GATE General Aptitude formula sheet

A past action with a present result, or a period that runs up to now. Never with a finished past time (yesterday, ago, last year, in 2019).

An action that began in the past and is still going on: 'She has been teaching here since June' / 'for three months'. It is also used for an activity that has only just stopped, leaving a visible result: 'The roads are wet; it has been raining.' Use since or for here, not from.

Here $\leftrightarrow$ is read 'means exactly the same as'. For 'can be inferred', 'is implied' and 'must be true', an option passes only if it holds in every situation in which all the passage's sentences hold. 'Probably true' and 'true in real life' do not pass. Ordinary word meanings may be used in applying the test; facts about the topic that the passage does not give may not.

Of the three standard rearrangements of an if-then statement (converse, inverse, contrapositive), only the contrapositive keeps the meaning. The converse (if B then A) and the inverse (if not A then not B) do NOT follow; they are equivalent to each other, not to the original.

For parts of one whole (a pie, a stacked bar, a column of a table with its total). The shares of all the parts add to 100%, apart from rounding in the display.

The base is the old (earlier) value unless the question names another. A positive result is an increase and a negative one a decrease. For a quantity that cannot go below zero, a decrease can never exceed 100%; an increase can (a rise of 100% is a doubling).

Scale both ratios so that the common term $b$ has the same value ($qr$) in each.

The shares add back to $N$. If only the difference between two shares is given, divide it by the difference of their ratio terms to get the value of one ratio unit.

Any simple polygon with $n$ sides (sides do not cross), convex or not: $180^{\circ }$ for a triangle, $360^{\circ }$ for a quadrilateral, $540^{\circ }$ for a pentagon.

One exterior angle taken at each vertex of a convex polygon; the sum is $360^{\circ }$ whatever the value of $n$. At every vertex, interior angle $+$ exterior angle $=180^{\circ }$.

Uses every observation, so one extreme value can move it a lot. Total of all values $=n\bar{x}$, and many mean questions become simple once they are worked through totals.

Weights $w_i\ge 0$, not all zero. For a frequency table put $w_i=f_i$, the frequency of the value $x_i$. For grouped data (class intervals), take $x_i$ as the mid-point of each class.

Always equivalent to the original. The converse $Q\to P$ and the inverse $\neg P\to \neg Q$ do NOT follow from $P\to Q$ (they are equivalent to each other, not to the original).

'If P, then Q' is false only when P is true and Q is false. So the denial of 'If it rains, the match is called off' is 'It rains and the match is not called off', not 'If it rains, the match is not called off'.

Every point moves by the same amount. Size, shape and orientation are unchanged.

These are exact special cases of the rotation rule. For any other centre, apply them to each point's position relative to that centre.