Assertion-Reason MCQs for Sub-Topics of Topic 3: Quantitative Aptitude

Question 1. Assertion (A): The ratio of $2 \text{ kg}$ to $500 \text{ grams}$ is $4 : 1$.

Reason (R): To find the ratio of two quantities, their units must be the same.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): If four quantities $a, b, c, d$ are in proportion, $a:b :: c:d$, then $ad=bc$.

Reason (R): The product of the extreme terms in a proportion is equal to the product of the mean terms.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): If 5 pens cost $\textsf{₹}50$, then 7 pens cost $\textsf{₹}70$ using the unitary method.

Reason (R): The unitary method involves finding the value of a single unit before calculating the value of the required number of units.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The mean proportional between 4 and 9 is 6.

Reason (R): The mean proportional between two positive numbers $a$ and $b$ is $\sqrt{ab}$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If $A:B = 2:3$ and $B:C = 3:4$, then $A:C = 1:2$.

Reason (R): When the consequent of the first ratio is equal to the antecedent of the second ratio, the ratio of the first antecedent to the second consequent gives the ratio of A to C.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): The ratio 5:3 can be written as the improper fraction $5/3$.

Reason (R): In a ratio $a:b$, the first term 'a' is called the antecedent and the second term 'b' is called the consequent, and it can be written as $a/b$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): If $y$ varies directly as $x$, then $\frac{y}{x}$ is a constant.

Reason (R): Direct variation means that as one quantity increases, the other quantity increases proportionally, defined by the equation $y=kx$ where $k$ is the constant of variation.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): If $y$ varies inversely as $x$, then the product $xy$ is a constant.

Reason (R): Inverse variation means that as one quantity increases, the other quantity decreases proportionally, defined by the equation $y=\frac{k}{x}$ where $k$ is the constant of variation.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): For a fixed amount of work, the number of workers is inversely proportional to the time taken to complete the work.

Reason (R): The total work is equal to the product of the number of workers and the time taken, assuming a constant rate of work per worker.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The graph of $y = kx$ where $k$ is a positive constant, is a straight line passing through the origin.

Reason (R): When $x=0$, the value of $y$ is $k \times 0 = 0$, indicating the point (0,0) is on the graph.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): The force of gravitational attraction between two objects is an example of inverse square law variation.

Reason (R): The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): If $A \propto B$ and $B \propto C$, then $A \propto C$.

Reason (R): If two quantities are in direct variation with a third quantity, they are in direct variation with each other.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): 25% is equivalent to the decimal 0.25 and the fraction $\frac{1}{4}$.

Reason (R): Percentage means 'per hundred', so a percentage $P\%$ can be written as $P/100$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): If a quantity increases from 100 to 120, the percentage increase is 20%.

Reason (R): Percentage increase is calculated as $\frac{\text{Increase}}{\text{Original Value}} \times 100$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): A 10% increase followed by a 10% decrease in price results in an overall decrease of 1%.

Reason (R): Successive percentage changes are calculated on the changed value, not the original value for the second change.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): If 20% of a number is 50, the number is 250.

Reason (R): To find the original quantity when a percentage is given, divide the given value by the percentage and multiply by 100.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If A's income is 20% less than B's income, then B's income is 25% more than A's income.

Reason (R): The base for calculating the percentage changes is different in the two statements.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): To convert a fraction to a percentage, multiply the fraction by 100.

Reason (R): Percentage literally means 'out of 100'.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): If the selling price of an article is greater than its cost price, the transaction results in a profit.

Reason (R): Profit is defined as the excess of selling price over cost price (Profit = $\text{SP} - \text{CP}$).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): Profit percentage is always calculated on the selling price.

Reason (R): Profit or loss percentage is conventionally calculated on the cost price to determine the profitability of the purchase.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): Discount is the reduction offered on the marked price of an article.

Reason (R): The selling price is obtained by subtracting the discount from the marked price (SP = MP - Discount).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): A dishonest shopkeeper selling goods at cost price but using a faulty weight of 900 grams for 1 kg earns a profit.

Reason (R): He effectively sells a smaller quantity than what he charges for, leading to a gain.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Successive discounts of 20% and 10% on an item are equivalent to a single discount of 30%.

Reason (R): To calculate the equivalent single discount for successive discounts, you add the percentages.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): If CP of 10 articles = SP of 12 articles, there is a loss.

Reason (R): When the quantity sold for a certain SP is more than the quantity bought for the same CP, there is a loss.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Simple Interest is calculated only on the original principal amount throughout the loan or investment period.

Reason (R): In Simple Interest, the interest earned in each time period is fixed and does not get added to the principal for calculating future interest.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): For a principal amount invested for more than one year, Compound Interest is always greater than or equal to Simple Interest at the same rate.

Reason (R): In Compound Interest, interest is earned not only on the principal but also on the accumulated interest from previous periods.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The difference between Compound Interest and Simple Interest for 2 years on a sum P at R% p.a. is given by $\frac{PR^2}{100^2}$.

Reason (R): The difference arises because Compound Interest includes 'interest on interest', which is equal to the Simple Interest on the first year's interest for the second year.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): When the interest is compounded more frequently (e.g., half-yearly instead of annually), the effective annual rate of interest increases.

Reason (R): Compounding more frequently allows interest earned within the year to start earning interest itself sooner.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Problems related to the growth or depreciation of values over time at a fixed percentage rate are applications of the Compound Interest formula.

Reason (R): In such problems, the change in value in each period is a percentage of the value at the beginning of that period, similar to how interest is compounded.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): If a sum of money doubles itself in 5 years at Simple Interest, it will triple itself in 10 years at the same rate.

Reason (R): In Simple Interest, the amount of interest earned is the same for every equal period of time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): Goods and Services Tax (GST) in India is a destination-based consumption tax.

Reason (R): The tax is levied at the point where goods or services are consumed, rather than where they are produced.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): For an intra-state supply of goods or services (within the same state), both CGST and SGST are levied.

Reason (R): CGST goes to the Central Government and SGST goes to the respective State Government.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): IGST is levied on inter-state supplies of goods or services (between different states).

Reason (R): IGST is collected by the Central Government and is the sum of the applicable CGST and SGST.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Input Tax Credit (ITC) is a mechanism under GST that allows businesses to get a refund of taxes paid on their inputs.

Reason (R): ITC prevents the cascading effect of taxes by enabling tax paid on inputs to be offset against tax payable on outputs.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If the price of an article before GST is $\textsf{₹}1000$ and the GST rate is 18%, the final price including GST is $\textsf{₹}1180$.

Reason (R): The amount of GST is calculated on the price before GST and added to it to find the final price.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): GST is a single tax that replaced all previous indirect taxes like Income Tax, Sales Tax, and Property Tax.

Reason (R): GST primarily subsumed various indirect taxes at the central and state levels, aimed at simplifying the tax structure.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): If a person can complete a piece of work in 10 days, their work rate is $1/10$ of the work per day.

Reason (R): Work rate is defined as the amount of work done per unit of time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): If A can do a work in 10 days and B can do it in 15 days, they can complete the work together in 6 days.

Reason (R): The combined work rate of A and B is the sum of their individual work rates ($1/10 + 1/15$), and the time taken together is the reciprocal of the combined work rate.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): If A is twice as efficient as B, A will take half the time B takes to complete the same work.

Reason (R): Efficiency is inversely proportional to the time taken for a fixed amount of work.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The number of men required to complete a fixed amount of work is directly proportional to the number of days taken.

Reason (R): For a constant amount of work, the product of the number of men and the number of days is constant.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): A pipe that empties a tank has a negative work rate when combined with filling pipes.

Reason (R): The net rate of change in the tank volume is the sum of the filling rates minus the emptying rates.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): If A and B work on alternate days starting with A, the total time taken is always the sum of the time they would take individually divided by 2.

Reason (R): The total work is completed through cycles of work by each person involved, and the time taken depends on the work done in each cycle and the total work.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): If a car travels at a constant speed of $60 \text{ km/hr}$ for 2 hours, the distance covered is $120 \text{ km}$.

Reason (R): Distance is calculated as the product of speed and time (Distance = Speed $\times$ Time).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): To convert a speed from km/hr to m/s, you should multiply the value by $5/18$.

Reason (R): This conversion factor comes from converting kilometers to meters ($1 \text{ km} = 1000 \text{ m}$) and hours to seconds ($1 \text{ hour} = 3600 \text{ s}$), so $1 \text{ km/hr} = \frac{1000}{3600} \text{ m/s} = \frac{5}{18} \text{ m/s}$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): When two trains are moving in the same direction, their relative speed is the sum of their individual speeds.

Reason (R): Relative speed is used to find how quickly the distance between moving objects changes.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The time taken by a train to cross a stationary object of negligible length (like a pole or a man) is the time it takes to cover its own length.

Reason (R): For a point object, the effective distance covered by the train to cross it is equal to the length of the train itself.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If a boat's speed in still water is $V_b$ and stream speed is $V_s$, its speed upstream is $V_b + V_s$.

Reason (R): Upstream movement is against the flow of the stream, which reduces the effective speed of the boat.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): The average speed for a round trip from A to B and back to A at different speeds $S_1$ and $S_2$ is the arithmetic mean of $S_1$ and $S_2$.

Reason (R): Average speed is defined as Total Distance / Total Time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The average of a set of numbers is a measure of central tendency.

Reason (R): The average value tends to lie somewhere in the middle of the data set.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): If a number equal to the current average is added to a set of numbers, the average remains unchanged.

Reason (R): The addition increases the sum by the value of the number, and increases the count by one, such that the sum divided by the count stays the same.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): If each number in a set is multiplied by a constant $k$, the average of the new set is $k$ times the original average.

Reason (R): Multiplication distributes over addition, so the sum of the new numbers is $k$ times the original sum, while the count remains the same.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The average of any 7 consecutive integers is the middle integer.

Reason (R): Consecutive integers form an arithmetic progression, and the average of an odd number of terms in an AP is the middle term.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): Weighted average is used when different items in a data set have different levels of importance or different frequencies.

Reason (R): In a weighted average calculation, each value is multiplied by its corresponding weight before summing and dividing by the total weight.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): If a person joins a group and the average age increases, the new person is older than the original average age.

Reason (R): Adding a value greater than the current average pulls the average upwards.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The minute hand moves $6^\circ$ per minute, and the hour hand moves $0.5^\circ$ per minute.

Reason (R): The minute hand covers 360 degrees in 60 minutes, while the hour hand covers 360 degrees in 12 hours (720 minutes).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): The relative speed of the minute hand with respect to the hour hand is $5.5^\circ$ per minute.

Reason (R): This is the difference between the speeds of the minute hand ($6^\circ$/min) and the hour hand ($0.5^\circ$/min).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The hands of a clock are at right angles exactly 24 times in a 12-hour period.

Reason (R): The hands are at right angles twice every hour, except between 2 and 3, and 8 and 9, where they are at right angles only once.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): If a clock gains time, it shows a time ahead of the correct time.

Reason (R): A clock that gains time runs faster than a normal clock, covering more than 360 degrees in 12 hours for the hour hand cycle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): The hands of a clock coincide exactly at 12:00 and also at some point between every consecutive hour.

Reason (R): The minute hand gains 360 degrees over the hour hand in approximately $65 \frac{5}{11}$ minutes, which is the interval between successive coincidences.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): The angle between the hour hand and the minute hand at any given time can be calculated using their speeds and the time elapsed from the previous hour mark.

Reason (R): The position of each hand is determined by the time elapsed and its constant angular speed.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): A year is a leap year if it is divisible by 4.

Reason (R): Every fourth year is a leap year to account for the extra quarter day in Earth's revolution around the sun.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): An ordinary year has 1 odd day, and a leap year has 2 odd days.

Reason (R): Odd days are the number of days remaining after dividing the total number of days by 7.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): The calendar for the year 2016 (a leap year) will repeat after 28 years, i.e., in the year 2044.

Reason (R): The calendar of a leap year repeats after 28 years because the accumulation of odd days over 28 years becomes a multiple of 7.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): The last day of a century year cannot be Tuesday, Thursday, or Saturday.

Reason (R): The number of odd days in 100, 200, 300, and 400 years are 5 (Friday), 3 (Wednesday), 1 (Monday), and 0 (Sunday) respectively, and this pattern repeats.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If 1st January 2005 was a Saturday, then 1st January 2006 was a Sunday.

Reason (R): The year 2005 is an ordinary year, and the day of the week shifts forward by one day in an ordinary year.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): The year 1900 was not a leap year.

Reason (R): A century year is a leap year only if it is divisible by 400.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): In a linear arrangement, if A is third to the right of B, there are exactly two persons sitting between A and B.

Reason (R): The position "third to the right" means there are two positions between the person and the reference point on the right side.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): In a circular arrangement facing the center, "X is to the immediate right of Y" means X is in the position reached by moving clockwise from Y.

Reason (R): When facing the center, a person's right side corresponds to the clockwise direction relative to the center of the circle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): In a row of 50 students, if a student's rank from the top is 15th, their rank from the bottom is 36th.

Reason (R): In a row of N persons, if a person is Rth from one end, their rank from the other end is given by (N - R + 1).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Drawing diagrams or sketches is a useful technique for solving arrangement puzzles.

Reason (R): Visual representations help in organizing the given information and deducing the positions of individuals relative to each other.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): In a circular arrangement of an odd number of people facing the center, no two people can be exactly opposite to each other.

Reason (R): Exact opposite positions in a circle require an even number of equally spaced positions.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): Identifying the persons sitting at the extreme ends is a good starting point for solving linear arrangement problems.

Reason (R): Extreme ends provide fixed reference points from which other positions can be determined.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 1. Assertion (A): The rule of alligation can be used to find the ratio in which two ingredients at different prices must be mixed to obtain a mixture at a desired mean price.

Reason (R): Alligation is a method derived from the concept of weighted average.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 2. Assertion (A): In a partnership, if two partners invest different amounts for the same period, the total profit is shared equally between them.

Reason (R): Profit is shared in the ratio of the products of the amount invested and the time period of investment.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 3. Assertion (A): When water is added to a milk and water mixture, the percentage of milk in the mixture decreases.

Reason (R): Adding water increases the total volume of the mixture while the quantity of milk remains unchanged.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 4. Assertion (A): Solving problems involving a combination of Time and Work and Pipes and Cisterns requires using the concept of work rate per unit time.

Reason (R): Pipes filling or emptying a tank are treated as individuals doing a certain amount of work (filling or emptying) in a given time.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 5. Assertion (A): If a train travels a certain distance at speed S1 and returns at speed S2, the average speed for the entire journey is the simple average $(S1+S2)/2$.

Reason (R): Average speed is defined as the total distance traveled divided by the total time taken.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.

Question 6. Assertion (A): Problems involving coins of different denominations in a bag, where the total value is given, can be solved using ratio and algebraic equations.

Reason (R): The value contributed by each denomination is the product of the number of coins of that denomination and its face value.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is NOT the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

(E) Both A and R are false.