BCS Written Math & Mental Ability flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

HCF-LCM product rule

For any two positive integers a and b, HCF(a, b) multiplied by LCM(a, b) equals a times b. This holds only for two numbers, not for three or more.

Terminating decimal test

A fraction in lowest terms gives a terminating decimal only if its denominator has no prime factors except 2 and 5. Otherwise the decimal repeats forever.

Successive percentage change

Two successive changes of a percent and b percent produce a net change of a plus b plus ab divided by 100 percent. Signs matter: use negative values for decreases.

Reverse percentage rule

If A is r percent more than B, then B is 100r divided by (100 plus r) percent less than A. The base switches, so the two percentages are never equal.

Equal selling price trap

Selling two items at the same price with a gain of x percent on one and a loss of x percent on the other always yields a net loss of x squared divided by 100 percent.

Cost price from selling price

Cost price equals 100 times selling price divided by (100 plus profit percent), or by (100 minus loss percent). Always divide by a factor above or below 100.

Single equivalent discount

Successive discounts of a percent and b percent equal one discount of a plus b minus ab divided by 100 percent. The result is always smaller than the simple sum.

Markup and discount profit

With markup m percent on cost and discount d percent on marked price, profit percent equals the product (100 plus m)(100 minus d) divided by 100, minus 100.

Partnership profit share

Profit shares are proportional to capital multiplied by time invested. Capitals in ratio a to b and periods in ratio x to y give shares in ratio ax to by.

Mean proportional

The mean proportional between two positive numbers a and c is the positive square root of their product ac. It satisfies a divided by m equals m divided by c.

Combined work rate

If A finishes in x days and B in y days, together they finish in xy divided by (x plus y) days. Add their per-day rates and take the reciprocal.

Efficiency and time

If A is k times as efficient as B, A takes one-kth of B's time. Their working times are in the ratio 1 to k, the inverse of their rates.

Filling with a leak

An inlet filling in x hours and a leak emptying in y hours, with y greater than x, fill the tank in xy divided by (y minus x) hours. Subtract the leak rate.

Average speed equal distances

For two equal distances covered at speeds u and v, average speed is 2uv divided by (u plus v). It is always less than the arithmetic mean of the speeds.

Train crossing platform

A train of length L crossing a platform of length P travels a total distance of L plus P. Time equals (L plus P) divided by speed, with consistent units.

Relative speed of trains

Trains moving in opposite directions have relative speed equal to the sum of their speeds; moving in the same direction, the difference. Crossing time uses total length over relative speed.

Boat and stream

Downstream speed equals boat speed plus stream speed, upstream equals boat minus stream. Boat speed is the average of the two, stream speed half their difference.

Replacement in average

When one item is replaced, the change in average multiplied by the number of items equals the difference between the new item and the removed item.

Weighted combined average

The average of two groups with sizes n1 and n2 and averages a1 and a2 is (n1 a1 plus n2 a2) divided by (n1 plus n2). Larger groups pull the mean toward themselves.

Alligation ratio rule

Mixing two components of prices c and d to reach mean price m gives quantities in the ratio (m minus c) to (d minus m), where c is below m and d above.

Repeated replacement formula

If x litres are removed from a vessel of volume V and replaced by water n times, the pure liquid remaining is V times (1 minus x divided by V) raised to n.

Simple interest formula

Simple interest equals principal times rate times time divided by 100, with rate as a percentage per year and time in years. Amount equals principal plus interest.

Compound interest difference

For two years, compound interest minus simple interest equals principal times (rate divided by 100) squared. For three years the difference is multiplied by (3 plus rate/100).

Half-yearly compounding adjustment

When interest compounds half-yearly, halve the annual rate and double the number of periods. Quarterly compounding uses a quarter of the rate and four times the periods.

Quadratic root relations

For ax squared plus bx plus c equals zero, the sum of roots is minus b over a and the product is c over a. The discriminant b squared minus 4ac decides the nature of roots.

Inequality sign reversal

Multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality sign. Adding or subtracting a number never reverses it.

Reciprocal power identities

If x plus 1 over x equals k, then x squared plus 1 over x squared equals k squared minus 2, and x cubed plus 1 over x cubed equals k cubed minus 3k.

Heron's area formula

The area of a triangle with sides a, b, c equals the square root of s(s minus a)(s minus b)(s minus c), where s is half the perimeter.

Cone slant height relation

For a cone of radius r and height h, slant height l equals the square root of r squared plus h squared. Curved surface area is pi r l and volume is one-third pi r squared h.

Polygon angle sums

The interior angles of an n-sided polygon sum to (n minus 2) times 180 degrees. Each exterior angle of a regular n-gon measures 360 divided by n degrees.

Opposite alphabet letters

In the English alphabet, letters opposite each other sum to 27: A pairs with Z, B with Y, and so on. This converts reverse-alphabet coding into simple arithmetic.

Two interleaved series

When consecutive differences look irregular, split the series into odd-position and even-position terms. Each subsequence often follows its own simple rule, such as adding 3 or doubling.