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Reasoning and Maths Key Facts

Short cards on reasoning rules, number patterns, school maths and English usage for the admission test practice.

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What is the difference between a premise and a conclusion?
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1
What is the difference between a premise and a conclusion?
A premise is a statement given as evidence; the conclusion is the claim the premises are meant to support.
2
What does 'all A are B' tell you about an item that is A?
The item must be B. It does not tell you that every B is an A.
3
If 'if P then Q' is true and Q is false, what follows?
P is false. This is the valid reverse of the rule.
4
If 'if P then Q' is true and Q is true, what follows about P?
Nothing definite: Q may be true for other reasons.
5
What does 'only if' express?
A requirement: the condition is necessary, but meeting it does not guarantee the result.
6
What is a hidden assumption in an argument?
An unstated idea that must be true for the evidence to support the conclusion.
7
How can you weaken a cause-and-effect claim?
Show another factor that could explain the result, or that the effect happens without the cause.
8
What is a generalisation flaw?
Drawing a claim about all cases from one or a few examples.
9
What is the quickest way to disprove 'all swans are white'?
Find one swan that is not white.
10
How do you find the rule in a number pattern?
Check the differences between terms, then check for multiplying by a constant or for squares.
11
What are the first six square numbers?
1, 4, 9, 16, 25 and 36.
12
What is the sum of the whole numbers from 1 to n?
n x (n + 1) / 2.
13
How do you find the least common multiple of two numbers?
Break both into prime factors and take each prime to its highest power.
14
What is the order of operations?
Brackets, powers, then multiplication and division, then addition and subtraction.
15
How do you find the average of a set of numbers?
Add the numbers and divide by how many there are.
16
How do you increase a number by 20 percent and then decrease by 20 percent?
Multiply by 1.2 then by 0.8, which gives 0.96: a 4 percent fall overall.
17
What is the area of a triangle?
Half of base times height.
18
What do the interior angles of a triangle add up to?
180 degrees.
19
How many degrees do the interior angles of a polygon with n sides add up to?
(n - 2) x 180 degrees.
20
What does the Pythagorean theorem say for a right-angled triangle?
The square of the longest side equals the sum of the squares of the two shorter sides.
21
What is the circumference of a circle with radius r?
2 x pi x r.
22
How do you share an amount in the ratio 3:5?
Add the parts to get 8, divide the amount by 8, then multiply by 3 and by 5.
23
In a first conditional sentence, which tense follows 'if'?
The present simple, for example: 'If it rains, we will stay at home.'
24
Which verb form follows 'neither of' and 'each of'?
A singular verb: 'Neither of them is late.'
25
What is the difference between 'for' and 'since' with the present perfect?
'For' goes with a length of time; 'since' goes with a starting point.

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