IPMAT Indore flashcards

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

Successive percentage change

Net change from applying a% then b% equals a + b + ab/100. A 20% increase followed by a 20% decrease yields a net 4% decrease, because the base changes between steps.

Constant expenditure rule

If price rises by r%, consumption must fall by 100r/(100 + r)% to keep spending fixed. If price falls by r%, consumption can rise by 100r/(100 - r)%.

Combined work time

When A alone finishes in a days and B alone in b days, working together they finish in ab/(a + b) days, since their rates 1/a and 1/b add.

Alligation ratio

To blend two items of values x and y into a mixture of mean value m, the quantity ratio is (m - y) : (x - m), assuming x exceeds m exceeds y.

Rule of 72

Money invested at R% compounded annually doubles in roughly 72/R years. The exact doubling time is ln 2 divided by ln(1 + R/100).

Relative speed of trains

Trains moving in opposite directions add their speeds; moving the same way, speeds subtract. Crossing time equals the sum of their lengths divided by relative speed.

Compound interest two years

For two years, compound interest equals P[(1 + R/100)^2 - 1], which is twice the first-year simple interest plus interest earned on that first-year interest.

Circular arrangement count

n distinct people can be seated around a circle in (n - 1)! ways. Clockwise and anticlockwise orders count separately unless the problem specifies garlands or necklaces.

Syllogism valid conclusion

From 'All A are B' and 'All B are C', 'All A are C' follows. A 'some' premise can support a 'some' conclusion but never a universal 'all' conclusion.

Calendar weekday shift

An ordinary year shifts the weekday of a date by 1 day, a leap year by 2. A century year is a leap year only when divisible by 400.

Data sufficiency test

A statement is sufficient only if it forces a single unique answer. If it allows two different valid values, it is insufficient even when both satisfy the question stem.

Direction sense displacement

Track net east-west and net north-south movement separately, then combine them with the Pythagorean theorem to get straight-line distance from the start.

Coding by letter position

Map letters to numbers A=1 through Z=26, test constant or increasing shifts, then try reverse-alphabet mapping (A=26, Z=1) if forward shifts fail.

Blood relation tree

Draw generations in rows: vertical links mean parent to child, horizontal links mean spouse or sibling. Re-anchor every relation to the person actually asked about.

Number series check order

Test first differences, then ratios, then alternating odd-even sub-series, and only then a polynomial or square-cube pattern before concluding no rule exists.

One of plus plural noun

In 'one of the + plural noun + relative clause', the verb of the main clause is singular, but the verb inside the relative clause agrees with the plural noun.

Dangling modifier rule

An introductory participle phrase must describe the subject of the main clause. 'Walking home, the rain started' is wrong because the rain was not walking.

Since versus for

Use 'since' with a starting point in time (since 2010) and 'for' with a duration (for five years). Pair 'between' with 'and' and 'from' with 'to'.

Parallel structure requirement

Items joined by and, or, or not only...but also must share grammatical form: all nouns, all infinitives, or all clauses, never a mix of forms.

Article choice by sound

Choose 'a' before consonant sounds and 'an' before vowel sounds, so 'an hour' and 'a university' are correct because spelling does not decide.

Third conditional form

Unreal past conditionals use 'If + had + past participle' in the condition and 'would have + past participle' in the result, as in 'If I had studied, I would have passed'.

Comprise usage

'Comprise' means 'consist of' and takes a direct object without 'of'. Write 'The team comprises five members', not 'comprises of five members'.

Reading option validity

A correct answer must be directly supported by the passage. Options that are true in general but absent from the text are wrong for comprehension questions.

Collective noun agreement

Collective nouns like team or jury take a singular verb when acting as one unit and a plural verb when members act individually, as in 'The jury disagree'.

Quadratic root relations

For ax^2 + bx + c = 0, the roots sum to -b/a and multiply to c/a. The discriminant b^2 - 4ac decides whether roots are real, equal, or complex.

Remainder and factor theorem

Dividing polynomial p(x) by (x - k) leaves remainder p(k). The binomial is a factor exactly when p(k) equals zero.

Logarithm product and power rules

log(xy) = log x + log y, log(x/y) = log x - log y, and log(x^n) = n log x. Also log base b of a equals 1 over log base a of b.

AP nth term and sum

Arithmetic progression with first term a and common difference d has nth term a + (n - 1)d and sum of n terms n/2 times [2a + (n - 1)d].

GP sum formula

Geometric progression with first term a and ratio r has nth term ar^(n-1) and sum a(r^n - 1)/(r - 1) when r is not 1.

Permutation versus combination

Use nPr = n!/(n - r)! when order matters and nCr = n!/[r!(n - r)!] when it does not. Note nCr equals nC(n - r).

Addition rule probability

For events A and B, P(A or B) = P(A) + P(B) - P(A and B). For independent events, P(A and B) = P(A) times P(B).

Perpendicular slope condition

Two lines are perpendicular exactly when the product of their slopes equals -1. Parallel lines have equal slopes, and a vertical line has undefined slope.