SPJAT flashcards
SPJAT · Build recall with a focused review session.
31 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Net percentage change
- For successive changes of a% and b%, the net change is a + b + (ab/100) percent. A rise then equal fall of x% always gives a net loss of x squared divided by 100.
- Compound interest formula
- CI equals P times (1 + R/100) raised to T, minus P. For two years the gap between CI and SI equals P times (R/100) squared.
- Average speed unequal distances
- When equal distances are covered at speeds u and v, average speed is 2uv divided by (u + v). This harmonic mean is always less than the arithmetic mean.
- Work together formula
- If A finishes a job in a days and B in b days, working together they take ab divided by (a + b) days. Efficiency is inversely proportional to time taken.
- Alligation rule
- To mix two components at prices p and q to get mean price m, the required quantity ratio is (m minus q) to (p minus m). Useful for mixture and profit problems.
- Combination formula
- nCr equals n factorial divided by r factorial times (n minus r) factorial. It counts selections where order does not matter, unlike nPr which counts arrangements.
- Divisibility shortcuts
- A number is divisible by 3 or 9 if its digit sum is; by 4 if its last two digits are; by 8 if its last three digits are; by 11 if the alternating digit-sum difference is.
- Stream and boat speeds
- Downstream speed equals boat speed plus stream speed; upstream equals boat speed minus stream speed. Boat speed is the mean of the two, stream speed half their difference.
- Syllogism validity test
- A conclusion follows only if it holds in every Venn diagram consistent with the premises. If one valid diagram contradicts it, the conclusion does not follow.
- Clock hand angle
- The angle between hour and minute hands equals the absolute value of 30H minus 5.5M degrees, where H is the hour and M the minutes.
- Leap years in a century
- A century contains 24 leap years, except centuries divisible by 400, which contain 25. Thus 1600 and 2000 are leap years but 1700 and 1900 are not.
- Coding letter positions
- Assign A to 1 through Z to 26, then test fixed shifts, reversals, or alternating patterns. Opposite-letter codes pair positions summing to 27, as A with Z.
- Direction sense displacement
- Plot each move on a grid, tracking net horizontal and vertical change. Final straight-line distance is the square root of the sum of squared components.
- Seating arrangement facing rules
- For people facing the centre, left is clockwise and right is anticlockwise. For people facing outward, the directions reverse, so fix orientation before placing anyone.
- Blood relation resolution
- Draw a tree marking gender and generation, then simplify phrases step by step. Terms like 'only son' or 'only daughter' collapse the tree to a single person.
- Statement and assumption
- An assumption is what the speaker must believe for the statement to make sense. It must be necessary, not merely plausible or generally true in the world.
- Subject-verb agreement traps
- Each, every, either, and neither take singular verbs. With neither nor, the verb agrees with the nearer subject, so 'neither the boys nor the girl was' is correct.
- Dangling modifier rule
- An introductory participial phrase modifies the subject of the main clause. 'Walking home, the rain started' is wrong because the rain was not walking.
- Parallelism in lists
- Items joined by and, or, or but must share grammatical form. A series should use all infinitives or all gerunds, never a mixture of both.
- Comparative constructions
- Use than after a comparative and as as for equality. Avoid double comparatives such as more better, and do not follow superior with than.
- Fixed preposition pairs
- Certain words take set prepositions: superior to, prefer to, capable of, consist of, comprise without of, and married to. Memorizing these prevents idiom errors.
- Main idea versus detail
- A main-idea answer must cover the entire passage, not a single paragraph. Options with extreme words like always or never are usually wrong.
- Pronoun antecedent clarity
- Every pronoun needs one unambiguous antecedent. If it, they, or this could refer to more than one noun, rewrite the sentence to name the referent.
- Contextual vocabulary inference
- Infer an unfamiliar word's meaning from contrast cues, cause-effect signals, or appositives nearby. The passage's logic, not a memorized definition, decides the answer.
- Pie chart sector angle
- Each sector's central angle equals its value divided by the total, multiplied by 360 degrees. Equivalently, a one percent share occupies 3.6 degrees of the circle.
- Percentage share comparison
- Share equals part divided by total, times 100. To compare shares across years, recompute each year's total instead of comparing raw values directly.
- Compound annual growth rate
- CAGR equals the nth root of (final divided by initial), minus one, for n years. It uses the geometric mean, unlike simple average growth which overstates volatile series.
- Unit and scale check
- Before computing, confirm whether axes, legends, and tables use thousands, lakhs, or units. Mismatched scales cause most data interpretation calculation errors.
- Approximation decision rule
- Round to two significant figures when answer options are widely spaced. Keep exact values when options differ by less than about five percent.
- Table total verification
- Check that row and column sums match the stated totals before answering. A mismatch signals a misread cell or a hidden footnote changing the data.
- Selective series extraction
- Read only the series the question names and ignore unrelated legends. Extracting every number first wastes time and invites transcription errors.