COMSATS Admission Test Quantitative Reasoning Syllabus

Quantitative 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 Reasoning in COMSATS Admission Test, not a summary of it.

1. 1

   Arithmetic

   6 topics

   • Ratios and Proportions
   • Percentages
   • Profit, Loss and Discount
   • Averages
   • Time, Speed and Distance
   • Time and Work
2. 2

   Algebra

   4 topics

   • Linear Equations
   • Quadratic Equations
   • Algebraic Expressions and Factorization
   • Exponents and Surds
3. 3

   Geometry

   4 topics

   • Lines and Angles
   • Triangles and Polygons
   • Circles
   • Area, Perimeter and Volume
4. 4

   Number Properties

   3 topics

   • Factors and Multiples
   • Divisibility Rules
   • HCF and LCM
5. 5

   Data Interpretation

   2 topics

   • Tables and Charts
   • Basic Probability and Statistics

Quantitative Reasoning flashcards for COMSATS Admission Test

25 of 50 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. What is the fundamental property of a proportion a/b = c/d (the cross-multiplication rule)?

   The cross-products are equal: a x d = b x c.

2. In a ratio a : b, if both terms are multiplied or divided by the same nonzero number, what happens to the ratio?

   The ratio remains unchanged (its value stays the same).

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

   a : b : c = 8 : 12 : 15 (make b common: multiply first by 4, second by 3).

4. What is the mean proportional (geometric mean) between two numbers a and b?

   It is the square root of their product, sqrt(a x b).

5. How do you divide an amount N between two people in the ratio a : b?

   First share = N x a/(a+b); second share = N x b/(a+b).

6. What is the formula to convert a fraction or decimal into a percentage?

   Multiply by 100 and add the percent sign (e.g., 0.25 = 0.25 x 100 = 25%).

7. How do you express x as a percentage of y?

   Percentage = (x / y) x 100%.

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

   Net change = a - b - (a x b)/100 (positive means increase, negative means decrease).

9. If a value increases from A to B, what is the percentage increase?

   Percentage increase = ((B - A) / A) x 100%.

10. A number is increased by 20%. By what percentage must the result be decreased to return to the original?

    By 100 x 20/(100+20) = 16.67% (approximately 16 2/3%).

11. Define Cost Price (CP), Selling Price (SP), and the condition for profit versus loss.

    CP is the buying price, SP is the selling price; profit occurs when SP > CP, loss occurs when SP < CP.

12. What are the formulas for Profit Percent and Loss Percent?

    Profit% = (Profit/CP) x 100; Loss% = (Loss/CP) x 100. Both are calculated on Cost Price.

13. What is the difference between Marked Price (MP), Discount, and Selling Price?

    MP is the listed/tag price; Discount is the reduction on MP; SP = MP - Discount, where Discount% is taken on MP.

14. Given Cost Price and Profit%, what is the formula for Selling Price?

    SP = CP x (100 + Profit%)/100.

15. A shopkeeper marks goods 40% above cost and gives a 25% discount. What is the net profit percent?

    5%. CP=100, MP=140, SP=140 x 0.75=105, so profit=5%.

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

    Average = (Sum of all observations) / (Number of observations).

17. If the average of n numbers is A, what is their total sum?

    Sum = A x n (average multiplied by the count).

18. The average of the first n natural numbers (1 to n) equals what?

    (n + 1) / 2.

19. A person's average over 10 innings is 40. After the 11th inning the average becomes 42. What did they score in the 11th inning?

    62. New total = 11 x 42 = 462; old total = 10 x 40 = 400; difference = 62.

20. What is the average speed for a round trip covering equal distances at speeds x and y?

    Average speed = 2xy/(x+y) (the harmonic mean), not the simple arithmetic mean.

21. State the basic relationship between distance, speed, and time.

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

22. How do you convert a speed from km/h to m/s?

    Multiply by 5/18 (since 1 km/h = 1000m/3600s = 5/18 m/s).

23. Two trains move toward each other at speeds u and v. What is their relative speed?

    The sum, u + v (relative speed for opposite directions).

24. Two objects move in the same direction at speeds u and v. What is their relative speed?

    The difference, |u - v| (relative speed for same direction).

25. A boat's speed in still water is b and stream speed is s. What are its downstream and upstream speeds?

    Downstream = b + s; Upstream = b - s.

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