Negative Questions MCQs for Sub-Topics of Topic 3: Quantitative Aptitude

Question 1. Which of the following is NOT a property of a ratio?

(A) The terms of a ratio must be of the same kind.

(B) The ratio of two quantities has no unit.

(C) The value of a ratio changes if the order of the terms is reversed.

(D) A ratio must always be expressed in its simplest form.

Question 2. Which pair of ratios does NOT form a proportion?

(A) $2:3$ and $4:6$

(B) $5:10$ and $1:2$

(C) $3:4$ and $6:8$

(D) $10:15$ and $15:20$

Question 3. Which of the following problems CANNOT be solved directly using the unitary method?

(A) If $5$ kg of sugar costs $\textsf{₹}200$, find the cost of $8$ kg of sugar.

(B) If a car travels $180$ km in $3$ hours, find the time taken to travel $300$ km.

(C) If $6$ men can do a work in $12$ days, find the time taken by $9$ men to do the same work.

(D) Find the area of a rectangle given its length and width.

Question 4. If four quantities $a, b, c, d$ are in proportion, $a:b :: c:d$, which of the following is NOT necessarily true?

(A) $ad = bc$

(B) $a/b = c/d$

(C) $a:c :: b:d$ (Alternendo)

(D) $a, b, c, d$ are in continued proportion.

Question 5. In a ratio $5:8$, which statement is FALSE?

(A) The antecedent is 5.

(B) The consequent is 8.

(C) The ratio can be written as the fraction $5/8$.

(D) The inverse ratio is 5:8.

Question 6. If a sum of $\textsf{₹}1000$ is divided among A, B, and C in the ratio $2:3:5$, which share is NOT correctly calculated?

(A) A's share is $\textsf{₹}200$.

(B) B's share is $\textsf{₹}300$.

(C) C's share is $\textsf{₹}500$.

(D) B's share is $\textsf{₹}350$.

Question 7. Which of the following is NOT an example of quantities that are typically inversely proportional when applying unitary method variations?

(A) Number of workers and time taken for a fixed work.

(B) Speed of a vehicle and time taken to cover a fixed distance.

(C) Amount of money and quantity of items purchased at a fixed price.

(D) Number of pipes filling a tank and the time taken to fill it.

Question 8. If $a, b, c$ are in continued proportion, $a:b :: b:c$, which of the following is FALSE?

(A) $b$ is the mean proportional between $a$ and $c$.

(B) $b^2 = ac$

(C) $a/b = b/c$

(D) $a:c :: b:a$

Question 9. Which of the following ratios is NOT in its simplest form?

(A) $3:4$

(B) $10:15$

(C) $7:9$

(D) $1:2$

Question 10. If $6$ men can do a work in $10$ days, which statement about $8$ men is NOT true (assuming constant work rate)?

(A) The total work is 60 man-days.

(B) 1 man takes 60 days to do the work.

(C) 8 men will take less than 10 days.

(D) 8 men will take 8 days ($6 \times 10 / 8 = 7.5$ days).

Question 1. Which of the following is NOT an example of direct variation?

(A) The distance covered by a car at constant speed and the time taken.

(B) The cost of a certain number of identical items and the number of items.

(C) The amount of work done by a machine and the time it operates at a constant rate.

(D) The speed of a vehicle and the time taken to cover a fixed distance.

Question 2. Which of the following is NOT an example of inverse variation?

(A) The number of workers on a job and the time taken to complete it.

(B) The pressure of a gas and its volume at constant temperature.

(C) The speed of a train and the time taken to cover a fixed distance.

(D) The perimeter of a square and its side length.

Question 3. If $y$ varies directly as $x$, i.e., $y \propto x$, which relationship is FALSE?

(A) $y = kx$ for some constant $k$.

(B) $\frac{y}{x}$ is a constant.

(C) When $x$ increases, $y$ also increases.

(D) $xy$ is a constant.

Question 4. If $y$ varies inversely as $x$, i.e., $y \propto \frac{1}{x}$, which relationship is FALSE?

(A) $xy$ is a constant.

(B) $y = k/x$ for some constant $k$.

(C) When $x$ increases, $y$ also increases.

(D) $\frac{y_1}{y_2} = \frac{x_2}{x_1}$ for any two pairs $(x_1, y_1)$ and $(x_2, y_2)$.

Question 5. If $z$ varies jointly as $x$ and $y$, and $z=10$ when $x=2, y=5$, which statement is FALSE?

(A) $z \propto xy$

(B) $z = kxy$ for some constant $k$.

(C) The constant of variation $k=1$.

(D) When $x=4$ and $y=3$, $z=12$.

Question 6. If $A$ varies directly as $B$ and inversely as $C$, which equation is NOT necessarily valid?

(A) $A = k \frac{B}{C}$ for some constant $k$.

(B) $A C \propto B$

(C) $\frac{A C}{B}$ is a constant.

(D) $A B = k C$

Question 7. The graph of which variation type is NOT a straight line?

(A) Direct variation ($y=kx$)

(B) $y$ varies directly as the square of $x$ ($y=kx^2$)

(C) $x$ varies directly as $y$ ($x=ky$)

(D) Linear relationship ($y = mx + c$ where $c=0$)

Question 8. The cost of petrol is directly proportional to the distance covered by a car (fixed mileage). Which statement about this relationship is FALSE?

(A) Cost / Distance = Constant.

(B) As distance increases, cost increases.

(C) If distance is doubled, cost is doubled.

(D) Cost $\times$ Distance = Constant.

Question 9. If $a \propto 1/b^2$, which relationship is INCORRECT?

(A) $a b^2 = k$ for some constant $k$.

(B) $a_1 b_1^2 = a_2 b_2^2$ for any two pairs $(a_1, b_1)$ and $(a_2, b_2)$.

(C) If $b$ is doubled, $a$ becomes one-fourth.

(D) If $a$ is halved, $b$ is doubled.

Question 10. Which statement about the constant of variation $k$ is FALSE?

(A) It is a non-zero number.

(B) It is a ratio or product of the variables depending on the type of variation.

(C) It remains constant for a given variation relationship.

(D) It changes if the values of the variables change.

Question 1. Which of the following is NOT equivalent to 75%?

(A) 0.75

(B) $3/4$

(C) $75/100$

(D) 7.5

Question 2. What is NOT the correct decimal representation for 30%?

(A) 0.3

(B) 0.30

(C) $3/10$

(D) 3.0

Question 3. Which statement about percentage change is FALSE?

(A) Percentage increase = $\frac{\text{Increase}}{\text{Original Value}} \times 100$

(B) Percentage decrease = $\frac{\text{Decrease}}{\text{Original Value}} \times 100$

(C) The base for calculating percentage change is the new value.

(D) A 10% increase followed by a 10% decrease results in a net decrease.

Question 4. If a quantity increases by 20%, which multiplier is NOT correct for finding the new value?

(A) 1.20

(B) $120/100$

(C) $6/5$

(D) $1 + 20$

Question 5. If a quantity decreases by 15%, which multiplier is NOT correct for finding the new value?

(A) 0.85

(B) $85/100$

(C) $1 - 0.15$

(D) $1 - 15$

Question 6. If 40% of a number is 80, which statement about the number is FALSE?

(A) The number is 200.

(B) 10% of the number is 20.

(C) 50% of the number is 100.

(D) The number can be found by calculating $80 \times 0.40$.

Question 7. Which of the following is NOT a correct calculation for percentage change?

(A) To find percentage increase from A to B: $\frac{B-A}{A} \times 100$

(B) To find percentage decrease from A to B: $\frac{A-B}{A} \times 100$

(C) To find percentage change from A to B: $\frac{\text{Change}}{\text{New Value}} \times 100$

(D) To find net percentage change for successive changes $r_1, r_2$: $r_1 + r_2 + \frac{r_1 r_2}{100}$ (for increases)

Question 8. If a price is increased by 10% and then decreased by 20%, which statement about the net change is FALSE?

(A) The price after a 10% increase is 1.10 times the original price.

(B) The final price is $1.10 \times (1-0.20)$ times the original price.

(C) The final price is $1.10 \times 0.80 = 0.88$ times the original price.

(D) The net change is an increase of 12%.

Question 9. Which of the following conversions is INCORRECT?

(A) 0.5 = 50%

(B) $1/5$ = 20%

(C) Ratio $2:5$ = 40%

(D) 1.5 = 15%

Question 10. If a student scores 60 out of 80 marks, which percentage statement is FALSE?

(A) The student scored 75% marks.

(B) The marks obtained are 75% of the total marks.

(C) The student scored 20 marks less than the maximum.

(D) The student needed 40% to pass and scored 60 marks, so they failed.

Question 1. Which of the following is NOT a basic term used in Profit and Loss calculations?

(A) Cost Price (CP)

(B) Selling Price (SP)

(C) Marked Price (MP)

(D) Simple Interest (SI)

Question 2. Profit or Loss is NOT calculated on which of the following?

(A) Cost Price (CP)

(B) Selling Price (SP)

(C) Base for percentage calculation

(D) Original price

Question 3. Discount is NOT usually calculated on which of the following?

(A) Marked Price (MP)

(B) List Price

(C) Selling Price (SP)

(D) Tagged Price

Question 4. Which formula is INCORRECT regarding Profit, Loss, CP, and SP?

(A) Profit = SP - CP (if SP > CP)

(B) Loss = CP - SP (if CP > SP)

(C) SP = CP + Profit

(D) CP = SP + Profit

Question 5. If an article is sold at a profit of 15%, which statement is FALSE?

(A) SP is 15% more than CP.

(B) SP is 115% of CP.

(C) SP = 1.15 $\times$ CP.

(D) Profit percentage is $\frac{SP-CP}{SP} \times 100$.

Question 6. If an article is sold at a loss of 10%, which statement is FALSE?

(A) SP is 10% less than CP.

(B) SP is 90% of CP.

(C) SP = 0.90 $\times$ CP.

(D) Loss percentage is $\frac{CP-SP}{SP} \times 100$.

Question 7. Which of the following is NOT a valid way to calculate the Selling Price (SP)?

(A) MP - Discount

(B) CP + Profit

(C) CP - Loss

(D) CP $\times$ Profit Percentage

Question 8. Which statement about a dishonest shopkeeper using false weights is FALSE?

(A) If he uses a lower weight than charged, he makes a profit.

(B) If he uses a higher weight than charged, he incurs a loss.

(C) His profit/loss percentage is calculated on the actual weight used.

(D) His gain percentage, using 900g for 1kg, is 10%.

Question 9. Which of the following is NOT a correct method to find a single equivalent discount for successive discounts of $d_1\%$ and $d_2\%$?

(A) $(100 - \text{Equivalent Discount}) \% = (100 - d_1)\% \text{ of } (100 - d_2)\%$

(B) Equivalent Discount $= d_1 + d_2 - \frac{d_1 d_2}{100}$

(C) Equivalent Discount = $d_1 + d_2$

(D) Calculate SP after $d_1\%$, then apply $d_2\%$ on the resulting price.

Question 10. If CP of 15 articles = SP of 10 articles, which statement about the transaction is FALSE?

(A) There is a profit.

(B) The profit percentage is 50%.

(C) SP of 1 article > CP of 1 article.

(D) The difference between CP and SP of one article is 5/10 of its SP.

Question 1. Which statement is FALSE about Simple Interest?

(A) Interest is calculated on the initial principal.

(B) The interest amount is the same for each period.

(C) Amount = Principal + Simple Interest.

(D) The principal increases with the interest earned.

Question 2. Which statement is FALSE about Compound Interest?

(A) Interest is calculated on the principal plus accumulated interest.

(B) The interest amount increases with each compounding period (assuming a positive rate).

(C) The growth is linear over time.

(D) Amount = $P \left(1 + \frac{R}{100}\right)^n$ where $n$ is the number of periods.

Question 3. For a principal amount invested for more than one year at a positive rate, which statement comparing SI and CI is FALSE?

(A) Compound Interest is always greater than Simple Interest.

(B) The difference between CI and SI increases with time.

(C) The difference between CI and SI increases with the rate.

(D) The amount under CI is always less than the amount under SI.

Question 4. When interest is compounded half-yearly at an annual rate R% for T years, which adjustment is NOT made for the formula $P \left(1 + \frac{r}{100}\right)^n$?

(A) The rate per period ($r$) is $R/2$.

(B) The number of periods ($n$) is $2T$.

(C) The rate per period ($r$) is $R$.

(D) The annual rate is effectively higher than R%.

Question 5. If a sum doubles at Simple Interest in 10 years, which statement about its growth at Simple Interest is FALSE?

(A) The rate of interest is 10% per annum.

(B) The interest earned is equal to the principal in 10 years.

(C) In 20 years, the sum will become 3 times itself.

(D) In 5 years, the sum will become 1.5 times itself.

Question 6. If a sum doubles at Compound Interest in 5 years, which statement about its growth at Compound Interest is FALSE?

(A) In 10 years, the sum will become 4 times itself.

(B) In 15 years, the sum will become 8 times itself.

(C) The amount after $n$ blocks of 5 years is $P \times 2^n$.

(D) In 10 years, the sum will become 3 times itself.

Question 7. Which formula is INCORRECT for calculating amounts or interests?

(A) $\text{Simple Interest} = \frac{P \times R \times T}{100}$

(B) $\text{Amount (CI)} = P \left(1 + \frac{R}{100}\right)^T$

(C) $\text{Compound Interest} = \text{Amount} - \text{Principal}$

(D) $\text{Amount (SI)} = P (1 + R/100)^T$

Question 8. Depreciation of an asset is NOT analogous to Compound Interest in which way?

(A) The value changes by a fixed percentage of the current value in each period.

(B) The value decreases instead of increasing.

(C) The formula uses $(1 - R/100)$ instead of $(1 + R/100)$.

(D) The absolute amount of decrease is the same in each period.

Question 9. Which statement is FALSE about the effective annual rate of interest?

(A) It is the actual rate of interest earned in a year when compounding occurs more than once annually.

(B) It is higher than the nominal rate when compounded more than once annually (for positive rates).

(C) The formula for effective rate with R% nominal rate compounded n times a year is $\left[\left(1 + \frac{R/n}{100}\right)^n - 1\right] \times 100$.

(D) It is the same as the nominal rate regardless of compounding frequency.

Question 10. The difference between CI and SI for 2 years is NOT directly proportional to which of the following?

(A) The principal amount (P).

(B) The square of the rate of interest (R^2).

(C) The time period (T).

(D) The method of compounding (annual, half-yearly etc.).

Question 1. Which of the following taxes was NOT subsumed under GST in India?

(A) Central Excise Duty

(B) Service Tax

(C) Value Added Tax (VAT)

(D) Income Tax

Question 2. Which component of GST is NOT applicable for an intra-state supply of goods or services (within the same state)?

(A) CGST

(B) SGST

(C) IGST

(D) UTGST (in Union Territories)

Question 3. Which component of GST is NOT applicable for an inter-state supply of goods or services (between different states)?

(A) CGST

(B) SGST

(C) UTGST

(D) IGST

Question 4. If the price of an article before GST is $\textsf{₹}P$ and the rate is R%, the final price is NOT given by which expression?

(A) $P \times (1 + R/100)$

(B) $P + P \times R/100$

(C) $P \times R/100$

(D) $P \times (100 + R)/100$

Question 5. Which statement about Input Tax Credit (ITC) under GST is FALSE?

(A) It allows businesses to reduce their tax liability.

(B) It is credit for the tax paid on input goods or services.

(C) It helps in avoiding the cascading effect of taxes.

(D) It is available even if the business is not registered under GST.

Question 6. Which of the following is NOT a primary benefit of GST?

(A) Simplification of indirect tax structure.

(B) Reduction in compliance burden for all businesses (including small ones).

(C) Creation of a common national market.

(D) Elimination of cascading of taxes.

Question 7. If the final price of an item including tax is known, to find the price before tax, you should NOT do which of the following?

(A) Divide the final price by (1 + Tax Rate/100).

(B) Multiply the final price by (100 / (100 + Tax Rate)).

(C) Subtract the tax amount from the final price (where tax amount is a percentage of final price).

(D) Subtract the tax amount from the final price (where tax amount is a percentage of price before tax).

Question 8. Which of the following is NOT a feature of the GST system?

(A) It is a multi-stage tax.

(B) It is a tax on value addition.

(C) It has an Input Tax Credit mechanism.

(D) It is a direct tax on income.

Question 9. Which statement comparing Sales Tax and GST is FALSE?

(A) Sales Tax was generally a single-point tax.

(B) GST is a multi-stage tax.

(C) Sales Tax had a comprehensive ITC system for all inputs.

(D) GST has a comprehensive ITC system for eligible inputs.

Question 10. UTGST is NOT applicable in which of the following?

(A) Andaman & Nicobar Islands

(B) Lakshadweep

(C) Delhi

(D) Pondicherry

Question 1. If a person can do a work in $x$ days, which statement about their work rate is FALSE?

(A) Their work rate is $1/x$ per day.

(B) In $y$ days, they do $y/x$ of the work.

(C) If they work for $x/2$ days, they complete half the work.

(D) If they work at double efficiency, they take $2x$ days.

Question 2. If A takes 10 days and B takes 15 days to do a work, which statement about their combined work is FALSE?

(A) A's daily work is 1/10.

(B) B's daily work is 1/15.

(C) Their combined daily work is $1/10 + 1/15 = 1/6$.

(D) They will take 12 days to complete the work together.

Question 3. If A is thrice as efficient as B, which statement is FALSE?

(A) A does 3 times the work B does in the same time.

(B) A takes $1/3$ the time B takes to do the same work.

(C) If B takes 12 days, A takes 4 days.

(D) B's work rate is 3 times A's work rate.

Question 4. Which formula is INCORRECT for calculating combined work rate of individuals A, B, C with individual daily rates $r_A, r_B, r_C$?

(A) $r_A + r_B + r_C$ (if they work together)

(B) $1 / (1/r_A + 1/r_B + 1/r_C)$ (gives time, not rate)

(C) Net rate = Sum of filling rates - Sum of emptying rates (for pipes)

(D) Average of their individual times.

Question 5. If 10 men can do a work in 12 days, which statement about men and days is FALSE?

(A) The total work is 120 man-days.

(B) 1 man can do the work in 120 days.

(C) The number of men and the number of days are in inverse variation.

(D) 5 men can do the work in 6 days.

Question 6. Which of the following is NOT a common type of Time and Work problem?

(A) Individual workers doing a job alone.

(B) Multiple workers doing a job together.

(C) Workers with different efficiencies.

(D) Calculating the rate of depreciation of an asset.

Question 7. If Pipe A fills a tank and Pipe B empties it, the net rate is NOT given by which method (assuming rates $r_A$ and $r_B$)?

(A) $r_A - r_B$ (if $r_A > r_B$)

(B) $1/T_A - 1/T_B$ where $T_A$ is filling time and $T_B$ is emptying time.

(C) Sum of individual rates.

(D) Reciprocal of the net time taken to fill or empty.

Question 8. If A and B work on alternate days, which statement about the total time taken is FALSE?

(A) The work done in each cycle (e.g., 2 days if A and B work one day each) is calculated by summing their work rates for the days they work.

(B) The total number of cycles needed is found by dividing the total work by the work done in one cycle.

(C) The total time is the number of cycles multiplied by the duration of each cycle.

(D) The total time is always equal to the average of the time they would take individually.

Question 9. If 4 men can do a work in 10 days and 6 women can do it in 12 days, which statement about their efficiency is FALSE?

(A) Total work is 40 man-days.

(B) Total work is 72 woman-days.

(C) 40 man-days = 72 woman-days.

(D) A man is more efficient than a woman ($1 \text{ man} = 72/40 = 1.8 \text{ women}$).

Question 10. If a work is completed by a group, the total work done is NOT equal to which of the following?

(A) Sum of the work done by each individual or subgroup.

(B) Product of the total number of person-days/hours involved (considering efficiency).

(C) 1 (representing the whole work).

(D) The average daily work rate of the group multiplied by the number of individuals in the group.

Question 1. Which of the following is NOT a correct formula relating Distance (D), Speed (S), and Time (T)?

(A) D = S $\times$ T

(B) S = D / T

(C) T = D / S

(D) S = T / D

Question 2. Which of the following unit conversions is INCORRECT?

(A) 1 km = 1000 meters

(B) 1 hour = 60 minutes

(C) 1 minute = 60 seconds

(D) 1 km/hr = 1000 m/s

Question 3. When two objects are moving, their relative speed is NOT calculated by which method?

(A) Subtracting speeds if moving in the same direction.

(B) Adding speeds if moving in opposite directions.

(C) Finding the geometric mean of their speeds.

(D) Used to determine the time taken for them to meet or cross each other.

Question 4. The time taken by a train to cross an object is NOT calculated based on crossing which of the following?

(A) A stationary pole.

(B) A stationary man.

(C) A stationary platform.

(D) The time of day.

Question 5. Which statement about the average speed for a journey is FALSE?

(A) Average speed = Total Distance / Total Time.

(B) If distances covered in different segments are equal, average speed is the harmonic mean of speeds.

(C) If times taken in different segments are equal, average speed is the arithmetic mean of speeds.

(D) Average speed is always the arithmetic mean of speeds for any journey.

Question 6. If a boat's speed in still water is $V_b$ and stream speed is $V_s$, which statement is FALSE?

(A) Speed downstream = $V_b + V_s$.

(B) Speed upstream = $V_b - V_s$.

(C) $V_b = (\text{Downstream Speed} + \text{Upstream Speed})/2$.

(D) $V_s = (\text{Downstream Speed} + \text{Upstream Speed})/2$.

Question 7. In a race, if A beats B by a certain distance, which statement about their speeds or distances covered is FALSE?

(A) When A covers the full distance, B covers a shorter distance.

(B) The ratio of their speeds is equal to the ratio of the distances they cover in the same time.

(C) The ratio of their speeds is equal to the ratio of the times they take to cover the same distance.

(D) If A beats B by 10m in a 100m race, B covers 90m when A covers 100m.

Question 8. Excluding stoppages, the speed of a bus is $S_1$, and including stoppages, it's $S_2$. The time the bus stops per hour is NOT given by which formula?

(A) $\frac{S_1 - S_2}{S_1} \times 1 \text{ hour}$

(B) $\frac{\text{Difference in speeds}}{\text{Speed without stoppages}} \times 60 \text{ minutes}$

(C) $\frac{S_1 - S_2}{S_2} \times 1 \text{ hour}$

(D) The time taken to cover the distance $(S_1 - S_2) \times 1 \text{ hour}$ at speed $S_1$.

Question 9. If a man walks at speed $S_m$ and a train travels at speed $S_t$ ($S_t > S_m$) in the same direction, their relative speed is NOT calculated as?

(A) $S_t - S_m$

(B) Used to find the time for the train to overtake the man.

(C) Used to find the time for the man to overtake the train.

(D) The speed at which the distance between them decreases.

Question 10. Which scenario does NOT typically involve the concept of relative speed?

(A) A train crossing a stationary platform.

(B) Two cars moving towards each other.

(C) A boat moving upstream in a river.

(D) Calculating the speed of light.

Question 1. Which of the following is NOT a correct method to calculate the simple average of a set of $N$ numbers?

(A) Sum of numbers divided by $N$.

(B) $(\sum x) / N$

(C) The middle value in the sorted list (for any $N$).

(D) A measure of central tendency.

Question 2. The average of a set of numbers is NOT affected by which of the following operations on each number in the set?

(A) Adding a constant to each number.

(B) Subtracting a constant from each number.

(C) Multiplying each number by a non-zero constant.

(D) Rearranging the order of the numbers.

Question 3. If a value $x$ is added to a data set of $N$ numbers with average $A$, the new average is NOT calculated by which method?

(A) $(NA + x) / (N+1)$

(B) $A + (x - A) / (N+1)$

(C) $A + (x - NA) / (N+1)$

(D) Sum of new set / new count.

Question 4. If a value $x$ is removed from a data set of $N$ numbers with average $A$, the new average is NOT calculated by which method?

(A) $(NA - x) / (N-1)$

(B) $A - (x - A) / (N-1)$

(C) $A + (A - x) / (N-1)$

(D) Sum of remaining numbers / $(N-1)$.

Question 5. If an item in a data set is replaced by another item with a different value, which statement about the average is FALSE?

(A) If the new value is greater than the old value, the average increases.

(B) If the new value is less than the old value, the average decreases.

(C) If the new value is equal to the old value, the average remains unchanged.

(D) The change in average depends only on the number of items, not on the original average or the difference in values.

Question 6. Which statement about weighted average is FALSE?

(A) It gives more importance to values with higher weights.

(B) It is calculated by summing the products of each value and its weight, then dividing by the sum of the weights.

(C) If all weights are equal, the weighted average is the same as the simple average.

(D) It is only used for calculating the average of grouped data.

Question 7. The average of consecutive integers is NOT always which of the following?

(A) The middle term (if the number of terms is odd).

(B) The average of the first and last term.

(C) An integer or a value ending in .5.

(D) Equal to the mode.

Question 8. If the average of $N$ numbers is $A$, the sum of the numbers is NOT equal to which of the following?

(A) $N \times A$

(B) $\sum x_i$

(C) $A / N$

(D) The total sum of the given data points.

Question 9. If a group is divided into two subgroups, and their individual averages and sizes are known, which statement about the overall average is FALSE?

(A) The overall average is the weighted average of the subgroup averages.

(B) The overall average is calculated using the total sum of values and the total count.

(C) The overall average is the simple average of the two subgroup averages (unless the subgroups have the same size).

(D) The overall average must lie between the averages of the two subgroups.

Question 10. If there is an error in recording one data point in a set, which statement about finding the correct average is FALSE?

(A) Calculate the incorrect sum using the incorrect average and count.

(B) Subtract the incorrect value and add the correct value to get the correct sum.

(C) Divide the correct sum by the original count to get the correct average.

(D) The correct average is found by simply taking the average of the incorrect average and the correct value.

Question 1. Which of the following statements about the angular speed of clock hands is FALSE?

(A) Minute hand speed = $6^\circ$ per minute.

(B) Hour hand speed = $0.5^\circ$ per minute.

(C) Minute hand speed = $360^\circ$ per hour.

(D) Hour hand speed = $30^\circ$ per minute.

Question 2. How many times are the hands of a clock NOT at right angles in a 12-hour period?

(A) They are at right angles 22 times.

(B) The question asks for the number of times they are NOT at right angles.

(C) This is equivalent to asking for the total number of minutes in 12 hours minus the number of times they are at right angles.

(D) They are at right angles at precisely 3:00 and 9:00.

Question 3. How many times do the hands of a clock NOT coincide in a 12-hour period?

(A) They coincide 11 times.

(B) They coincide 12 times.

(C) The question asks for the number of times they do NOT coincide.

(D) They coincide exactly at 12:00.

Question 4. How many times are the hands of a clock NOT in a straight line (coincide or opposite) in a 12-hour period?

(A) They are in a straight line 22 times.

(B) They are in a straight line 24 times.

(C) The question asks for the number of times they are NOT in a straight line.

(D) They are in a straight line at exactly 6:00 and 12:00.

Question 5. At what time between 2 and 3 o'clock are the hands of a clock NOT at right angles?

(A) At approximately $2:27 \frac{3}{11}$.

(B) At approximately $2:32 \frac{8}{11}$.

(C) The hands are at right angles twice between 2 and 3 o'clock.

(D) The hands are at right angles only once between 2 and 3 o'clock.

Question 6. If a clock gains time, which statement is FALSE?

(A) It runs faster than a standard clock.

(B) It shows a time ahead of the correct time.

(C) The minute hand overtakes the hour hand in less than $65 \frac{5}{11}$ minutes.

(D) It loses a certain amount of time per hour or per day.

Question 7. If a clock loses time, which statement is FALSE?

(A) It runs slower than a standard clock.

(B) It shows a time behind the correct time.

(C) The minute hand overtakes the hour hand in more than $65 \frac{5}{11}$ minutes.

(D) It gains a certain amount of time per hour or per day.

Question 8. The angle between the hands of a clock at a specific time is NOT calculated using which principle?

(A) The angular speed of the hour hand.

(B) The angular speed of the minute hand.

(C) The time elapsed since the last hour mark.

(D) The colour of the clock face.

Question 9. The mirror image of a clock showing a certain time will NOT show which reflected time property?

(A) The sum of the original time and the reflected time is approximately 12 hours.

(B) If the time is $H:M$, the reflected time is approximately $(11-H): (60-M)$.

(C) The relative positions of the hands are reversed left-to-right.

(D) The angle between the hands is also reversed left-to-right.

Question 10. The time interval between successive coincidences of the minute hand and hour hand is NOT equal to?

(A) Approximately $65.45$ minutes.

(B) $65 \frac{5}{11}$ minutes.

(C) The time it takes for the minute hand to gain 360 degrees over the hour hand at their relative speed.

(D) 60 minutes.

Question 1. Which of the following is NOT a leap year?

(A) 2004

(B) 2012

(C) 2000

(D) 1900

Question 2. Which of the following is NOT the number of odd days in a century year?

(A) 5 (in 100 years)

(B) 3 (in 200 years)

(C) 1 (in 300 years)

(D) 2 (in 400 years)

Question 3. Which statement about ordinary years and leap years is FALSE?

(A) An ordinary year has 365 days.

(B) A leap year has 366 days.

(C) A leap year occurs every 4 years.

(D) Every year divisible by 4 is a leap year.

Question 4. How many odd days are there NOT in an ordinary year?

(A) 1

(B) 0

(C) The remainder when 365 is divided by 7.

(D) The day of the week shifts forward by 1 day in the next year.

Question 5. How many odd days are there NOT in a leap year?

(A) 2

(B) 1

(C) The remainder when 366 is divided by 7.

(D) The day of the week shifts forward by 2 days in the next year.

Question 6. If today is Monday, what day will it NOT be after 28 days?

(A) Monday

(B) The same day as today.

(C) Sunday.

(D) The day after adding $28 \div 7$ remainder to today's day index.

Question 7. The calendar of which of the following years will NOT be the same as the calendar of an ordinary year that started on a specific day?

(A) The year 6 years later (if no leap year crosses).

(B) The year 11 years later (if one leap year crosses).

(C) The year 28 years later (for any year).

(D) The next year (unless it's a leap year).

Question 8. Which of the following days CANNOT be the last day of a century year?

(A) Monday

(B) Wednesday

(C) Friday

(D) Sunday

Question 9. Which statement about calculating the day of the week for a given date is FALSE?

(A) The number of odd days from a reference date is calculated.

(B) Odd days in centuries and years are summed up.

(C) Odd days in months and days are added.

(D) The total odd days are used to calculate the day of the week relative to a fixed starting day (e.g., 0=Sunday).

Question 10. How many days does February NOT have in a leap year?

(A) 28

(B) 29

(C) 30

(D) 31

Question 1. Which of the following is NOT a type of arrangement problem?

(A) Linear Arrangement

(B) Circular Arrangement

(C) Seating Arrangement

(D) Calculation of percentages.

Question 2. In a linear arrangement facing North, if A is to the immediate right of B, which statement is FALSE?

(A) There is no person between A and B.

(B) B is to the immediate left of A.

(C) A is one position to the right of B.

(D) There is exactly one person between A and B.

Question 3. In a circular arrangement facing the center, if X is second to the right of Y, which statement is FALSE?

(A) There is exactly one person between Y and X in the clockwise direction from Y.

(B) Moving clockwise from Y, X is two positions away.

(C) Moving anti-clockwise from Y, X is one position away.

(D) Y is second to the left of X when facing the center.

Question 4. Which statement about immediate neighbours in an arrangement is FALSE?

(A) Immediate neighbours sit next to each other.

(B) In a linear arrangement, a person can have at most two immediate neighbours.

(C) In a circular arrangement, a person always has exactly two immediate neighbours (for N > 2).

(D) Immediate neighbours always sit opposite each other.

Question 5. In a row of $N$ persons, if a person is Rth from one end, their rank from the other end is NOT given by which formula?

(A) $N - R + 1$

(B) Total persons - Rank from one end + 1.

(C) $R - N + 1$

(D) $(N - R) + 1$

Question 6. If an arrangement puzzle provides contradictory clues, which statement is FALSE?

(A) The given information is inconsistent.

(B) A valid arrangement satisfying all conditions cannot be determined.

(C) There might be multiple possible valid arrangements.

(D) The puzzle cannot be solved with the given information.

Question 7. Which of the following is NOT a useful technique for solving arrangement problems?

(A) Drawing diagrams or sketches.

(B) Starting with the most definite information (e.g., extreme ends, opposite positions).

(C) Using symbols or abbreviations for individuals.

(D) Guessing the arrangement randomly until one fits.

Question 8. In a square arrangement, if persons at corners face inwards and those in the middle face outwards, which statement about facing directions is FALSE?

(A) All persons at corners face the same direction (inwards).

(B) All persons in the middle of sides face the same direction (outwards).

(C) A person at a corner faces the same direction as a person in the middle of a side.

(D) Opposite persons might face in different directions (e.g., corner vs middle).

Question 9. If A is sitting between B and C in a linear arrangement, which statement is FALSE?

(A) B and C are on opposite sides of A.

(B) A is between B and C.

(C) B, A, C are in that order OR C, A, B are in that order.

(D) A is an immediate neighbour of both B and C.

Question 10. If several persons are sitting around a circular table facing outwards, which statement about left and right directions is FALSE?

(A) Left is in the clockwise direction.

(B) Right is in the anti-clockwise direction.

(C) Left and Right directions are relative to the person's perspective.

(D) Moving clockwise is moving to the right of a person facing outwards.

Question 1. Which of the following problem types CANNOT involve the application of ratios?

(A) Sharing a sum of money among individuals.

(B) Comparing two quantities of the same kind.

(C) Solving Time and Work problems (e.g., efficiency ratio).

(D) Finding the square root of a number.

Question 2. Which of the following is NOT a typical application area for percentage calculations?

(A) Calculating discounts on marked prices.

(B) Determining profit or loss percentage.

(C) Finding percentage increase or decrease in values.

(D) Measuring angles in geometry.

Question 3. Which concept is NOT typically used when solving Time and Work problems?

(A) Work Rate (Work done per unit time).

(B) Total Work (often considered as 1 or LCM).

(C) Inverse proportionality between workers and time.

(D) Speed of the wind.

Question 4. Which formula is NOT relevant to Time, Speed, and Distance problems?

(A) Speed = Distance / Time.

(B) Relative Speed.

(C) Average Speed formula.

(D) Area = Length $\times$ Width.

Question 5. Which statement about calculating averages is FALSE?

(A) Average = Sum of values / Number of values.

(B) Weighted average considers the importance of different values.

(C) Adding a value equal to the average changes the average.

(D) Removing a value less than the average increases the average.

Question 6. Which calculation is NOT typically performed in Simple or Compound Interest problems?

(A) Calculating the amount after a certain period.

(B) Finding the principal amount.

(C) Determining the rate of interest.

(D) Finding the volume of a sphere.

Question 7. Which of the following is NOT a component or concept related to GST in India?

(A) CGST

(B) IGST

(C) Input Tax Credit (ITC)

(D) Professional Tax

Question 8. Alligation and Mixture problems do NOT involve which principle?

(A) Mixing quantities with different properties.

(B) Finding the mean value of the mixture.

(C) Determining the ratio of quantities to be mixed.

(D) Calculating the square root of the quantity.

Question 9. In a partnership, profits are NOT shared based on which factor?

(A) Amount of capital invested.

(B) Time period for which capital is invested.

(C) The colour of the partners' clothes.

(D) The ratio of (Investment $\times$ Time) for each partner.

Question 10. Which statement about combined quantitative problems is FALSE?

(A) They often require applying concepts from two or more quantitative topics.

(B) Solving them requires identifying the different concepts involved and their relationships.

(C) A systematic approach is usually needed to break down the problem.

(D) They can always be solved by applying a single formula directly.