FPSC General Recruitment Test Quantitative Ability and Numerical Reasoning Syllabus

Quantitative Ability and Numerical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Ability and Numerical Reasoning in FPSC General Recruitment Test, not a summary of it.

1. 1

   Arithmetic

   6 topics

   • Number System
   • HCF and LCM
   • Fractions and Decimals
   • Percentages
   • Ratio and Proportion
   • Average
2. 2

   Commercial Mathematics

   4 topics

   • Profit and Loss
   • Simple and Compound Interest
   • Partnership
   • Discount
3. 3

   Time and Measurement

   4 topics

   • Time and Work
   • Time, Speed and Distance
   • Problems on Trains
   • Pipes and Cisterns
4. 4

   Algebra and Geometry

   4 topics

   • Basic Algebra and Equations
   • Mensuration (Area and Volume)
   • Lines and Angles
   • Geometry Basics
5. 5

   Data Interpretation

   5 topics

   • Tables
   • Bar Graphs
   • Pie Charts
   • Line Graphs
   • Probability and Basic Statistics

Quantitative Ability and Numerical Reasoning flashcards for FPSC General Recruitment Test

21 of 50 cards from the Quantitative Ability and Numerical Reasoning deck — real questions with worked answers.

1. What are natural numbers, and what is the smallest natural number?

   Natural numbers are the counting numbers: 1, 2, 3, 4, ... The smallest natural number is 1.

2. What is the difference between whole numbers and natural numbers?

   Whole numbers include 0 along with all natural numbers (0, 1, 2, 3, ...), whereas natural numbers start from 1.

3. Define prime and composite numbers, and state how many prime numbers lie between 1 and 20.

   A prime number has exactly two factors (1 and itself); a composite number has more than two factors. There are 8 primes between 1 and 20: 2, 3, 5, 7, 11, 13, 17, 19.

4. State the divisibility rules for 3, 9, and 11.

   Divisible by 3 if the sum of digits is divisible by 3; by 9 if the sum of digits is divisible by 9; by 11 if the difference between the sum of digits at odd and even positions is 0 or a multiple of 11.

5. What is the relationship between two numbers, their HCF, and their LCM?

   Product of two numbers = HCF x LCM. So HCF x LCM = first number x second number.

6. How do you find the HCF and LCM of two numbers using prime factorization?

   HCF = product of the lowest powers of common prime factors; LCM = product of the highest powers of all prime factors appearing in either number.

7. What is the formula for the HCF and LCM of fractions?

   HCF of fractions = HCF of numerators / LCM of denominators; LCM of fractions = LCM of numerators / HCF of denominators.

8. How do you convert a fraction to a decimal and a decimal to a fraction?

   Convert a fraction to a decimal by dividing numerator by denominator. Convert a terminating decimal to a fraction by writing it over a power of 10 (e.g., 0.75 = 75/100 = 3/4) and simplifying.

9. What is a recurring (repeating) decimal, and give an example as a fraction?

   A recurring decimal has digits repeating infinitely, e.g., 0.333... = 1/3 and 0.666... = 2/3. They represent rational numbers.

10. How do you compare two fractions such as 3/5 and 4/7?

    Cross-multiply: 3x7 = 21 and 4x5 = 20. Since 21 > 20, 3/5 > 4/7. The fraction with the larger cross product (placed over the matching numerator side) is greater.

11. How do you convert a fraction or a decimal into a percentage?

    Multiply by 100. For a fraction, multiply by 100 (e.g., 1/4 = 25%). For a decimal, multiply by 100 (e.g., 0.35 = 35%).

12. If a quantity increases from A to B, what is the percentage increase formula?

    Percentage increase = ((B - A) / A) x 100. For a decrease, use ((A - B) / A) x 100.

13. A number is increased by 20% and then decreased by 20%. What is the net percentage change?

    Net change = a + b + (ab/100) = 20 + (-20) + (20 x -20)/100 = -4%, i.e., a net 4% decrease.

14. What is the formula linking percentage error or successive percentage changes of x% then y%?

    Net percentage change = x + y + (xy/100), using positive signs for increases and negative for decreases.

15. Define ratio and proportion. When are four quantities said to be in proportion?

    A ratio compares two quantities (a:b = a/b). A proportion is an equality of two ratios (a:b = c:d). Four quantities are in proportion when a x d = b x c (product of extremes = product of means).

16. If a:b = 2:3 and b:c = 4:5, what is a:b:c?

    Make b common: a:b = 8:12 and b:c = 12:15, so a:b:c = 8:12:15.

17. What is the mean proportional between two numbers a and b?

    The mean proportional (geometric mean) between a and b is the square root of (a x b).

18. What is the formula for the average (arithmetic mean) of n numbers?

    Average = (sum of all observations) / (number of observations).

19. What is the average of the first n natural numbers?

    Average of first n natural numbers = (n + 1) / 2.

20. The average of 10 numbers is 15. If one number 20 is removed, what is the new average?

    Total = 10 x 15 = 150; after removing 20, sum = 130 over 9 numbers, so new average = 130/9 ≈ 14.44.

21. Define cost price (CP), selling price (SP), profit, and loss.

    CP is the buying price; SP is the selling price. If SP > CP, Profit = SP - CP; if SP < CP, Loss = CP - SP.

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