pattern-recognition fundamentals from confirmed FPSC papers.
What is the next number in the series: 2, 4, 6, 8, 10, 12, ...?
Show explanation
Differences: 2, 2, 2, 2, 2. Constant → AP with d = 2. Next term = 12 + 2 = 14.
Repeated CSS MPT 2023 Special
What is the next number in the series: 1.5, 2.5, 3.5, 4.5, ...?
Show explanation
Differences: 1, 1, 1, 1. Constant → AP with d = 1. Next term = 4.5 + 1 = 5.5.
Repeated CSS MPT 2023 Special
Find the next number in the Fibonacci-style series: 4, 7, 11, 18, 29, ...
Show explanation
Test: 4+7=11, 7+11=18, 11+18=29. Fibonacci rule confirmed. Next term = 18 + 29 = 47.
Repeated CSS MPT 2023 Special Q114
Find the number which does NOT fit the series: 10, 25, 45, 54, 75, 85.
Show explanation
Shared property: all are multiples of 5. 10÷5=2, 25÷5=5, 45÷5=9, 54÷5=10.8, 75÷5=15, 85÷5=17. 54 is not a multiple of 5 — it is the odd one out.
Repeated CSS MPT 2023 Special Q126
What is the next number in the series: 3, 2, 7, 6, 11, 10, ...?
Show explanation
Differences: −1, +5, −1, +5, −1. Alternating pattern. Last diff was −1 (from 11 to 10). Next = +5. Next term = 10+5 = 15.
Repeated CSS MPT 2023 Special Q138
Part B — Trap-Based
Second-order AP, negative multiplication, perfect squares and primes.
Find the next term in the series: 11, 20, 35, 56, 83, ...
Show explanation
1st diff: 9, 15, 21, 27 (increasing by 6). Next 1st diff = 27+6 = 33. Next term = 83+33 = 116.
Trap: FPSC's printed key listed 122 — appears to be a typographical error. Mathematically verified answer is 116.
Repeated CSS MPT 2024
Evaluate the expression: (−2) − 3 − (−3) × (−3)
Show explanation
Step 1: Multiplication first: (−3)×(−3) = +9. Step 2: (−2) − 3 − 9. Step 3: Left to right: −2−3 = −5; −5−9 = −14. None of the options (−3, 27, −27) equal −14.
Trap: Option C (−27) attracts candidates who write (−3)×(−3) = −9. Correct method gives −14.
Repeated CSS MPT 2022 Q93
What is the next term in the series: 1, 4, 9, 16, 25, ...?
Show explanation
Series: 1, 4, 9, 16, 25 — perfect squares: 1², 2², 3², 4², 5². Next = 6² = 36. (Differences: 3,5,7,9 → next diff=11 → 25+11=36.)
Repeated CSS MPT 2022 — Perfect squares
Find the odd one out: 2, 3, 5, 7, 9, 11, 13.
Show explanation
Series claims to list prime numbers: 2, 3, 5, 7, 9, 11, 13. Test 9: 9 = 3×3 — not prime. All others are prime. Answer: 9 is the odd one out.
Trap: Option A (2) attracts candidates who see 2 as the only even number. But 2 IS prime. The property is 'prime numbers' — and 9 breaks it.
If position 20 from one end of a row equals position 20 from the other end, how many people are in the row?
Show explanation
Formula: Total = 2X − 1 where X = position from either end. Total = 2(20) − 1 = 39. Verify: in a row of 39, position 20 from left = 39−20+1 = 20.
Repeated CSS MPT 2023 — Row position formula
Part C — Elite Simulation
Higher-order patterns, GP, pure Fibonacci, BODMAS and statement sets.
Find the next term in the series: 2, 6, 12, 20, 30, 42, ...
Show explanation
Differences: 4, 6, 8, 10, 12 — increasing by 2. Next diff = 12+2 = 14. Next term = 42+14 = 56.
Trap: FPSC Elite Trap — differences 4,6,8,10,12 → next diff = 14.
What is the missing number in the series: 5, 10, ?, 40, 80?
Show explanation
Check ratio: 10÷5=2, 40÷20=2, 80÷40=2. GP with ratio 2. Missing term = 10×2 = 20. Verify: 5, 10, 20, 40, 80 — each term doubles.
Trap: FPSC Elite Trap — Geometric progression, ratio 2.
Find the next number in the series: 1, 1, 2, 3, 5, 8, 13, ...
Show explanation
Pure Fibonacci: each term = sum of two before it. 8 + 13 = 21. Memorise: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
Repeated CSS MPT 2024 — Pure Fibonacci
Evaluate: 50 − 3 × 4 + (6 ÷ 2)
Show explanation
Brackets: 6÷2 = 3. Expression: 50−3×4+3. Multiplication: 3×4 = 12. Expression: 50−12+3. Left to right: 50−12 = 38; 38+3 = 41.
Trap: FPSC trap: doing addition before subtraction gives 50−15 = 35. Wrong — left to right applies equally to + and −.
Which statements about number series are correct? (1) In the series 2, 4, 8, 16, 32, each term is double the previous one. (2) In a Fibonacci-style series, each term equals the sum of the two terms before it. (3) If differences between consecutive terms are 3, 6, 9, 12, the next difference is 15.
Show explanation
Statement 1: Correct. 2, 4, 8, 16, 32 — GP with ratio 2. Statement 2: Correct — Fibonacci-style. Statement 3: Correct — differences 3,6,9,12 increase by 3; next = 15. All three are correct.
Trap: FPSC Elite Trap — All three statements are correct.
31.9 Answer Key & Trap Analysis
Number Series & Sequences (Q1–Q15)
| Q | Correct | Type | Primary Trap | Why Others Fail |
|---|
31.10 Quick Revision Panel — 60-Second Recap
Key Formulas.
- AP: aₙ = a₁ + (n−1)d ; Next term = last + d
- Second-Order AP: find 2nd differences; add next 2nd diff to get next 1st diff; add to last term
- Fibonacci-style: tₙ = tₙ₋₁ + tₙ₋₂
- GP: next term = last × r
- Row position: Total = 2X − 1
Common Number Patterns.
- Perfect squares: 1, 4, 9, 16, 25, 36, 49...
- Pure Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...
- Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23...
Solving Strategy — Step by Step.
- Step 1: Write differences between consecutive terms.
- Step 2: Constant differences → AP. Not constant → write 2nd differences.
- Step 3: If 2nd differences constant → Second-order AP.
- Step 4: Confirm Fibonacci rule if each term = sum of two before it.
- Step 5: Alternating differences → split into odd/even positions.
- Step 6: Odd-one-out → test simplest shared property first.
Critical Exam Reminders.
- Negative × Negative = Positive. ALWAYS. (−3)×(−3) = +9.
- BODMAS: brackets → multiplication/division → addition/subtraction (left to right).
- "None of these": only select after calculating your own complete answer.
- Second-order AP: FPSC 2024 paper had a typo (122). Correct answer = 116. Show your working.
- Row position: 15 from either end → total = 29 (NOT 30).
31.11 Mock Test 1 — CSS MPT General Ability & Quantitative Reasoning
| Examination Detail | Value |
|---|---|
| Total Questions | 30 MCQs |
| Total Marks | 30 |
| Time Allowed | 30 Minutes |
| Negative Marking | No |
| Difficulty Level | CSS MPT Standard |
| Coverage | Arithmetic · Algebra · Series · Geometry · Coding · Directions · Logic · Ratios |
Instructions.
- This test contains 30 multiple-choice questions.
- Each question carries one mark.
- There is no negative marking.
- Select the most appropriate option for each question.
- Attempt all questions within the 30-minute time limit.
Section A — Arithmetic & Percentages
Mock Test 1, Q1–Q5.
A price increases from Rs. 80 to Rs. 100. What is the percentage increase?
Show explanation
Increase = 100−80 = 20. % increase = (20/80)×100 = 25%. Trap: Option B (20%) uses the new value as denominator. Always divide by the OLD value.
Repeated CSS MPT 2022, 2023
Evaluate: 20 ÷ 5 × 4
Show explanation
BODMAS: division and multiplication have equal priority — solve left to right. 20÷5 = 4; then 4×4 = 16.
Trap: Option A (1) inserts brackets that do not exist (5×4=20, then 20÷20=1).
Repeated CSS MPT 2022, 2025
A salary increases by 10% and then decreases by 10%. What is the net change?
Show explanation
Net change = −x²/100 = −10²/100 = −1%. Verify: Rs.1,000 +10% = Rs.1,100; −10% of 1,100 = Rs.110; 1,100−110 = Rs.990. Loss = Rs.10 = 1%.
Repeated CSS MPT 2024
If 25% of a number is 75, what is the number?
Show explanation
25% of X = 75. X = 75 × (100÷25) = 75 × 4 = 300.
Repeated CSS MPT 2023
A man saves Rs. 1,200 after spending 60% of his salary. What is his total salary?
Show explanation
Spends 60% → saves 40%. 40% of salary = Rs.1,200. Salary = 1,200 × (100÷40) = Rs.3,000.
Trap: Using 60% as denominator gives Rs.2,000 (wrong).
Repeated CSS MPT 2022, 2025
Section B — Algebra & Word Problems
Mock Test 1, Q6–Q10.
Solve for x: 5x − 8 = 27
Show explanation
5x − 8 = 27 → 5x = 35 → x = 7. Verify: 5(7)−8 = 27.
Repeated CSS MPT 2022, 2024
The sum of two numbers is 50. Their difference is 10. What is the larger number?
Show explanation
Larger = (Sum + Difference) ÷ 2 = (50+10) ÷ 2 = 30. Smaller = 20. Verify: 30+20=50, 30−20=10.
Repeated CSS MPT 2023
A farmer has chickens and goats. The number of heads is 30 and the number of legs is 84. How many goats are there?
Show explanation
Heads: c+g=30. Legs: 2c+4g=84. Multiply heads by 2: 2c+2g=60. Subtract: 2g=24 → g=12. Verify: 18 chickens × 2 + 12 goats × 4 = 84 legs.
Repeated CSS MPT 2023, 2024
In a group of 150 people, 80 drink tea, 70 drink coffee, and 30 drink both. How many drink neither?
Show explanation
Neither = Total − Tea − Coffee + Both = 150−80−70+30 = 30.
Trap: Forgetting to add back the 'both' group gives a wrong result.
Repeated CSS MPT 2023 Special
A father is currently 3 times his son's age. In 10 years, he will be 2 times his son's age. What is the son's current age?
Show explanation
Son=x, Father=3x. In 10 yrs: 3x+10 = 2(x+10) → 3x+10 = 2x+20 → x=10. Verify: son=20, father=40 in 10 yrs; 40 = 2×20.
Trap: FPSC Elite Trap — set up equation with future ages, not current.
Section C — Number Series
Mock Test 1, Q11–Q14.
What is the next number in the series: 3, 6, 12, 24, 48, ...?
Show explanation
GP, ratio = 2. Each term doubles: 3,6,12,24,48. Next = 48×2 = 96.
Repeated CSS MPT 2022, 2024
Find the next number in the series: 2, 5, 10, 17, 26, ...?
Show explanation
Differences: 3, 5, 7, 9 (odd numbers, +2 each time). Next diff = 11. Next term = 26+11 = 37.
Repeated CSS MPT 2023
Find the number that does NOT fit: 4, 8, 12, 18, 20, 24.
Show explanation
All others are multiples of 4. 18 is NOT a multiple of 4 (18÷4 = 4.5).
Repeated CSS MPT 2023 Special
What is the next number in the series: 1, 4, 9, 16, 25, ...?
Show explanation
Series is 1², 2², 3², 4², 5²,... Next = 6² = 36.
Repeated CSS MPT 2022, 2025
Section D — Geometry Basics
Mock Test 1, Q15–Q18.
Supplementary angles are two angles whose sum equals:
Show explanation
Supplementary angles sum to 180° (straight line). Complementary sum to 90° (corner). Memory: S for Straight (180°).
Repeated CSS MPT 2023
A polygon with 6 sides is called:
Show explanation
Hexagon = 6 sides. Pentagon=5, Heptagon=7, Octagon=8.
Repeated CSS MPT 2022
A right-angled triangle has legs of 8 cm and 15 cm. What is the length of the hypotenuse?
Show explanation
Pythagoras: 8²+15² = 64+225 = 289 = 17². Hypotenuse = 17 cm. Key triples: 3-4-5, 5-12-13, 8-15-17.
Repeated CSS MPT 2024
The surface area of a hollow cylinder (open at both ends) with radius r and height h is:
Show explanation
Hollow cylinder (open both ends) = lateral surface only. Unrolled: rectangle width = 2πr, height = h. Area = 2πrh.
Repeated CSS MPT 2023 Special
Section E — Coding, Decoding & Analogies
Mock Test 1, Q19–Q21.
If COLD is coded as FROG using a letter shift, what is the shift applied?
Show explanation
C(3)→F(6): +3. O(15)→R(18): +3. L(12)→O(15): +3. D(4)→G(7): +3. Shift = +3.
Repeated CSS MPT 2023
Doctor is to Hospital as Judge is to:
Show explanation
Doctor works at Hospital (professional → workplace). Judge works at Court. Law = field; Verdict = output; Crime = subject matter.
Repeated CSS MPT 2022, 2024
If ME = 26 and MEET = 39, what is NUT?
Show explanation
Rule: position of first letter × number of unique letters. ME: M=13, unique={M,E}=2, 13×2=26. MEET: M=13, unique={M,E,T}=3, 13×3=39. NUT: N=14, unique={N,U,T}=3, 14×3=42. Answer = A (42).
Repeated CSS MPT 2023 Special
Section F — Directions & Spatial Reasoning
Mock Test 1, Q22–Q24.
A person faces South. He turns 90° clockwise. Which direction is he now facing?
Show explanation
Facing South, turn 90° clockwise: S → W. Clockwise: N→E→S→W→N. From South, one CW step = West.
Repeated CSS MPT 2022, 2023
P, Q, R and S each have different heights. R is taller than S but shorter than P. Q has no stated comparison. Who is the tallest?
Show explanation
Known order: P>R>S. Q has no stated comparison to P, R, or S. Q might be taller than P or shorter than S. Cannot determine who is tallest.
Repeated CSS MPT 2023 Special
At 7:00 PM, a man stands facing West. His shadow falls in which direction?
Show explanation
At 7:00 PM, the Sun is in the West (setting). Shadow falls OPPOSITE to the Sun → shadow falls East. A man facing West has the sun behind him.
Repeated CSS MPT 2024
Section G — Logical Deduction & Syllogisms
Mock Test 1, Q25–Q27.
All students are hardworking. Ali is hardworking. Which conclusion logically follows?
Show explanation
Affirming the consequent fallacy. All students are hardworking, but not all hardworking people are students. Ali's hardworking nature does not make him a student.
Trap: FPSC Elite Trap — affirming the consequent.
Some mangoes are sweet. All sweet things are healthy. Conclusion 1: Some mangoes are healthy. Conclusion 2: All mangoes are healthy. Which follows?
Show explanation
Some A are B + All B are C → Some A are C. Conclusion 1 (some mangoes are healthy) follows. Conclusion 2 (ALL mangoes) cannot be drawn from 'some' premises.
Repeated CSS MPT 2022, 2024
Show explanation
The statement is a qualified positive relationship. Option B matches this qualified language. Options A, C, D are all too absolute or introduce specific details not stated.
Repeated CSS MPT 2023
Section H — Ratios, Averages & Statistics
Mock Test 1, Q28–Q30.
Rs. 1,000 is divided between A and B in the ratio 2:3. What is A's share?
Show explanation
Total parts = 5. 1 part = 1,000÷5 = 200. A's share = 2×200 = Rs.400.
Trap: Option A (200) = value of 1 part only, not A's 2-part share.
Repeated CSS MPT 2022, 2023
The mean of 4 observations is 15. A 5th observation of 25 is added. What is the new mean?
Show explanation
Original sum = 15×4 = 60. New sum = 60+25 = 85. New mean = 85÷5 = 17.
Trap: Option D (20) averages the two means (15 and 25) — always use sums.
Repeated CSS MPT 2024
Class A has 25 students with an average score of 60. Class B has 25 students with an average score of 80. What is the combined average?
Show explanation
Equal group sizes (25 each) → simple average applies. (60+80)÷2 = 70. Verify: 25×60+25×80 = 3,500. 3,500÷50 = 70.
Trap: FPSC Elite Trap — equal-sized groups; weighted average shortcut works only when sizes match.
Mock Test 1 — Answer Key & Trap Analysis
Mock Test 1 — General Ability (Q1–Q30)
| Q | Correct | Type | Primary Trap | Why Others Fail |
|---|
31.12 Mock Test 2 — CSS MPT General Ability & Quantitative Reasoning
| Test Feature | Details |
|---|---|
| Total Questions | 30 MCQs |
| Total Marks | 30 |
| Time Allowed | 30 Minutes |
| Negative Marking | No |
| Difficulty Level | CSS MPT Standard |
| Coverage | Arithmetic · Algebra · Series · Geometry · Coding · Directions · Logic · Ratios |
Instructions.
- This test contains 30 multiple-choice questions.
- Each question carries one mark.
- There is no negative marking.
- Select the most appropriate option for each question.
- Attempt all questions within the 30-minute time limit.
Section A — Arithmetic & Percentages
Mock Test 2, Q1–Q5.
A price increases from Rs. 80 to Rs. 100. What is the percentage increase?
Show explanation
Increase = 100−80=20. % increase = (20/80)×100 = 25%.
Evaluate: 20 ÷ 5 × 4
Show explanation
BODMAS: 20÷5=4, then 4×4=16.
A salary increases by 10% and then decreases by 10%. What is the net change?
Show explanation
Start with 100. +10%=110. −10% of 110=11. Final=99. Net change = −1% (1% net loss).
If 25% of a number is 75, what is the number?
Show explanation
25% of x = 75 → x = 75÷0.25 = 300.
A man saves Rs. 1,200 after spending 60% of his salary. What is his total salary?
Show explanation
Saves 40% = Rs.1,200 → Total salary = 1200÷0.40 = Rs.3,000.
Section B — Algebra & Word Problems
Mock Test 2, Q6–Q10.
Solve for x: 5x − 8 = 27
Show explanation
5x − 8 = 27 → 5x = 35 → x = 7.
The sum of two numbers is 50. Their difference is 10. What is the larger number?
Show explanation
Larger = (Sum+Diff)/2 = (50+10)/2 = 30.
A farmer has chickens and goats. The number of heads is 30 and the number of legs is 84. How many goats are there?
Show explanation
c+g=30; 2c+4g=84. Multiply eq1 by 2: 2c+2g=60. Subtract: 2g=24 → g=12.
In a group of 150 people, 80 drink tea, 70 drink coffee, and 30 drink both. How many drink neither?
Show explanation
Neither = 150−80−70+30 = 30.
A father is currently 3 times his son's age. In 10 years, he will be 2 times his son's age. What is the son's current age?
Show explanation
Son=x, Father=3x. In 10 yrs: 3x+10=2(x+10) → x=10.
Section C — Number Series
Mock Test 2, Q11–Q14.
What is the next number in the series: 3, 6, 12, 24, 48, ...?
Show explanation
Rule: ×2 each term. 48×2 = 96.
Find the next number in the series: 2, 5, 10, 17, 26, ...?
Show explanation
Differences: +3, +5, +7, +9, +11. Next = 26+11 = 37.
Find the number that does NOT fit: 4, 8, 12, 18, 20, 24.
Show explanation
All others are multiples of 4. 18 is NOT a multiple of 4 (18÷4=4.5).
What is the next number in the series: 1, 4, 9, 16, 25, ...?
Show explanation
Series is 1², 2², 3², 4², 5²,... Next = 6² = 36.
Section D — Geometry
Mock Test 2, Q15–Q18.
Supplementary angles are two angles whose sum equals:
Show explanation
Supplementary angles sum to 180°. Complementary sum to 90°.
A polygon with 6 sides is called:
Show explanation
Hexagon = 6 sides. Pentagon=5, Heptagon=7, Octagon=8.
A right-angled triangle has legs of 8 cm and 15 cm. What is the length of the hypotenuse?
Show explanation
Pythagoras: 8²+15² = 289 = 17². Hypotenuse = 17 cm.
The surface area of a hollow cylinder (open at both ends) with radius r and height h is:
Show explanation
Hollow cylinder (open ends): curved surface only = 2πrh.
Section E — Coding & Analogies
Mock Test 2, Q19–Q21.
If COLD is coded as FROG using a letter shift, what is the shift applied?
Show explanation
C→F (+3), O→R (+3), L→O (+3), D→G (+3). Shift = +3.
Doctor is to Hospital as Judge is to:
Show explanation
Doctor works at Hospital. Relationship = professional → workplace. Judge works at Court.
If ME = 26 and MEET = 39, what is NUT?
Show explanation
First letter position × number of unique letters. ME: M(13)×2=26. MEET: M(13)×3=39. NUT: N(14)×3 unique letters = 42.
Section F — Directions & Rankings
Mock Test 2, Q22–Q24.
A person faces South. He turns 90° clockwise. Which direction is he now facing?
Show explanation
Facing South, turn 90° clockwise → facing West.
P, Q, R and S each have different heights. R is taller than S but shorter than P. Q has no stated comparison. Who is the tallest?
Show explanation
Known order: P>R>S. Q has no stated comparison to P, R, or S. Cannot determine who is tallest.
At 7:00 PM, a man stands facing West. His shadow falls in which direction?
Show explanation
At 7:00 PM, the sun is in the West. A man facing West has the sun behind him. Shadow falls in front = East.
Section G — Logical Reasoning
Mock Test 2, Q25–Q27.
All students are hardworking. Ali is hardworking. Which conclusion logically follows?
Show explanation
Affirming the consequent fallacy. All students are hardworking, but not all hardworking people are students. Ali's hardworking nature does not make him a student.
Some mangoes are sweet. All sweet things are healthy. Conclusion 1: Some mangoes are healthy. Conclusion 2: All mangoes are healthy.
Show explanation
Some A are B + All B are C → Some A are C. Conclusion 1 follows. Conclusion 2 (ALL mangoes) cannot be drawn from 'some' premises.
Show explanation
The statement is a qualified positive relationship. Option B matches this qualified language. Options A, C, D are all too absolute or introduce specific details not stated.
Section H — Ratios & Averages
Mock Test 2, Q28–Q30.
Rs. 1,000 is divided between A and B in the ratio 2:3. What is A's share?
Show explanation
Total parts=5. 1 part=1,000÷5=200. A's share=2×200=Rs.400.
The mean of 4 observations is 15. A 5th observation of 25 is added. What is the new mean?
Show explanation
Original sum=15×4=60. New sum=60+25=85. New mean=85÷5=17.
Class A has 25 students with an average score of 60. Class B has 25 students with an average score of 80. What is the combined average?
Show explanation
Equal group sizes (25 each) → simple average applies. (60+80)÷2=70. Verify: 25×60+25×80=3,500; 3,500÷50=70.
Mock Test 2 — Answer Key & Trap Analysis
Mock Test 2 — General Ability (Q1–Q30)
| Q | Correct | Type | Primary Trap | Why Others Fail |
|---|