FPSC General Recruitment Test Quantitative Ability and Numerical Reasoning Syllabus

Define cost price (CP), selling price (SP), profit, and loss.

CP is the buying price; SP is the selling price. If SP > CP, Profit = SP - CP; if SP < CP, Loss = CP - SP.

What are the formulas for profit percentage and loss percentage?

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

How do you find SP given CP and a profit (or loss) percentage?

SP = CP x (100 + Profit%)/100 for a profit, or SP = CP x (100 - Loss%)/100 for a loss.

What is the formula for Simple Interest, and what do the terms mean?

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

What is the formula for the amount under Compound Interest (compounded annually)?

A = P x (1 + R/100)^T, and Compound Interest = A - P.

How does the compound interest formula change when interest is compounded half-yearly?

Use A = P x (1 + (R/2)/100)^(2T): halve the rate and double the number of periods.

For the same P, R, and T = 2 years, what is the difference between CI and SI?

Difference (for 2 years) = P x (R/100)^2. CI is always greater than SI for more than one year.

In a partnership, how is profit shared when partners invest different amounts for different times?

Profit is divided in the ratio of each partner's (investment x time). This product is called the monthly/capital equivalent.

Distinguish between an active (working) 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 by investment ratio.

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

Marked price (MP) is the labelled price before reduction; discount is the reduction given on MP. SP = MP - Discount, and Discount% = (Discount/MP) x 100.

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

Single equivalent discount = x + y - (xy/100). For example, 10% and 20% give 10 + 20 - 2 = 28%.

If A can do a piece of work in n days, what fraction of the work does A do in one day?

A does 1/n of the work in one day. This unit-of-work-per-day idea is the basis of all time and work problems.

A can do a job in 10 days and B in 15 days. How long do they take working together?

Combined one-day work = 1/10 + 1/15 = 1/6, so together they finish in 6 days.

State the basic relationship between speed, distance, and time.

Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

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

Multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 to get km/h.

What is the average speed for equal distances travelled at speeds x and y?

Average speed = 2xy / (x + y) (the harmonic mean), not the simple average of x and y.

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

Time = L / speed, because crossing a point object requires covering only the train's own length.

How do you find the time for a train of length L to cross a platform of length P?

Time = (L + P) / speed, since the train must cover its own length plus the platform length.

What is the relative speed of two trains moving in the same direction and in opposite directions?

Same direction: relative speed = difference of speeds; opposite directions: relative speed = sum of speeds.

In pipes and cisterns, how are inlet and outlet pipes treated mathematically?

An inlet (fills) is taken as positive work (+1/time); an outlet (empties) is taken as negative work (-1/time). They are added like time-and-work rates.

Pipe A fills a tank in 6 hours and pipe B empties it in 8 hours. If both are open, how long to fill?

Net rate = 1/6 - 1/8 = 1/24 per hour, so the tank fills in 24 hours.

What is the standard form of a linear equation in one variable, and how is it solved?

Standard form: ax + b = 0. Solve by isolating x: x = -b/a (where a is not 0).

State the quadratic formula for solving ax^2 + bx + c = 0.

x = [-b ± sqrt(b^2 - 4ac)] / (2a). The term b^2 - 4ac is the discriminant, determining the nature of the roots.

What do the values of the discriminant (b^2 - 4ac) tell you about a quadratic's roots?

If > 0, two distinct real roots; if = 0, two equal real roots; if < 0, no real roots (the roots are complex).

What are the algebraic identities for (a+b)^2, (a-b)^2, and a^2 - b^2?

(a+b)^2 = a^2 + 2ab + b^2; (a-b)^2 = a^2 - 2ab + b^2; a^2 - b^2 = (a+b)(a-b).

State the formulas for the area and perimeter (circumference) of a circle of radius r.

Area = pi x r^2; Circumference = 2 x pi x r (or pi x diameter).

What are the formulas for the area of a triangle, a rectangle, and a parallelogram?

Triangle = 1/2 x base x height; Rectangle = length x breadth; Parallelogram = base x height.

Give the volume formulas for a cube, a cuboid, and a cylinder.

Cube = side^3; Cuboid = length x breadth x height; Cylinder = pi x r^2 x h.

Classify angles by measure: acute, right, obtuse, straight, and reflex.

Acute < 90 degrees; right = 90 degrees; obtuse between 90 and 180 degrees; straight = 180 degrees; reflex between 180 and 360 degrees.

Define complementary and supplementary angles, and state the angle sum of a triangle.

Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees. The three interior angles of any triangle sum to 180 degrees.