All Free Quantitative Methods MCQs with Answers

• A. 0
• B. 1
• C. 10
• D. 100

Explanation: The base period is conventionally assigned an index value of 100. Other periods are then expressed as percentages of the base period, so…

• A. Arithmetic mean of Laspeyres and Paasche indices
• B. Ratio of Laspeyres to Paasche indices
• C. Difference between Laspeyres and Paasche indices
• D. Geometric mean of Laspeyres and Paasche indices

Explanation: Fisher's price index is the geometric mean of the Laspeyres and Paasche price indices.

• A. Geometric mean of price and quantity indices
• B. Arithmetic mean of Laspeyres and Paasche price indices
• C. Difference between current and base expenditures
• D. Ratio of current expenditure to base quantities

Explanation: The Dorbish-Bowley index takes the arithmetic mean of the Laspeyres and Paasche price indices.

• A. It measures changes in total expenditure
• B. It measures changes in commodity prices
• C. It measures changes in physical quantities
• D. It measures changes in purchasing power

Explanation: A quantity index measures changes in the physical volume of goods or services, such as production or consumption.

• A. 18 percent
• B. twenty-eight percent
• C. 128 percent
• D. 28 percent

Explanation: The increase is 128 minus 100, or 28 index points. Since the base is 100, these 28 points represent a 28 percent rise, not a 128 percent…

• A. Unit test
• B. Circular test
• C. Factor reversal test
• D. Time reversal test

Explanation: The unit test requires an index to remain unchanged when units such as kilograms or grams are substituted consistently.

• A. Base-period expenditure
• B. Value index
• C. Current-period expenditure
• D. Simple aggregative index

Explanation: The factor reversal test requires P01 multiplied by Q01 to equal V01, the value index.

• A. The total physical output of an economy
• B. All goods produced by domestic industries
• C. A fixed basket of consumer goods and services
• D. The foreign exchange reserves of a country

Explanation: A consumer price index tracks the cost of a selected basket purchased by consumers.

• A. Show the same proportional rise
• B. Remain equal to 100
• C. Show a fall in total value
• D. Measure only the quantity change

Explanation: When every price changes by the same proportion and quantities do not change, the price index should reflect that common proportional…

• A. Increased by 15 percent
• B. Decreased by 15 percent
• C. Decreased by 85 percent
• D. Remained unchanged

Explanation: An index of 85 is 15 points below the base value of 100. Therefore, the measured level has fallen by 15 percent relative to the base…

• A. The restrictions imposed on decision variables
• B. The quantity to be maximized or minimized
• C. The set of values violating every restriction
• D. The list of constants used only in calculations

Explanation: The objective function expresses the goal of the problem, such as maximizing profit or minimizing cost.

• A. It occurs only at the origin of the graph
• B. It gives the largest possible value of the objective
• C. It satisfies every constraint and sign restriction
• D. It contains equal values for all decision variables

Explanation: A feasible solution satisfies all constraints, including non-negativity or other sign restrictions.

• A. At a point outside the feasible region
• B. At the midpoint of every feasible line segment
• C. At the point nearest to the coordinate origin
• D. At an extreme point of the feasible region

Explanation: The fundamental theorem of linear programming states that an optimum occurs at an extreme point when the feasible region is non-empty and…

• A. 8
• B. 9
• C. 10
• D. 12

Explanation: The relevant corner points include (2,2), (1,3), and the axis points. At (2,2), Z equals 3(2) + 2(2) = 10, which is greater than the…

• A. To remove the non-negativity requirement
• B. To change a maximization problem into minimization
• C. To convert the inequality into an equality
• D. To make the objective function nonlinear

Explanation: A non-negative slack variable s converts the constraint into 2x + 3y + s = 12.

• A. x + y ≤ 5 and x + y ≥ 2
• B. x + y ≤ 5 and x + y ≥ 5
• C. x + y ≤ 3 and x + y ≥ 5
• D. x + y ≥ 3 and x + y ≥ 5

Explanation: The two constraints in option C require the same expression to be at most 3 and at least 5 at the same time.

• A. Proportionality
• B. Divisibility
• C. Certainty
• D. Non-negativity

Explanation: Proportionality means that resource use and contribution to the objective change in direct proportion to each activity level.

• A. A maximization problem with equal constraints only
• B. A minimization problem with greater-than-or-equal constraints
• C. A minimization problem with less-than-or-equal constraints
• D. A feasibility problem with no objective function

Explanation: The standard dual of a primal maximization problem with ≤ constraints is a minimization problem with ≥ constraints.

• A. The sensitivity interval
• B. The objective function line
• C. The feasible region
• D. The infeasibility boundary

Explanation: The common area satisfying every constraint and sign restriction is called the feasible region.

• A. At least one basic variable has a zero value
• B. Every decision variable has a positive value
• C. The objective function has no coefficients
• D. The feasible region has no boundary

Explanation: Degeneracy occurs when one or more basic variables are zero in a basic feasible solution.