IBSAT cheat sheet

Subject-verb agreement: a singular subject takes a singular verb even when a plural noun sits inside a prepositional phrase ("The list of items is long").

Collective nouns (team, jury, committee) take a singular verb when acting as one unit and a plural verb when members act individually.

Parallelism rule: items joined by and/or, not only...but also, or either...or must share the same grammatical form.

Pronoun case: use the subject form after than/as when a verb is implied ("She is taller than I [am]"), object form after prepositions.

Misplaced modifier test: an introductory participial phrase must modify the noun immediately following the comma.

Vocabulary in context: infer meaning from surrounding contrast or cause-effect cues (but, although, because, therefore) rather than memorized glosses.

Idiomatic prepositions to fix: "comprise" takes no of; "differ from" for things, "differ with" for opinions; "superior to," not "superior than."

Cloze strategy: read the full sentence, predict the blank's meaning first, then eliminate options that fail grammar before meaning.

Main-idea questions ask for the passage's central claim; scope answers to what the whole passage supports, not one paragraph.

Tone and attitude answers must be defensible from word choice; extreme modifiers (never, always, entirely) usually signal wrong options.

Inference questions require a logical step from stated evidence; if an option needs outside knowledge, it is out of scope.

Detail questions are answered by locating the exact sentence; paraphrase, not verbatim copying, is the usual correct form.

Elimination heuristic: options that reverse cause and effect, swap the author's stance, or overgeneralize are distractors.

EXCEPT/NOT questions invert the task: three options are supported by the passage, one is not; verify each against the text.

Passage mapping: note each paragraph's function (claim, evidence, counterargument, conclusion) to answer structure questions fast.

Vocabulary-in-context: substitute each option into the original sentence and keep the one preserving the author's logic.

Percentage change: successive changes of a% and b% give a net change of a + b + (ab/100) percent, with signs carried.

Profit and loss: selling price = cost price x (100 + profit%)/100; discount is always computed on marked price.

Simple interest = P x R x T / 100; compound interest = P[(1 + R/100)^T - 1], and CI exceeds SI by P(R/100)^2 for two years.

Speed conversion: multiply km/h by 5/18 to get m/s; relative speed adds for opposite directions, subtracts for same direction.

Work: if A finishes in x days and B in y days, together they take xy/(x + y) days; rates add, times do not.

Average of n numbers shifts by the same amount as each element; weighted average = sum of (value x weight) / sum of weights.

Mensuration: cylinder volume = pi r^2 h; sphere volume = (4/3) pi r^3; cone volume = (1/3) pi r^2 h.

Permutation vs combination: order matters for permutations (nPr); for combinations use nCr = nPr / r!, and nCr = nC(n-r).

Data sufficiency format: decide whether the data is sufficient, not what the numeric answer is; stop calculating once sufficiency is clear.

Statement-pair logic: sufficient if either statement alone works, if only both together work, or if each alone works; only one option matches.

Never carry information from Statement 1 into Statement 2; evaluate each independently, then combine only if needed.

For a linear equation in two variables, one equation is insufficient; two distinct equations are sufficient unless they are multiples of each other.

Percentage-point vs percent: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.

In tables and bar charts, check units and scale on axes first; a truncated y-axis exaggerates visual differences.

Pie chart: each sector's angle = (component/total) x 360 degrees, and the percentage share equals angle/3.6.

Ratio comparison across years: convert all series to a common base (index = 100) before claiming one grew faster than another.