Civil Service Exam (Subprofessional) Numerical Ability — Basic Statistics & Consecutive NumbersExam Answer Templates

Marks

2

Topic

Basic Average Calculation

Difficulty

easy

Template Id

T1

Examiner Tip

Always show the addition step explicitly - examiners look for complete working

Model Answer

Given numbers: 16, 14, 22, 19, and 17 Formula: Average = Sum of all terms ÷ Number of terms Sum = 16 + 14 + 22 + 19 + 17 = 88 Number of terms = 5 Average = 88 ÷ 5 = 17.6 Therefore, the average is 17.6.

Question Type

short_answer

Answer Structure

• Line 1: Write given numbers and formula [0.5 marks]
• Line 2: Calculate the sum correctly [1 mark]
• Line 3: Apply formula and find average [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not showing the sum calculation
• Arithmetic errors
• Not stating the final answer clearly

Key Phrases To Include

• Sum of all terms
• Number of terms
• Average =
• Therefore

Marks

3

Topic

Finding Missing Terms in Average

Difficulty

medium

Template Id

T2

Examiner Tip

This is a classic 'missing term' problem - always find the total first, then subtract

Model Answer

Given: Average height of 5 members = 150 cm Heights of 4 members: 153, 150, 151, 152 cm To find: Height of fifth member Formula: Sum of all terms = Average × Number of terms Total height of 5 members = 150 × 5 = 750 cm Sum of 4 known heights = 153 + 150 + 151 + 152 = 606 cm Height of fifth member = 750 - 606 = 144 cm Therefore, the height of the fifth member is 144 cm.

Question Type

short_answer

Answer Structure

• Line 1: State given information and what to find [0.5 marks]
• Line 2: Find total sum using average formula [1 mark]
• Line 3: Calculate sum of known terms [1 mark]
• Line 4: Find missing term by subtraction [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not finding total sum first
• Addition errors in the four heights
• Subtraction errors

Key Phrases To Include

• Sum of all terms = Average × Number of terms
• Height of fifth member
• Therefore

Marks

3

Topic

Weighted Average

Difficulty

medium

Template Id

T3

Examiner Tip

Weighted average problems require finding the total for each group first - never average the averages directly

Model Answer

Given: 26 boys with average weight 40 kg 14 girls with average weight 35 kg To find: Average weight of all students Formula: Weighted Average = Sum of weighted terms ÷ Total number of terms Total weight of boys = 26 × 40 = 1,040 kg Total weight of girls = 14 × 35 = 490 kg Total weight of all students = 1,040 + 490 = 1,530 kg Total number of students = 26 + 14 = 40 Average weight = 1,530 ÷ 40 = 38.25 kg Therefore, the average weight of the students is 38.25 kg.

Question Type

short_answer

Answer Structure

• Line 1: Identify this as weighted average problem [0.5 marks]
• Line 2: Calculate total weight of each group [1 mark]
• Line 3: Find combined totals [1 mark]
• Line 4: Apply weighted average formula [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Using simple average instead of weighted average
• Calculation errors in multiplication
• Wrong final division

Key Phrases To Include

• Weighted Average
• Total weight
• Combined total
• Therefore

Marks

2

Topic

Unit Conversion

Difficulty

easy

Template Id

T4

Examiner Tip

Always use the given conversion factor and express the answer as a proper fraction

Model Answer

Given: 1 gallon = 8 pints To find: What part of a gallon is 5 pints Method: 5 pints × (1 gallon ÷ 8 pints) = 5 pints × 1/8 gallon per pint = 5/8 gallon Therefore, 5 pints is 5/8 of a gallon.

Question Type

short_answer

Answer Structure

• Line 1: State the conversion factor [0.5 marks]
• Line 2: Set up the proportion correctly [1 mark]
• Line 3: Calculate and express as fraction [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not using the given conversion
• Incorrect fraction
• Not simplifying the fraction

Key Phrases To Include

• Conversion factor
• proportion
• Therefore

Marks

2

Topic

Fraction Word Problems

Difficulty

medium

Template Id

T5

Examiner Tip

Remember that all fractions must add up to 1 (the whole group)

Model Answer

Given: 1/3 take public transportation, 2/5 drive cars To find: Fraction who walk to work Fraction using transportation or cars = 1/3 + 2/5 = 5/15 + 6/15 = 11/15 Fraction who walk = Total - (Transportation + Cars) = 1 - 11/15 = 15/15 - 11/15 = 4/15 Therefore, 4/15 of the workers walk to work.

Question Type

short_answer

Answer Structure

• Line 1: Add fractions for transportation and cars [1 mark]
• Line 2: Subtract from 1 to find remaining fraction [1 mark]

Scoring Breakdown

Common Mark Deductions

• Errors in adding fractions
• Not finding common denominator
• Arithmetic mistakes

Key Phrases To Include

• Common denominator
• Total fraction
• Therefore

Marks

1

Topic

Time Conversion

Difficulty

easy

Template Id

T6

Examiner Tip

For 1-mark questions, show the operation and give the final answer with units

Model Answer

644 days ÷ 7 days per week = 92 weeks

Question Type

very_short_answer

Answer Structure

• Single line: Division with correct answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Division errors
• Not stating units

Key Phrases To Include

• days per week
• weeks

Marks

3

Topic

Fraction Applications with Variables

Difficulty

hard

Template Id

T7

Examiner Tip

The difference in fractions equals the amount drawn out - this is the key insight

Model Answer

Given: Initially 7/9 full, after drawing 27 liters it becomes 4/9 full To find: Total capacity of tank Let x be the total capacity of the tank. Water drawn out = 7/9 x - 4/9 x = 3/9 x = 1/3 x Given that water drawn out = 27 liters Therefore: 1/3 x = 27 x = 27 × 3 = 81 liters Therefore, the total capacity of the tank is 81 liters.

Question Type

short_answer

Answer Structure

• Line 1: Set up equation with variable [1 mark]
• Line 2: Express water drawn as fraction of capacity [1 mark]
• Line 3: Solve equation to find capacity [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not setting up the equation correctly
• Fraction arithmetic errors
• Not solving for x properly

Key Phrases To Include

• Let x be
• Water drawn out
• Therefore

Marks

3

Topic

Finding Required Score for Target Average

Difficulty

medium

Template Id

T8

Examiner Tip

Always work backwards from the target average to find what total is needed

Model Answer

Given: Scores in first 4 games: 165, 135, 122, 154 Required average for 5 games = 147 To find: Score needed in 5th game Required total for 5 games = Average × Number of games = 147 × 5 = 735 Sum of first 4 games = 165 + 135 + 122 + 154 = 576 Score needed in 5th game = 735 - 576 = 159 Therefore, he must score 159 in his next game.

Question Type

short_answer

Answer Structure

• Line 1: Calculate required total using target average [1 mark]
• Line 2: Find sum of existing scores [1 mark]
• Line 3: Find missing score by subtraction [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not finding the required total first
• Addition errors
• Subtraction errors

Key Phrases To Include

• Required total
• Sum of first 4 games
• Therefore

Marks

1

Topic

Length Conversion

Difficulty

easy

Template Id

T9

Examiner Tip

Use the given conversion factor correctly and show the division

Model Answer

45 feet × (1 yard ÷ 3 feet) = 45 ÷ 3 = 15 yards

Question Type

very_short_answer

Answer Structure

• Single line: Conversion calculation with answer [1 mark]

Scoring Breakdown

Common Mark Deductions

• Using wrong conversion
• Division errors

Key Phrases To Include

• conversion factor
• yards

Marks

3

Topic

Algebraic Word Problems with Fractions

Difficulty

hard

Template Id

T10

Examiner Tip

Always check that both segments add up to the total length

Model Answer

Given: Total length = 12 meters One part is 1/3 of the other To find: Length of longer segment Let x = length of shorter segment Then longer segment = 12 - x Given: x = 1/3(12 - x) 3x = 12 - x 3x + x = 12 4x = 12 x = 3 meters (shorter segment) Longer segment = 12 - 3 = 9 meters Therefore, the longer segment is 9 meters.

Question Type

short_answer

Answer Structure

• Line 1: Define variable and relationship [0.5 marks]
• Line 2: Set up equation from given condition [1 mark]
• Line 3: Solve equation correctly [1 mark]
• Line 4: Find both segments and identify longer one [0.5 marks]

Scoring Breakdown

Common Mark Deductions

• Not setting up equation properly
• Algebraic errors
• Not identifying which segment is longer

Key Phrases To Include

• Let x
• equation
• longer segment
• Therefore

Marks

3

Topic

Effect of Adding New Member on Average

Difficulty

medium

Template Id

T11

Examiner Tip

Remember that increasing average by 4 means new average is 21 + 4 = 25

Model Answer

Given: 13 persons with average age 21 New average required = 21 + 4 = 25 To find: Age of new person Total age of 13 persons = 13 × 21 = 273 Total age of 14 persons = 14 × 25 = 350 Age of new person = 350 - 273 = 77 Therefore, the new person should be 77 years old.

Question Type

short_answer

Answer Structure

• Line 1: Calculate current total age [1 mark]
• Line 2: Calculate required total for new average [1 mark]
• Line 3: Find age of new person by subtraction [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not calculating the new average first
• Arithmetic errors
• Wrong approach to the problem

Key Phrases To Include

• Total age
• New average
• Therefore

Marks

2

Topic

Average Over Different Time Periods

Difficulty

medium

Template Id

T12

Examiner Tip

This is a weighted average over different time periods

Model Answer

Given: First 3 days average = 350, Next 4 days average = 420 To find: Average for whole week (7 days) Total expenditure for first 3 days = 3 × 350 = 1,050 Total expenditure for next 4 days = 4 × 420 = 1,680 Total expenditure for 7 days = 1,050 + 1,680 = 2,730 Average for whole week = 2,730 ÷ 7 = 390 Therefore, the average expenditure for the whole week is 390.

Question Type

short_answer

Answer Structure

• Line 1: Calculate total for each period [1 mark]
• Line 2: Find overall average [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not finding totals first
• Division errors
• Wrong number of days

Key Phrases To Include

• Total expenditure
• Average for whole week
• Therefore

Marks

1

Topic

Metric Conversion

Difficulty

easy

Template Id

T13

Examiner Tip

Use the exact conversion factor given in the question

Model Answer

25 inches × 25.4 mm/inch = 635 mm

Question Type

very_short_answer

Answer Structure

• Single line: Multiplication with conversion factor [1 mark]

Scoring Breakdown

Common Mark Deductions

• Using wrong conversion factor
• Multiplication errors

Key Phrases To Include

• conversion factor
• mm

Marks

2

Topic

Fraction Multiplication in Word Problems

Difficulty

medium

Template Id

T14

Examiner Tip

When finding a fraction of a fraction, multiply the fractions together

Model Answer

Given: Inherited 6/7 of estate, sold 2/3 of her share To find: What part of entire estate was sold Part of estate sold = (6/7) × (2/3) = (6 × 2)/(7 × 3) = 12/21 = 4/7 Therefore, she sold 4/7 of the entire estate.

Question Type

short_answer

Answer Structure

• Line 1: Set up multiplication of fractions [1 mark]
• Line 2: Simplify to lowest terms [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not multiplying fractions
• Not simplifying the answer
• Arithmetic errors

Key Phrases To Include

• multiplication of fractions
• Therefore

Marks

2

Topic

Mixed Numbers and Multiplication

Difficulty

medium

Template Id

T15

Examiner Tip

Always convert mixed numbers to improper fractions before multiplying

Model Answer

Given: 25 pieces, each 6⅕ cm long To find: Original length of rope Length of each piece = 6⅕ = 31/5 cm Original length = 25 × 31/5 = 775/5 = 155 cm Therefore, the original length of the rope was 155 cm.

Question Type

short_answer

Answer Structure

• Line 1: Convert mixed number to improper fraction [1 mark]
• Line 2: Multiply by number of pieces [1 mark]

Scoring Breakdown

Common Mark Deductions

• Not converting mixed number properly
• Multiplication errors
• Wrong final calculation

Key Phrases To Include

• mixed number
• improper fraction
• Therefore