PRC-2 · Chapter 2

Coordinate System and Its Application MCQs with Answers

45 multiple-choice questions on Coordinate System and Its Application for PRC-2 Quantitative Analysis for Business. Try each one before revealing the answer and explanation.

1. Question 1

   What is the term for a group of numbers used to indicate the exact position of a point or a line in a space of given dimensions?

   • A) Progression
   • B) Coordinate
   • C) Variable
   • D) Intercept
   Show answer & explanation

   Answer: B) Coordinate

   A coordinate is formally defined as a group of numbers used to specify the exact location or position of a point or line within a coordinate system.

2. Question 2

   If a point B is plotted at coordinates (12, 18), what does the number 12 represent?

   • A) The location on the y-axis
   • B) The location on the x-axis
   • C) The slope of the line
   • D) The y-intercept
   Show answer & explanation

   Answer: B) The location on the x-axis

   In a standard (x, y) coordinate pair, the first number (12) indicates the position on the horizontal x-axis, and the second number indicates the vertical y-axis.

3. Question 3

   What is the slope of the straight line defined by the equation y = 5 - 4x?

   • A) 5
   • B) -4
   • C) 4
   • D) -5
   Show answer & explanation

   Answer: B) -4

   When comparing the equation y = -4x + 5 to the standard line equation y = mx + c, the slope 'm' is the coefficient of x, which in this case is -4.

4. Question 4

   If a straight line has a slope of 2, what is the slope of a line that is perfectly perpendicular to it?

   • A) 2
   • B) -2
   • C) 0.5
   • D) -0.5
   Show answer & explanation

   Answer: D) -0.5

   Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1). If m1 = 2, then m2 must be -1 / 2 = -0.5.

5. Question 5

   What are the y-intercept and the slope of the equation 2y = 8 - 6x?

   • A) y-intercept 8, slope -6
   • B) y-intercept 4, slope -3
   • C) y-intercept -3, slope 4
   • D) y-intercept 8, slope 6
   Show answer & explanation

   Answer: B) y-intercept 4, slope -3

   Rearranging the equation into the y = mx + c format: dividing the entire equation by 2 gives y = -3x + 4. Therefore, the slope (m) is -3 and the y-intercept (c) is 4.

6. Question 6

   The mathematical equation y = c represents a straight line that is:

   • A) Parallel to the x-axis
   • B) Parallel to the y-axis
   • C) Diagonal through the origin
   • D) Perpendicular to the x-axis
   Show answer & explanation

   Answer: A) Parallel to the x-axis

   An equation in the simple form y = c has a slope of 0 (m = 0). This represents a purely horizontal line that runs perfectly parallel to the x-axis.

7. Question 7

   A manufacturer's fixed costs are Rs. 60,000 per month, and the variable cost is Rs. 15 per unit. What is the total cost function C(x) for producing 'x' units?

   • A) C(x) = 60,000x + 15
   • B) C(x) = 15x - 60,000
   • C) C(x) = 15x + 60,000
   • D) C(x) = 60,000 / 15x
   Show answer & explanation

   Answer: C) C(x) = 15x + 60,000

   Total cost equals the variable cost per unit multiplied by the number of units, plus the fixed costs. This translates algebraically to C(x) = 15x + 60,000.

8. Question 8

   A firm sells a product for Rs. 30 per unit. The variable cost is Rs. 20 per unit, and total fixed costs are Rs. 50,000. What is the break-even volume of sales in units?

   • A) 1,667 units
   • B) 2,500 units
   • C) 5,000 units
   • D) 10,000 units
   Show answer & explanation

   Answer: C) 5,000 units

   Break-even occurs when Total Revenue equals Total Cost: 30x = 20x + 50,000. Solving for x leaves 10x = 50,000, meaning x = 5,000 units.

9. Question 9

   Two vehicles are 10 km apart and moving directly towards each other. One moves at 3 km/hr and the other at 2 km/hr. Assuming they start at the same time, how long will it take for them to meet?

   • A) 1 hour
   • B) 2 hours
   • C) 3 hours
   • D) 4 hours
   Show answer & explanation

   Answer: B) 2 hours

   Using linear logic for relative speed: 3t + 2t = 10, which simplifies to 5t = 10. Therefore, t = 2 hours. They will meet in exactly 2 hours.

10. Question 10

    In a standard two-dimensional coordinate system, how many quadrants are formed by the intersection of the x-axis and y-axis?

    • A) Two
    • B) Three
    • C) Four
    • D) Six
    Show answer & explanation

    Answer: C) Four

    The horizontal x-axis and vertical y-axis intersect perfectly at the origin, dividing the entire coordinate plane into four distinct quadrants (Quadrant 1 through 4).

11. Question 11

    At which distinct point do the straight lines represented by y = 2x + 4 and y = x + 6 intersect?

    • A) (2, 8)
    • B) (3, 10)
    • C) (4, 12)
    • D) (1, 7)
    Show answer & explanation

    Answer: A) (2, 8)

    Set the equations equal: 2x + 4 = x + 6. Solving for x yields x = 2. Substituting x=2 back into either equation gives y = 2(2) + 4 = 8. The intersection is (2, 8).

12. Question 12

    What is the slope of the straight line passing through the coordinates (2, 5) and (4, 11)?

    • A) 2
    • B) 3
    • C) 4
    • D) 6
    Show answer & explanation

    Answer: B) 3

    The slope formula is m = (y2 - y1) / (x2 - x1). Substituting the points gives: m = (11 - 5) / (4 - 2) = 6 / 2 = 3.

13. Question 13

    If the total cost of producing 10 units is Rs. 500 and the total cost for producing 20 units is Rs. 800, what is the variable cost per unit assuming a linear relationship?

    • A) Rs. 30
    • B) Rs. 40
    • C) Rs. 50
    • D) Rs. 80
    Show answer & explanation

    Answer: A) Rs. 30

    The variable cost represents the slope of the cost function. Variable cost = Change in Cost / Change in Units = (800 - 500) / (20 - 10) = 300 / 10 = Rs. 30 per unit.

14. Question 14

    Which of the following represents the equation of a straight line where the y-intercept is -2 and the slope is 5?

    • A) 5x - y = 2
    • B) -5x + y = -2
    • C) x - 5y = -2
    • D) 5x + y = 2
    Show answer & explanation

    Answer: B) -5x + y = -2

    Using the slope-intercept form y = mx + c, plug in m = 5 and c = -2 to get y = 5x - 2. Rearranging this standard equation gives -5x + y = -2.

15. Question 15

    What is true about finding the intersection of two perfectly parallel lines in a coordinate system?

    • A) They intersect exactly at the origin.
    • B) They intersect at multiple points forming a curve.
    • C) They have the same slope and therefore never intersect.
    • D) They intersect at the y-intercepts only.
    Show answer & explanation

    Answer: C) They have the same slope and therefore never intersect.

    Parallel lines have identical slopes and distinct y-intercepts. Because they rise or fall at the exact same rate, they never cross or intersect at any point.

16. Question 16

    Assuming a linear cost relationship, if the total cost of producing 10 units is Rs. 250 and the cost of 15 units is Rs. 350, what is the estimated cost of producing 20 units?

    • A) Rs. 400
    • B) Rs. 450
    • C) Rs. 500
    • D) Rs. 550
    Show answer & explanation

    Answer: B) Rs. 450

    First, find the variable cost (slope): (350 - 250) / (15 - 10) = 100 / 5 = Rs. 20 per unit. Fixed cost is 250 - (10 * 20) = Rs. 50. The cost function is C = 20x + 50. For 20 units, C = 20(20) + 50 = Rs. 450.

17. Question 17

    A company has a linear cost function of C = 20x + 12,000, where x is the number of units produced. If the selling price is Rs. 35 per unit, at what volume of sales does the company break even?

    • A) 600 units
    • B) 750 units
    • C) 800 units
    • D) 1,000 units
    Show answer & explanation

    Answer: C) 800 units

    At break-even, total revenue equals total cost: 35x = 20x + 12,000. Subtracting 20x gives 15x = 12,000. Dividing by 15 yields x = 800 units.

18. Question 18

    A firm plans to sell a product for Rs. 50 per unit. The variable cost of production is Rs. 42 per unit, and the total fixed cost is Rs. 64,000. Assuming linear functions, what is the break-even volume of sales?

    • A) 1,500 units
    • B) 8,000 units
    • C) 12,000 units
    • D) 15,000 units
    Show answer & explanation

    Answer: B) 8,000 units

    The contribution margin per unit is Selling Price - Variable Cost (50 - 42) = Rs. 8. The break-even point is Fixed Costs / Contribution Margin = 64,000 / 8 = 8,000 units.

19. Question 19

    A product has a variable selling cost of Rs. 2 per unit and a total selling price of Rs. 8. If the total contribution margin per unit is Rs. 3, what is the variable production cost per unit?

    • A) Rs. 2
    • B) Rs. 3
    • C) Rs. 4
    • D) Rs. 5
    Show answer & explanation

    Answer: B) Rs. 3

    Contribution Margin = Selling Price - Total Variable Costs. Therefore, 3 = 8 - Total VC, making Total VC = Rs. 5. Since Total VC includes both production and selling costs, the Production VC = 5 - 2 = Rs. 3.

20. Question 20

    A company sells a product for Rs. 60 with a variable cost of Rs. 30 per unit. Next year, both the selling price and the variable cost will increase by exactly Rs. 5 each. What is the percentage change in the contribution margin per unit?

    • A) 0%
    • B) 5%
    • C) 10%
    • D) 16.67%
    Show answer & explanation

    Answer: A) 0%

    Current contribution margin is 60 - 30 = Rs. 30. New selling price is 65, new variable cost is 35. New contribution margin is 65 - 35 = Rs. 30. Because the absolute margin remains exactly Rs. 30, the percentage change is 0%.

21. Question 21

    What is the slope of the straight line passing through the coordinates (1, 3) and (5, 15)?

    • A) 2
    • B) 3
    • C) 4
    • D) 5
    Show answer & explanation

    Answer: B) 3

    The slope formula is m = (y2 - y1) / (x2 - x1). Substituting the points gives: m = (15 - 3) / (5 - 1) = 12 / 4 = 3.

22. Question 22

    What is the y-intercept of the linear equation 2x - 5y = 20?

    • A) 4
    • B) -4
    • C) 10
    • D) -10
    Show answer & explanation

    Answer: B) -4

    To find the y-intercept, set x to 0 and solve for y. 2(0) - 5y = 20, which leaves -5y = 20. Therefore, y = -4.

23. Question 23

    Which of the following equations correctly represents a straight line passing through the origin with a positive slope of 4?

    • A) y = 4x + 4
    • B) x = 4y
    • C) y = 4x
    • D) 4x - y = 4
    Show answer & explanation

    Answer: C) y = 4x

    A line passing through the origin has a y-intercept (c) of exactly 0. Given a slope (m) of 4, the standard equation y = mx + c becomes simply y = 4x.

24. Question 24

    If Line A is defined by the equation y = 3x - 4, what must be the slope of Line B for it to be perfectly perpendicular to Line A?

    • A) 3
    • B) -3
    • C) 1/3
    • D) -1/3
    Show answer & explanation

    Answer: D) -1/3

    Perpendicular lines have slopes that are negative reciprocals of one another (m1 * m2 = -1). Since the slope of Line A is 3, the slope of Line B must be -1/3.

25. Question 25

    Which of the following mathematical conditions must be met for two distinct straight lines to be strictly parallel?

    • A) They must intersect at exactly one point.
    • B) Their slopes must be negative reciprocals.
    • C) Their y-intercepts must be identical.
    • D) Their slopes must be exactly equal.
    Show answer & explanation

    Answer: D) Their slopes must be exactly equal.

    Parallel lines run perfectly alongside each other without ever intersecting. For this to happen in a coordinate plane, they must rise or fall at the exact same rate, meaning their slopes must be strictly equal.

26. Question 26

    Calculate the exact linear distance between the origin point (0,0) and the coordinate point (6,8).

    • A) 10
    • B) 12
    • C) 14
    • D) 100
    Show answer & explanation

    Answer: A) 10

    Using the standard distance formula d = √((x2 - x1)^2 + (y2 - y1)^2), the calculation is √( (6 - 0)^2 + (8 - 0)^2 ) = √(36 + 64) = √100 = 10.

27. Question 27

    What are the coordinates of the exact midpoint of a line segment connecting the points (4, -2) and (10, 6)?

    • A) (7, 2)
    • B) (6, 4)
    • C) (14, 4)
    • D) (3, 4)
    Show answer & explanation

    Answer: A) (7, 2)

    The midpoint formula averages the x and y coordinates: ((x1 + x2)/2 , (y1 + y2)/2). Here, ((4 + 10)/2 , (-2 + 6)/2) = (14/2 , 4/2) = (7, 2).

28. Question 28

    In a standard linear total cost function formatted as C(x) = mx + c, what specific financial component does the y-intercept 'c' represent?

    • A) Variable Cost per Unit
    • B) Total Revenue
    • C) Total Fixed Costs
    • D) Contribution Margin
    Show answer & explanation

    Answer: C) Total Fixed Costs

    In a linear cost model, the y-intercept is the point where production x is exactly zero. The cost incurred at zero production represents the total fixed costs of the operation.

29. Question 29

    Determine the x-intercept of the linear equation 4x + 3y = 24.

    • A) 4
    • B) 6
    • C) 8
    • D) 24
    Show answer & explanation

    Answer: B) 6

    To mathematically find the x-intercept, you must set y to 0 and solve for x. 4x + 3(0) = 24, meaning 4x = 24. Dividing by 4 gives x = 6.

30. Question 30

    At what specific coordinate point do the lines y = 2x + 10 and y = 4x - 2 intersect?

    • A) (4, 18)
    • B) (5, 20)
    • C) (6, 22)
    • D) (7, 26)
    Show answer & explanation

    Answer: C) (6, 22)

    Set the equations equal to each other: 2x + 10 = 4x - 2. Subtract 2x from both sides to get 10 = 2x - 2. Add 2 to get 12 = 2x, so x = 6. Substituting x = 6 back into the first equation yields y = 2(6) + 10 = 22.

31. Question 31

    What is the formula for calculating Simple Interest (I)?

    • A) I = P(1 + r)^n
    • B) I = P × r × n
    • C) I = P / (r × n)
    • D) I = A - P
    Show answer & explanation

    Answer: B) I = P × r × n

    Simple interest is calculated only on the original principal amount (P) for the specified period (n) at the given rate (r).

32. Question 32

    When interest is 'compounded', it means interest is calculated on:

    • A) Only the original principal.
    • B) The principal plus any previously earned interest.
    • C) Only the final year of the investment.
    • D) The principal divided by time.
    Show answer & explanation

    Answer: B) The principal plus any previously earned interest.

    Compounding means you earn 'interest on interest', leading to faster growth of the investment over time.

33. Question 33

    A series of equal periodic payments made at regular intervals is known as a/an:

    • A) Amortization
    • B) Annuity
    • C) Depreciation
    • D) Discounting
    Show answer & explanation

    Answer: B) Annuity

    Annuities involve regular payments like insurance premiums, pension contributions, or monthly loan installments.

34. Question 34

    In financial mathematics, 'Present Value' (PV) refers to:

    • A) The total value of an investment at the end of its term.
    • B) The current worth of a future sum of money, given a specific rate of return.
    • C) The total interest paid over the life of a loan.
    • D) The nominal rate after inflation.
    Show answer & explanation

    Answer: B) The current worth of a future sum of money, given a specific rate of return.

    Present value 'discounts' future money back to today's terms because money available today is worth more than the same amount in the future (Time Value of Money).

35. Question 35

    What is the effective annual rate (EAR) if the nominal rate is 12% compounded monthly?

    • A) 12%
    • B) 12.36%
    • C) 12.68%
    • D) 13%
    Show answer & explanation

    Answer: C) 12.68%

    Formula: (1 + r/m)^m - 1. Here, (1 + 0.12/12)^12 - 1 = (1.01)^12 - 1 ≈ 1.1268 - 1 = 12.68%.

36. Question 36

    An annuity where the payments are made at the *beginning* of each period is called a/an:

    • A) Ordinary Annuity
    • B) Annuity Due
    • C) Perpetuity
    • D) Deferred Annuity
    Show answer & explanation

    Answer: B) Annuity Due

    Most standard annuities (Ordinary) have payments at the end of the period. Annuity Due payments occur at the start (common for rent or insurance).

37. Question 37

    What happens to the Present Value of a future payment as the discount rate (interest rate) increases?

    • A) It increases.
    • B) It decreases.
    • C) It remains constant.
    • D) It becomes zero.
    Show answer & explanation

    Answer: B) It decreases.

    Because money can earn more elsewhere if rates are high, a future payment is worth significantly less in today's terms when the discount rate rises.

38. Question 38

    How long will it take for a sum to double itself at 10% Simple Interest per annum?

    • A) 7 years
    • B) 8 years
    • C) 10 years
    • D) 12 years
    Show answer & explanation

    Answer: C) 10 years

    For doubling, I must equal P. So, P = P × 0.10 × n -> 1 = 0.10n -> n = 10 years.

39. Question 39

    The process of systematically paying off a debt (like a mortgage) with regular payments over time is called:

    • A) Amortization
    • B) Capitalization
    • C) Appreciation
    • D) Arbitrage
    Show answer & explanation

    Answer: A) Amortization

    An amortization schedule shows how each payment is split between interest and principal reduction.

40. Question 40

    If you invest Rs. 1,000 at 5% interest compounded annually for 2 years, what is the Future Value (FV)?

    • A) Rs. 1,100
    • B) Rs. 1,102.5
    • C) Rs. 1,105
    • D) Rs. 1,110
    Show answer & explanation

    Answer: B) Rs. 1,102.5

    Formula: FV = P(1 + r)^n. FV = 1,000(1.05)^2 = 1,000 × 1.1025 = Rs. 1,102.5.

41. Question 41

    What is 'Depreciation' in a financial context?

    • A) The increase in value of an asset over time.
    • B) The systematic reduction in the recorded value of a physical asset over its useful life.
    • C) The total dividend paid to shareholders.
    • D) The cost of borrowing from a bank.
    Show answer & explanation

    Answer: B) The systematic reduction in the recorded value of a physical asset over its useful life.

    Depreciation reflects the wear and tear or obsolescence of assets like machinery or vehicles.

42. Question 42

    An investment produces Rs. 5,000 every year forever. This type of cash flow is called a/an:

    • A) Annuity Due
    • B) Sinking Fund
    • C) Perpetuity
    • D) Growing Annuity
    Show answer & explanation

    Answer: C) Perpetuity

    A perpetuity is a financial instrument that pays a fixed amount of money at regular intervals indefinitely.

43. Question 43

    In the 'Reducing Balance' method of depreciation, more depreciation is charged in:

    • A) The final years of the asset's life.
    • B) The earlier years of the asset's life.
    • C) Every year equally.
    • D) No years (it stays constant).
    Show answer & explanation

    Answer: B) The earlier years of the asset's life.

    Because the rate is applied to the book value (which is highest at the start), the absolute depreciation expense is largest in year 1 and decreases over time.

44. Question 44

    What is the standard formula for the Future Value of an Ordinary Annuity (FVAn)?

    • A) R [(1+i)^n - 1] / i
    • B) R [1 - (1+i)^-n] / i
    • C) R × (1+i)^n
    • D) R / i
    Show answer & explanation

    Answer: A) R [(1+i)^n - 1] / i

    This formula calculates the total accumulated value of several regular payments (R) made at the end of each period for 'n' periods at interest rate 'i'.

45. Question 45

    A 'Sinking Fund' is established primarily to:

    • A) Pay for daily office expenses.
    • B) Save up a specific sum of money over time to replace an asset or repay a debt in the future.
    • C) Hide losses from tax authorities.
    • D) Distribute all profits to owners immediately.
    Show answer & explanation

    Answer: B) Save up a specific sum of money over time to replace an asset or repay a debt in the future.

    Companies use sinking funds to ensure they have enough cash on hand to meet large future obligations by setting aside regular contributions.