GCE A/L Common General Test flashcards

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

Converse vs contrapositive

From 'If P then Q', the contrapositive 'If not Q then not P' is logically valid. The converse 'If Q then P' is not valid and is a common distractor in logic questions.

Meaning of 'unless'

'P unless Q' translates to 'If not Q, then P'. The condition Q is the exception that blocks P, so the absence of Q guarantees P in formal logic.

Negating 'All A are B'

The negation is 'Some A are not B', not 'No A are B'. Similarly, the negation of 'Some A are B' is 'No A are B'. Getting this wrong reverses the logic.

Harmonic mean average speed

For equal distances travelled at speeds x and y, average speed is 2xy/(x+y), not the arithmetic mean (x+y)/2, because more time is spent at the slower speed.

Successive percentage formula

Two successive changes of a% and b% combine to a + b + ab/100 percent. A rise and fall of the same rate r gives a net fall of r squared divided by 100.

Combined work formula

If worker A alone takes a days and worker B alone takes b days, together they finish in ab/(a+b) days, derived from adding their rates 1/a and 1/b.

Divisibility by 11

A number is divisible by 11 when the difference between the sum of digits in odd positions and the sum in even positions is zero or a multiple of 11.

Clock angle formula

The angle between clock hands is the absolute value of 30H minus 5.5M degrees, where H is the hour and M the minutes. If it exceeds 180, subtract from 360.

Mirror versus water image

A mirror image swaps left and right while keeping top and bottom fixed. A water image swaps top and bottom while keeping left and right fixed. Both preserve size.

Opposite faces on a die

On a standard die, opposite faces always sum to seven: 1 opposite 6, 2 opposite 5, 3 opposite 4. Two faces summing to seven cannot be adjacent.

Cube net opposite faces

In a cube net, two squares are opposite faces when they lie in the same straight row or column separated by exactly one square between them.

Rotation versus reflection

Rotation preserves orientation, so a rotated figure can be matched to the original. Reflection reverses orientation, producing a mirror form that no rotation can align with the original.

Sri Lanka Parliament size

The Sri Lankan Parliament has 225 members: 196 elected by district proportional representation and 29 appointed from national lists to ensure proportionality.

UN Security Council membership

The Security Council has 15 members: five permanent members with veto power and ten elected members serving two-year terms chosen by the General Assembly.

SAARC membership

SAARC has eight members: Afghanistan, Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka. Its permanent secretariat is located in Kathmandu, Nepal.

Nobel Peace Prize location

The Nobel Peace Prize is awarded in Oslo, Norway, while the prizes in Physics, Chemistry, Medicine, Literature and Economic Sciences are awarded in Stockholm, Sweden.

Commonwealth member count

The Commonwealth is a voluntary association of 56 member states, most of which were formerly territories of the British Empire, with a secretariat in London.

Sri Lanka official languages

Sinhala and Tamil are the official languages of Sri Lanka, and English functions as the link language under the constitutional framework following the 13th Amendment.

Reading comprehension evidence rule

The correct answer must be directly supported by words in the passage. Options that are true in general but absent from the text are distractors unless inference is requested.

Prefix meanings list

Anti- means against, circum- around, hyper- excess, hypo- deficiency, mal- bad, mis- wrongly, post- after, pre- before, and sub- under. These decode unfamiliar vocabulary.

Analogy relation direction

Identify the exact relation in the given pair, such as part to whole or cause to effect, then apply it in the same direction. A reversed relation is a wrong option.

Syllogism with 'some'

Two 'some' premises yield no valid conclusion. One 'all' premise plus one 'some' premise yields a 'some' conclusion only when the middle term links them correctly.

Family tree notation

Draw relations as a tree with gender marked, then read the target relation along the path. 'Brother of my father' is uncle; 'son of my sister' is nephew.

Number series checking order

Check first differences, then second differences, then ratios. Alternating series often interleave two independent patterns, so test odd and even positions separately.

Water jug reachability rule

With two jugs, only amounts that are multiples of the greatest common divisor of the jug capacities can be measured. Repeatedly fill the smaller and pour into the larger.

Weighing puzzle capacity

With k weighings on a balance, there are 3^k possible outcomes. When one coin is known heavier or lighter, up to (3^k - 1)/2 suspect coins can be resolved.

Calendar odd-day shift

A normal year shifts the weekday by one odd day, a leap year by two. A century of 100 years shifts by five, and 400 years shift by zero.

Clock hand coincidence count

The minute and hour hands coincide 11 times in every 12 hours and point in opposite directions 11 times, meeting again every 65 and five-elevenths minutes.

Data sufficiency question aim

The task is to decide whether the given statements supply enough information, not to compute the value. Test each statement alone before combining both.

Compound versus simple interest

Simple interest is PRT/100 on the original principal. Compound interest is P(1 + r/100)^n minus P, and the gap between them widens as the number of years grows.

Profit percentage base

Profit percent is calculated on cost price unless the question states otherwise. Selling price equals cost price multiplied by (100 plus profit percent) divided by 100.

Replacement mixture formula

After n replacements from a container of total volume V, the pure component remaining equals the initial amount multiplied by (1 minus replaced volume divided by V) raised to n.