YPIP Quantitative Reasoning Syllabus

What is the mode of a data set?

The mode is the value that occurs most frequently in the data set. A data set can have no mode, one mode, or multiple modes.

What is the empirical relationship between mean, median, and mode?

Mode = 3 x Median - 2 x Mean (approximately, for a moderately skewed distribution).

If the average of n numbers is A and a new number x is added, what is the new average?

New average = (n x A + x) / (n + 1).

In a partnership, how is profit shared when all partners invest for the same time period?

Profit is divided in the ratio of their capital (investment) amounts. If A invests P and B invests Q, profit ratio = P:Q.

How is profit shared in a partnership when partners invest different amounts for different time periods?

Profit is shared in the ratio of (Capital x Time) for each partner. This product is called the monthly/effective equivalent capital.

What is the difference between a working (active) partner and a sleeping (dormant) partner?

A working partner manages the business and may receive a salary or extra share for effort. A sleeping partner only invests capital and shares profit based on investment, without managing the business.

In alligation, what is the rule (rule of alligation) for mixing two ingredients?

(Quantity of cheaper)/(Quantity of dearer) = (CP of dearer - Mean price)/(Mean price - CP of cheaper). The ratio of quantities is inversely related to the distances of their prices from the mean.

A container has x litres of milk; y litres is drawn and replaced with water, repeated n times. What is the milk left?

Milk remaining = x x (1 - y/x) raised to the power n. After n operations the fraction of original liquid left is (1 - y/x)^n.

How do you convert a fraction to a percentage and vice versa?

Fraction to percentage: multiply by 100. Percentage to fraction: divide by 100 (drop the % sign). For example, 3/5 = 60% and 40% = 40/100 = 2/5.

If a quantity increases from A to B, what is the percentage increase?

Percentage increase = ((B - A) / A) x 100, i.e., (Increase / Original) x 100.

If a number is increased by x% and then decreased by x%, what is the net change?

There is a net decrease of (x squared / 100)%. For example, +10% then -10% gives a net decrease of 1%.

Define Cost Price (CP), Selling Price (SP), Profit, and Loss.

CP is the price at which an item is bought; SP is the price at which it is sold. Profit = SP - CP (when SP > CP); Loss = CP - SP (when CP > SP).

How do you calculate profit percentage and loss percentage?

Profit% = (Profit / CP) x 100. Loss% = (Loss / CP) x 100. Both are always calculated on the cost price.

If an article is sold at a profit of P%, what is the relation between SP and CP?

SP = CP x (100 + P)/100. For a loss of L%, SP = CP x (100 - L)/100.

When two articles are each sold at the same SP, one at x% profit and one at x% loss, what is the net result?

There is always a net loss of (x squared / 100)% on the whole transaction, regardless of the selling price.

What is the simple interest formula?

SI = (P x R x T)/100, where P is principal, R is rate percent per annum, and T is time in years. Amount = P + SI.

Using simple interest, in how does the amount relate to principal, rate, and time?

Amount A = P(1 + (R x T)/100). The principal can be found as P = (100 x SI)/(R x T).

What is the compound interest formula for annual compounding?

Amount = P(1 + R/100)^T, and Compound Interest = Amount - P, where P is principal, R is annual rate, and T is the number of years.

How is the compound interest formula adjusted for half-yearly and quarterly compounding?

Half-yearly: A = P(1 + (R/2)/100)^(2T). Quarterly: A = P(1 + (R/4)/100)^(4T). The rate is divided and the time period multiplied by the number of compounding periods per year.

What is the difference between CI and SI for 2 years at the same rate?

Difference = P x (R/100) squared. For 2 years, CI - SI = P(R/100)^2.

What is the difference between marked price (list price) and discount?

Marked price (MP) is the price labelled/listed on an item before any reduction. Discount is the reduction given on the marked price. Discount = MP - SP, and Discount% = (Discount/MP) x 100.

How is selling price calculated from marked price after a discount of D%?

SP = MP x (100 - D)/100. Discount is always calculated on the marked price, not the cost price.

How do you find the single equivalent discount for two successive discounts of x% and y%?

Single equivalent discount = (x + y - (x x y)/100)%. The successive discounts are applied one after the other on the reducing price.

In Time and Work, if a person completes a job in n days, what is their one day's work?

One day's work = 1/n of the total work. If A does a job in 'a' days and B in 'b' days, together they do (1/a + 1/b) per day.

If A and B together can do a work in T days, how is T found from individual times a and b?

T = (a x b)/(a + b), since their combined one day's work is (1/a + 1/b) and time = 1/(combined rate).

What is the relationship between number of workers and time taken (work constant)?

Workers and time are inversely proportional: M1 x D1 / W1 = M2 x D2 / W2, where M is men, D is days, W is work. More workers means fewer days.

In Pipes and Cisterns, how do inlet and outlet pipes affect the tank?

An inlet pipe filling in 'a' hours does +1/a per hour (positive work). An outlet pipe emptying in 'b' hours does -1/b per hour (negative work). Net rate = sum of all rates.

If pipe A fills a tank in a hours and pipe B empties it in b hours (b > a), how long to fill together?

Net fill rate = (1/a - 1/b) per hour, so time to fill = (a x b)/(b - a) hours.

What is the basic relationship between speed, distance, and time?

Speed = Distance / Time. Therefore Distance = Speed x Time and Time = Distance / Speed.

How do you convert km/hr to m/s and m/s to km/hr?

km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.

What is average speed when equal distances are covered at speeds x and y?

Average speed = 2xy/(x + y), the harmonic mean of the two speeds (not the simple arithmetic mean).

How long does a train of length L metres take to cross a stationary pole or man, at speed S?

Time = L / S (the train must cover its own length). The pole is treated as a point with zero length.

How long does a train of length L take to cross a platform/bridge of length P at speed S?

Time = (L + P) / S, because the train must cover its own length plus the length of the platform.

What are the relative speeds of two trains moving in the same and opposite directions?

Opposite directions (or crossing): relative speed = sum of speeds (u + v). Same direction (overtaking): relative speed = difference of speeds (u - v).