PPSC Test Mathematics & Analytical Reasoning Syllabus

Mathematics & Analytical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics & Analytical Reasoning in PPSC Test, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number System and HCF/LCM
   • Percentages, Profit and Loss
   • Ratio, Proportion and Averages
   • Time, Speed, Distance and Work
2. 2

   Algebra and Basic Mathematics

   3 topics

   • Linear and Quadratic Equations
   • Simplification and Algebraic Expressions
   • Simple and Compound Interest
3. 3

   Logical and Analytical Reasoning

   4 topics

   • Series and Pattern Completion
   • Coding-Decoding and Blood Relations
   • Direction Sense and Seating Arrangement
   • Logical Deductions and Syllogisms
4. 4

   Data Interpretation

   2 topics

   • Tables and Charts
   • Graphs and Pie Charts

Mathematics & Analytical Reasoning flashcards for PPSC Test

19 of 51 cards from the Mathematics & Analytical Reasoning deck — real questions with worked answers.

1. What is the difference between a prime number and a composite number?

   A prime number has exactly two factors (1 and itself), e.g. 2, 3, 5, 7. A composite number has more than two factors, e.g. 4, 6, 8, 9. The number 1 is neither prime nor composite.

2. What is the relationship between the HCF and LCM of two numbers a and b?

   HCF(a, b) x LCM(a, b) = a x b. So the product of the HCF and LCM equals the product of the two numbers.

3. What is the difference between HCF and LCM?

   HCF (Highest Common Factor) is the largest number that divides both/all given numbers exactly. LCM (Lowest Common Multiple) is the smallest number that is a multiple of all the given numbers.

4. How do you find the HCF and LCM of fractions?

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

5. What is the divisibility rule for 3 and for 9?

   A number is divisible by 3 if the sum of its digits is divisible by 3. It is divisible by 9 if the sum of its digits is divisible by 9.

6. What is the divisibility rule for 11?

   A number is divisible by 11 if the difference between the sum of digits at odd positions and the sum of digits at even positions is 0 or a multiple of 11.

7. How do you convert a fraction into a percentage and a percentage into a fraction?

   To convert a fraction to a percentage, multiply by 100 (e.g. 1/4 = 25%). To convert a percentage to a fraction, divide by 100 (e.g. 40% = 40/100 = 2/5).

8. If a quantity increases by x% and then decreases by x%, what is the net change?

   There is a net decrease of (x^2/100)%. For example, a 10% increase followed by a 10% decrease gives a net 1% decrease, not zero.

9. What are the formulas for Profit, Loss, Profit% and Loss%?

   Profit = SP - CP; Loss = CP - SP. Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Percentages are always calculated on the Cost Price.

10. How do you find the Selling Price (SP) given Cost Price (CP) and Profit% or Loss%?

    SP = CP x (100 + Profit%)/100 for a profit, and SP = CP x (100 - Loss%)/100 for a loss.

11. What is the difference between marked price (MP), discount and selling price?

    Marked Price is the listed/tag price. Discount is a reduction on the MP. Selling Price = MP - Discount = MP x (100 - Discount%)/100.

12. How do you calculate the percentage change between an old value and a new value?

    Percentage change = ((New value - Old value) / Old value) x 100. A positive result is an increase; a negative result is a decrease.

13. How do you divide a number into a given ratio a : b?

    Each part's share = (its ratio term / sum of ratio terms) x total. For ratio a : b of total T, first part = aT/(a+b) and second part = bT/(a+b).

14. What is the difference between a ratio and a proportion?

    A ratio compares two quantities (a : b). A proportion states that two ratios are equal (a : b = c : d, or a/b = c/d). In a proportion, the product of the means equals the product of the extremes (bc = ad).

15. In the proportion a : b = c : d, what are the means and extremes, and what rule connects them?

    a and d are the extremes; b and c are the means. The rule: product of means = product of extremes, i.e. b x c = a x d (cross-multiplication).

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

    Average = (Sum of all observations) / (Number of observations). Equivalently, Sum = Average x Number of observations.

17. How does adding a new value affect an average, and how do you find a new average?

    New average = (Old sum + new value) / (new count). If the added value is above the old average, the average rises; if below, it falls.

18. What is the formula relating speed, distance and time?

    Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

19. How do you convert km/h to m/s and m/s to km/h?

    To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

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