Quantitative Interview Practice Test

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• How can you identify the defective coin-producing machine with only one weighing?
• With 50 cards of 5 different colors, what is the probability that 2 randomly picked cards are neither of the same color nor the same number?
• What is the probability that Player A wins if they have n+1 coins, while Player B has n coins, considering all coins are flipped?
• How many weighings are required to determine which one of 12 balls is different and whether it is heavier or lighter?
• When would a callable bond typically be called by the issuer?
• How many possible outcomes are there when rolling three dice?
• How many socks do you need to pull out to guarantee a matching pair from a drawer containing blue and black socks?
• When given three light switches controlling three bulbs, what problem-solving method allows you to determine which switch controls which bulb?
• How does volatility affect the price of a call option?
• In a scenario where two players flip coins, what probability outlines that one player could end up with equal heads as the other?
• If you complete one mile at 30 miles per hour, what speed do you need to average 60 miles per hour over two laps?
• If a company has 10 machines with one defective machine producing lighter coins, how can identifying the defective machine be achieved?
• What is the sum of all the numbers from 1 to 100?
• What does the notional principal in an interest rate collar relate to?
• What happens to the price of zero coupon bonds as interest rates increase?
• If you have socks in two colors and reach for three, what can you infer about the colors you will have?
• When a one rupee coin and a fifty paise coin are drawn from a bag, how is the probability of drawing a one rupee coin calculated after one coin is removed?
• What is the primary purpose of a stock split?
• What is the probability of drawing two cards from a deck and both being aces?
• What is the probability that the last person to board the plane will sit in their proper seat (#100)?
• Which financing option would generally be considered cheaper for a company?
• If interest rates are expected to rise, which bond should you prefer?
• What typically causes stocks to increase in value on their first day of trading after an IPO?
• When flipping n coins, what scenario guarantees that one player will have a more favorable outcome?
• How long will it take for four people with different crossing times to cross a bridge if only two can cross at a time and they have only one flashlight?
• Why is the yield on a corporate bond higher than a treasury bond?
• When the first person of a group boards a plane and sits in a random seat, what is the outcome on the seating arrangement?
• According to a mathematical principle regarding temperature on Earth, what can be said about two opposite points on the Earth?
• If given an unfair coin, how can one generate fair odds using this coin?
• What is the main factor that influences the slope of the yield curve?
• How does the random behavior of the first passenger influence the last passenger's seating outcome?
• In the scenario with socks, how can the number of red socks affect the outcome?
• What does PIK stand for in finance?
• When calculating the expectation of card values, what is the strategy for maximizing value after flipping?
• Which outcome is associated with the conditional probability of survival in the revolver game?
• If you draw a circle and choose two random chords, what is the probability those chords will intersect?
• Is the number 1027 classified as a prime number?
• What influences a company’s decision to issue debt or equity?
• Which bond should you buy if Bond A trades under the yield curve and Bond B trades above the yield curve?
• What does a forward contract involve?
• How many small cubes of a 10x10x10 cube will have paint after the outside is painted?
• What is the function of a reverse repo?
• When do yield curves typically invert?
• What is the convexity of a Mortgage Backed Security?
• In a situation where a drunk passenger randomly picks a seat, what happens if they sit in seat #1?
• What must be true about an interest rate cap and floor in a collar?
• What type of debt has the highest seniority in the capital structure?
• If three friends each say it's rainy and have a 1/3 chance of lying, what is the probability it is rainy given the base chance of rain is 0.25?
• Which principle is illustrated by needing to draw a minimum number of socks to ensure you have a pair of the same color?
• Which of the following is NOT a type of bond based on their issuers?
• What is the probability that two witches will meet at a coffee shop if each arrives at a random time between 0:00 and 1:00 and stays for 30 minutes?
• What does Yield to Maturity (YTM) represent?
• What must happen if a bond is issued at a discount?
• What characterizes an amortized bond?
• What is the duration of a zero coupon bond?
• What is generally true about the relationship between maturity and duration in bonds?
• What strategy can be employed to ensure that at least 3 ants are covered when placing a square card on a table with 51 ants?
• Which of the following time periods cannot be measured using two ropes that burn in one hour?
• In a knockout tennis tournament with 3,182 players, how many matches must be played to determine a winner?
• Was the man necessarily at the same point on the path at the same time on both days when he climbed a mountain?
• In probability terms, how does the last passenger's fate rely on the choices made by earlier passengers?
• What is a mortgage backed security (MBS)?
• When selecting two red cards from a deck with 104 cards, which deck provides a higher winning chance?
• What are nonconvertible debentures?
• What is an effective way to demonstrate the probability of winning a game with unequal coin numbers?
• Which of the following best describes the benefit of discovering the price effect of volatility on options?
• What is the expected outcome when playing a coin flip game that stops upon landing tails?
• To correctly identify the contents of mislabelled egg boxes, what is the minimum number of boxes you need to open?
• What does the term "Irrational Exuberance" refer to?
• What is an interest rate collar?
• What is the main difference between a primary market and a secondary market?
• In the scenario of three ants at the corners of an equilateral triangle, what is the probability that none of the ants collide?
• How many digits are in 99 raised to the power of 99?
• What is the expected number of coin tosses required to get n consecutive heads?
• How does inflation affect creditors?
• How long does it take for one rope to burn completely when lit?
• What is true about non-convertible debentures (NCDs)?
• How likely is it for a seven-game series to go to 7 games?
• When a stick is broken into three parts, what is the probability that it can form a triangle?
• What is the least multiple of 15 that consists only of the digits 1 and 0?
• What approach could help demonstrate your enthusiasm during an interview when discussing your background?
• How can the market respond to better-than-expected earnings despite reported decreases?
• What is a yield curve?
• What typically happens to a company's shares if they undergo a reverse stock split?
• What characteristic does a callable bond exhibit at lower yields?
• What is the expected number of coin flips needed to get two consecutive heads?
• In a World Series with two teams, what are the odds it goes to 7 games with each team having an equal chance of winning?
• What is the effect of an interest rate increase in the U.S. on the USDCAD exchange rate?
• In a random experiment with points p and q, what is the probability that the ratio p/q lies between 1 and 2?
• What method of pairing numbers helps to calculate the sum of numbers from 1 to 100?
• What is the primary benefit of a callable bond for the issuer?
• What is a repurchase agreement (repo)?
• What does managing risk effectively signify in trading?
• Why is calculating the average salary among individuals challenging while maintaining secrecy?
• In a three-set tennis match, under what condition would betting on it finishing in two sets be favorable?
• What can indicate a positive economic sentiment in the yield curve?
• What do swaps involve?
• In the game involving players A and B, what is the probability that team AB wins if both players can guess correctly?
• In the context of the first question, after traveling a distance of 60 miles at 30 mph, how much time has passed?
• What effect do higher interest rates have on put options?
• Using the Pigeonhole principle, what is the minimum number of socks you must draw to guarantee a pair of the same color from 10 black and 10 white socks?
• What is the last digit of 2 raised to the power of 230?
• If you cross a mile at 30 mph, what conclusion can be drawn about average speed for the second lap to meet a desired average?
• Why might two bonds from the same issuer with identical coupons differ in price?
• What is a limitation of using duration as a measure of bond price volatility?
• What role do investment banks play in the structuring of MBS?
• What defines a term bond?
• Is it possible for a group to determine their average salary without revealing individual salaries?
• What is the probability of rolling three dice and obtaining the numbers in a strictly increasing order?
• How many times a day do the hands of a clock overlap?
• If there is a 1 in 1000 chance of having a disease and a 98% accuracy if the test is positive, what are the odds of having the disease if one tests positive?
• In a flexible exchange rate system, how is a currency's value affected?
• What can cause swap spreads to widen?
• If Charles buys x oranges, how many does Pat buy if he buys five times more?
• What is the expected number of rolls needed to see all 6 sides of a fair die?
• How can you split a group of coins into two groups so that the same number of coins are heads-up in each group without knowing the orientation of the coins?
• What does convexity measure in relation to bonds?
• What are the typical uses for municipal bonds?
• Out of 5 balls (3 red, 2 black), what is the probability that a random ordering does not have the two black balls next to each other?
• What are municipal bonds primarily issued for?
• How much did you and your friend each effectively pay for the meal after receiving change from the waiter?
• What is the formula used to derive the probability of a picked snowflake being of type "Stellar Dendrite"?
• Which bond is likely to have a greater duration?
• In a game with coins, if the game continues until a tail appears, what is the probability of winning?
• What is the probability of a candidate getting at least one job offer when interviewed for three posts with 3, 4, and 2 candidates?
• What is the condition for the three sides of a triangle made from sections of a broken stick?
• What property of bonds does convexity particularly relate to?
• What is the singles digit for 2²³⁰?
• What do you sacrifice when using an interest rate collar?
• What is the sum of the numbers from 1 to 100?
• Which expression accurately represents 119 squared, calculated mentally?
• How many total minutes did it take for a group of four to cross the bridge with the given conditions?
• What is the probability that three dots placed randomly on the four edges of a square fall on distinct edges?
• What is the probability of getting an even number of heads when flipping 100 coins?
• In Bayes' theorem specific to coin flips, which term represents the likelihood of seeing the outcome given the coin type?
• Why can an 8x8 chessboard with two opposite corners removed not be covered by 31 dominoes?
• When assessing content labeling accuracy, what percentage of non-diligent raters label content as non-spam?
• How do higher interest rates affect call options?
• What is the distinction between currency depreciation and devaluation?
• What is the probability that a randomly chosen number from a set of 10 unique numbers is neither even nor odd?
• How many smaller cubes of a 10x10x10 cube are not painted when the outer surface is painted?
• How can you profit if you expect an inverted yield curve to revert?
• When rolling a fair six-sided die twice, what is the probability of rolling a 1 first and not rolling a 6 second?
• What is the survival probability when choosing not to re-spin in a Russian roulette scenario with adjacent bullets?
• In the rabbit problem, what mathematical sequence represents the total ways the rabbit can ascend to n stairs?
• What is an adjustment bond?
• What is the probability that you are flipping the unfair coin after observing 5 tails in a row?
• What does a standard 6-chamber revolver signify in the Russian roulette scenario?
• At 3:30 PM, what is the angle between the hour hand and the minute hand of a clock?
• How is duration relevant in bond investment?
• What is the minimum number of different languages spoken in a group of 70 members, according to the conditions imposed on their interaction?
• What approach would determine the probability of getting at least one ace in six draws from a standard deck?
• What is a key characteristic of high yield bonds?
• What is the sum of the numbers from 1 to 50?
• What is the largest number of McNuggets that cannot be obtained using boxes of 6, 9, and 20?
• How can you measure out exactly 4 gallons using a 3 gallon jug and a 5 gallon jug?
• What is a defining feature of a call provision in bonds?
• What is the probability represented by 25/51 in drawing cards?
• What is the average speed of a driver who travels to a store at 20 mph and returns at 30 mph, excluding store time?
• What graphical representation helps define the probability of witches meeting at the coffee shop?
• For the number 3,599, is it a prime number?
• When choosing two chords from a randomly drawn circle, how many configurations allow them to intersect?
• What is the probability of drawing two cards of the same color without replacement from a standard 52-card deck?
• What is the formula to calculate GDP?
• What is the average speed required for a car to average 60 mph over a total distance of 120 miles, given it has already traveled 60 miles at 30 mph?
• What is a simple option strategy for uncertain price direction?
• What is the primary benefit of the interest rate collar for fixed income investors?
• If a fair coin shows tails 5 times in a row, what is the probability of this occurring?
• What is the delta of an at-the-money option?
• If 10 people in a room each shake hands, how many total handshakes will occur?
• What is the formula of put call parity?
• What is a stock buyback?
• For any given group of murderers, what must you communicate to prevent them from escaping?
• How should you distribute 100 balls (50 black, 50 white) in 2 buckets to maximize the chance of selecting a black ball?
• How should you demonstrate your risk assessment skills in an interview for a trading position?
• Given that a rater has labeled 4 pieces of content as good, what is the probability that they are a diligent rater?
• What approach should be taken to prevent murderers from escaping when only one bullet is available?
• In a game with 2 blue and 2 red balls where you guess the color of a ball, what is the expected amount to pay to play?
• What main factors should you know about a firm during an interview?
• What is one of the key drivers of the Black-Scholes model?
• What could be a determining factor in getting an offer according to the probability discussed?
• What strategy can be used to mitigate the risk of rising interest rates when investing in bonds?
• How many cards would you expect to draw from a standard deck before seeing the first ace?
• In the game where you and your friend toss a coin until HH or TH shows up, what is your likelihood of winning?
• In a foreign currency swap, is the principal exchanged?
• Which of the following bonds would typically exhibit more price sensitivity to interest rate changes?
• If you have one more canary than cages when placing one canary per cage, and one fewer cage than needed when placing two canaries per cage, how many canaries and cages do you have?
• What is the product of 39 and 41 using an algebraic identity?
• Which bond is less risky in the event of a default?
• When A, B, and C share wood to cook and C gives $8 for not contributing wood, how much does A receive if they share equally?
• When considering statistical sums, why is pairing numbers beneficial for calculations?
• What do non-farm payrolls refer to in the economic context?
• What is the least number of times you can use a balance scale to determine which one of nine marbles is lighter?
• How can one ensure the correct distribution of wood brought by A and B when cooking with C contributing money instead?
• What is the key computational aspect of finding the ball that is different among 12 balls?
• Which type of bond typically has a higher risk?
• What is the expected number of bananas a monkey will eat after rolling a die repeatedly?
• When considering the removal of coins in probability calculations, what should be accounted for?
• What defines an angel bond?
• How many congruent triangles are formed in the unit square when evaluating the conditions for forming a triangle from the stick parts?
• What is essential to articulate when asked about reasons for not acquiring a sales/trading role after university?
• What are the major factors affecting the yield on a corporate bond?
• What color bear would walk one mile north, one mile west, and one mile south and end up in the same place?
• If you have 17 coins and your opponent has 16, what is your probability of winning after flipping all coins simultaneously?
• What is the probability that the last passenger to board the plane will sit in their proper seat (#100)?
• What is a primary consequence of significant market bubbles?
• In a game of chance with a fair player, what can we say about two players of equal strength with respect to match duration?
• If there are N socks and the probability of picking two red socks is 1/2, what is the smallest value of N?
• What is the expected amount of money a player can win after buying a ticket for a gambling game involving dice rolls?
• Why is it important to justify your choice of university during an interview?
• What is the maximum expected payout one could achieve in the described dice gambling game when betting Rs 1?
• What is the probability that the largest number rolled on a fair die after rolling n times is r?
• What is the primary purpose of issuing nonconvertible debentures?
• In probability, what does drawing without replacement mean?
• What distinguishes a callable bond?
• What ethical concern does consuming meat typically raise?
• Why might a company's stock price rise despite decreased quarterly earnings?