KVS Recruitment (PGT/TGT/PRT) Reasoning and Quantitative Aptitude Flashcards

24 sample cards from the Reasoning and Quantitative Aptitude deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is the difference between a "standard" die and an "ordinary" die in dice reasoning?

   Standard die: opposite faces sum to 7. Ordinary die: opposite faces are simply the two faces that cannot be seen together in any given view; their sum need not be 7. You deduce opposites from the views shown.

2. Rule for finding hidden/opposite faces from two views of a die: if one face is common in both positions, how do you find the opposite of the common face?

   If a face is common (same number, same position) in two views, then the remaining four visible faces are all adjacent to it; the one face NOT visible in either view is opposite the common face.

3. When a cube of side n units is painted on all faces and cut into n³ unit cubes, how many small cubes have exactly 3 painted faces?

   Always 8 (the corner cubes), for any n ≥ 2.

4. For an n-side painted cube cut into unit cubes, how many small cubes have exactly 2 faces painted, and how many have exactly 1 face painted?

   Exactly 2 faces: 12(n−2) (the edge cubes). Exactly 1 face: 6(n−2)² (the face-center cubes). 0 faces (interior): (n−2)³.

5. State the divisibility rules for 3 and for 9.

   Divisible by 3 if the sum of its digits is divisible by 3. Divisible by 9 if the sum of its digits is divisible by 9.

6. State the divisibility rules for 4 and for 8.

   Divisible by 4 if the last two digits form a number divisible by 4. Divisible by 8 if the last three digits form a number divisible by 8.

7. State the divisibility rule for 11.

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

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

   For two numbers, Product of the numbers = LCM × HCF. So LCM × HCF = a × b.

9. What is the formula for the sum of the first n natural numbers, and the sum of their squares?

   Sum of first n natural numbers = n(n+1)/2. Sum of squares = n(n+1)(2n+1)/6. Sum of cubes = [n(n+1)/2]².

10. Define HCF (GCD) and LCM of two or more numbers.

    HCF (Highest Common Factor) is the largest number that divides all the given numbers exactly. LCM (Least Common Multiple) is the smallest number that is exactly divisible by all the given numbers.

11. What is the simple interest formula, and what does each symbol mean?

    SI = (P × R × T)/100, where P = principal, R = rate of interest per annum (%), T = time in years.

12. What is the compound interest formula for amount compounded annually?

    A = P(1 + R/100)ᵀ, where A = amount, P = principal, R = annual rate (%), T = time in years. Compound Interest = A − P.

13. How do you calculate profit percentage and loss percentage?

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

14. What are the formulas for Selling Price (SP) given cost price and profit% or loss%?

    SP = CP × (100 + Profit%)/100 for profit; SP = CP × (100 − Loss%)/100 for loss.

15. How is discount calculated, and on what value?

    Discount is calculated on the Marked Price (MP). Discount = MP × (Discount%)/100, and Selling Price = MP − Discount.

16. What is the formula relating Speed, Distance, and Time?

    Speed = Distance/Time; Distance = Speed × Time; Time = Distance/Speed. To convert km/hr to m/s, multiply by 5/18; m/s to km/hr, multiply by 18/5.

17. 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 of the two speeds (not the arithmetic mean), because equal distances are covered at different speeds.

18. What is the formula for the average of a set of numbers?

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

19. How do you convert a fraction or ratio into a percentage and vice versa?

    Fraction → percentage: multiply by 100. Percentage → fraction: divide by 100. E.g., 3/4 = 75%; 40% = 40/100 = 2/5.

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

    There is a net decrease of (x²/100)%. Successive increase and decrease by the same percent never returns to the original; it always results in a loss of x²/100 percent.

21. What is Data Interpretation (DI), and what are the common forms in which data is presented?

    DI is the analysis and interpretation of data to answer questions. Common forms: tables, bar graphs, line graphs, pie charts, and combination/caselet data.

22. In a pie chart, how do you convert a percentage of data into the central angle (degrees), and vice versa?

    Central angle = (Percentage/100) × 360°, i.e., each 1% = 3.6°. Conversely, Percentage = (Angle/360) × 100. The whole circle (100%) = 360°.

23. In Data Interpretation, what is the formula for percentage increase/decrease between two values?

    Percentage change = [(New value − Old value)/Old value] × 100. A positive result is an increase; a negative result is a decrease, always taken with respect to the original (old) value.

24. In a bar graph or line graph DI set, how do you find the ratio of one category to another?

    Read the exact values (heights/data points) of the two categories from the graph, then express them as Value₁ : Value₂ and simplify to lowest terms. Ensure both use the same unit/scale.

What this deck covers

Reasoning and Quantitative Aptitude flashcards FAQ