Series: SSC CGL Reasoning

Formulas (1)

• Letter positions and the gap rule · Reverse position and wrapping round
  $$n_{\text{reverse}} = 27 - n \qquad n > 26 \Rightarrow n - 26 \qquad n < 1 \Rightarrow n + 26$$

Watch out for (5)

• Counting the starting letter as a step
  → Letter positions and the gap rule
• Stopping at Z
  → Letter positions and the gap rule
• Opposite letters add to 27, not 26
  → Pairs of letters, one letter at a time
• Reading the pair as one jump
  → Pairs of letters, one letter at a time
• Checking only the first blank
  → Runs of the alphabet with blanks

Watch out for (5)

• Checking only the first letter
  → Every letter moves by the same step
• Wrapping in the middle of a cluster
  → Every letter moves by the same step
• Assuming all columns go the same way
  → Each column has its own step
• Wrapping backwards
  → Each column has its own step
• Forcing a fixed step on a growing column
  → Steps that grow and vowel columns

Watch out for (4)

• Taking the first repeat you see as the block
  → Find the repeating block
• Losing count of the places
  → Find the repeating block
• Stopping once the first half fits
  → Series built from two letters
• Hunting for an exact repeat that is not there
  → Blocks where one letter moves

Formulas (1)

• Steady and evenly growing differences · Next term when the difference grows by a fixed step
  $$t_{n+1} = t_n + d_n \qquad d_{n+1} = d_n + k$$

Watch out for (5)

• Not checking the term after the blank
  → Steady and evenly growing differences
• Mixing up the sign of the difference
  → Steady and evenly growing differences
• Counting 1 or 9 as a prime
  → Differences that follow their own rule
• Skipping a prime
  → Differences that follow their own rule
• Putting the blank in the wrong series
  → Two rules taking turns

Formulas (3)

• A steady ratio · Term n of a geometric progression
  $$T_n = a\,r^{\,n-1}$$
• Multiply, then add or take away a fixed amount · Times a fixed number, plus a fixed amount
  $$t_{n+1} = a\,t_n + b$$
• The multiplier or the amount added changes · A multiplier that rises with each step
  $$t_{n+1} = (m + n)\,t_n + c_n$$

Watch out for (5)

• Raising the ratio to the power n
  → A steady ratio
• Checking the rule on one pair only
  → Multiply, then add or take away a fixed amount
• Forcing a fixed multiplier
  → The multiplier or the amount added changes
• Using the wrong multiplier for the missing step
  → The multiplier or the amount added changes
• Using differences on a series that takes turns
  → Operations that take turns, and terms built from earlier terms

Formulas (2)

• One step away from a square or a cube · Common near-square and near-cube terms
  $$n^2 \pm 1 \qquad n^3 \pm 1 \qquad n(n+1) \qquad n^3 - n = (n-1)\,n\,(n+1)$$
• Primes, factorials and sums · Sums and factorials
  $$1 + 3 + \dots + (2n - 1) = n^2 \qquad 1 + 2 + \dots + n = \frac{n(n+1)}{2} \qquad n! = n \times (n-1)!$$

Watch out for (3)

• Calling the list too early
  → Squares, cubes and powers
• Plus one or minus one
  → One step away from a square or a cube
• Numbers that look prime
  → Primes, factorials and sums

Watch out for (3)

• Right letters, wrong number
  → Letters and numbers as separate series
• Continuing the wrong series
  → Two series woven together, and letters with their positions
• Using one order for every step
  → Rearranged letters and word series

Watch out for (3)

• Blaming the term after the break
  → Find the rule from the terms that agree
• Changing the rule to fit the wrong term
  → Find the rule from the terms that agree
• Checking only one direction
  → The wrong cluster or term