Classification: SSC CGL Reasoning

Formulas (2)

• Prime and composite numbers · Prime test
  $$n \text{ is prime if no prime } p \le \sqrt{n} \text{ divides } n$$
• Squares, cubes and divisibility tests · Last digits and divisibility
  $$n^2 \text{ ends in } 0, 1, 4, 5, 6, 9 \qquad 3 \mid n \text{ when } 3 \mid \text{digit sum} \qquad 11 \mid n \text{ when } 11 \mid \text{alternating digit sum}$$

Watch out for (7)

• Stopping at a rule that fits all four
  → Finding the odd one out: the order of tests
• Answering a different question from the one printed
  → Finding the odd one out: the order of tests
• Counting 1 as a prime
  → Prime and composite numbers
• Trusting an odd last digit
  → Prime and composite numbers
• Calling a number a square because of its last digit
  → Squares, cubes and divisibility tests
• Missing that a number can be both a square and a cube
  → Squares, cubes and divisibility tests
• Missing a run that goes the other way
  → Digit patterns and true statements

Formulas (3)

• Pair rules made of multiplying, adding and fixed ratios · Common pair rules
  $$y = kx + c \qquad y - x = d \qquad x : y = p : q$$
• Pair rules with squares, cubes and roots · Power rules for pairs
  $$y = x^2 \pm c \qquad y = (x \pm c)^2 \qquad y = x^3 \pm x \qquad y = k x^2 \qquad y = \sqrt{x} \pm c$$
• Products and powers of neighbouring numbers · Neighbouring numbers
  $$n(n+1) = n^2 + n \qquad (n+1)^2 - n^2 = 2n + 1 \qquad (n+1)^3 - n^3 = 3n^2 + 3n + 1$$

Watch out for (6)

• Reading k from the smallest pair
  → Pair rules made of multiplying, adding and fixed ratios
• Only testing the rule from first to second
  → Pair rules made of multiplying, adding and fixed ratios
• Taking a square on the right as proof
  → Pair rules with squares, cubes and roots
• Looking for a multiplier when the numbers grow too fast
  → Pair rules with squares, cubes and roots
• Mixing up n(n + 1) and n(n − 1)
  → Products and powers of neighbouring numbers
• Treating n × n as n times its neighbour
  → Products and powers of neighbouring numbers

Formulas (2)

• Equal steps, equal ratios and growing gaps in a set · Steps and ratios in a set a, b, c
  $$b - a = c - b \qquad \frac{b}{a} = \frac{c}{b}$$
• One number of a set made from the other two · Rules linking a set a, b, c
  $$c = k(a + b) \qquad c = k(a - b) \qquad c = ab \pm k \qquad a + c = k b$$

Watch out for (4)

• Mixing up equal steps and equal ratios
  → Equal steps, equal ratios and growing gaps in a set
• Checking only one link of a triad
  → Two numbers of a triad built from one
• Taking a rule that only two options obey
  → One number of a set made from the other two
• Throwing out an option because a step gives a fraction
  → One number of a set made from the other two

Formulas (2)

• Letter positions and clusters with equal steps · Reverse position and wrapping round
  $$\text{reverse position} = 27 - \text{position} \qquad \text{position after Z} = \text{position} - 26$$
• Opposite letters, whose positions add to 27 · Opposite letters
  $$\text{position}(L) + \text{position}(\text{opposite of } L) = 27$$

Watch out for (3)

• Counting the starting letter as a step
  → Letter positions and clusters with equal steps
• Stopping at Z
  → Letter positions and clusters with equal steps
• Using 26 as the total for opposite letters
  → Opposite letters, whose positions add to 27

Watch out for (4)

• Checking only the first gap
  → Gaps that grow or shrink by a rule
• Losing count when a step passes Z
  → Gaps that grow or shrink by a rule
• Dropping the direction of a step
  → Letters that move forward and back
• Wrapping the wrong way at the start of the alphabet
  → Letters that move forward and back

Watch out for (4)

• Checking the letters but not the numbers
  → The number tied to the letter's position
• Counting from the wrong end of the alphabet
  → The number tied to the letter's position
• Stopping once the letters and numbers fit
  → Checking every part of the group
• Missing a direction change
  → Checking every part of the group

Watch out for (7)

• Stopping at a group that holds all four
  → Naming the kind of thing
• Taking the category word for a member
  → Naming the kind of thing
• Answering from the broad group
  → Narrowing the group
• Confusing a big city with the capital
  → Narrowing the group
• Calling two near words opposites
  → Grouping words by meaning
• Reading the pair in the other order
  → The relation inside a word pair
• Ignoring a wrong fact inside a correct relation
  → The relation inside a word pair