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SSC CGL Reasoning · Formula sheet

Series formulas

7 formulas and 33 common traps for SSC CGL Reasoning Series, grouped by subtopic.

Full notes with worked examples

Letter Positions and Gaps

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Letter positions and the gap rule

Reverse position and wrapping round

nreverse=27−nn>26⇒n−26n<1⇒n+26n_{\text{reverse}} = 27 - n \qquad n > 26 \Rightarrow n - 26 \qquad n < 1 \Rightarrow n + 26
  • nnthe letter's place counted from A

Common traps

Counting the starting letter as a step

Three steps forward from D is G (4 + 3 = 7), not F. Work with the numbers, not by tapping letters, and the off-by-one slip cannot happen.

Stopping at Z

A series does not end at Z. When the number passes 26, take away 26 and carry on from A: W (23) plus 5 is 28, which is B.

Opposite letters add to 27, not 26

F is 6 and its opposite U is 21, and 6+21=276 + 21 = 27. Using 26 gives T, one letter off, and SSC often prints that letter as an option.

Reading the pair as one jump

In AZ, BY, CX the two letters move in opposite directions. Treating the pair as one block that moves forward gives a wrong second letter. Follow each letter on its own.

Checking only the first blank

Two or three options usually start with the same letter. Fill every blank and make sure the whole run keeps its pattern before you choose.

Letter Clusters

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Common traps

Checking only the first letter

SSC's wrong options usually share the right first letter and change the last one. After the first column, always check the last column too.

Wrapping in the middle of a cluster

V + 6 is 28, and 28−26=228 - 26 = 2, so the letter is B. A cluster can wrap in one column while the others do not, so wrap each letter on its own.

Assuming all columns go the same way

If the first column moves forward 3, the second may still move back 2. Copying the first column's step to the others is the error most wrong options are built on.

Wrapping backwards

C moved back 5 is 3−5=−23 - 5 = -2, and −2+26=24-2 + 26 = 24, which is X. Add 26 when the number drops below 1.

Forcing a fixed step on a growing column

In a column of K, M, P, T the steps are 2, 3, 4. A fixed step of 3 gives W, but the next step is 5, so the letter is Y.

Letter Series with Blanks

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Common traps

Taking the first repeat you see as the block

A letter can appear twice inside one block: NABANA holds two Ns and three As. Check the block length against the total number of places before trusting it.

Losing count of the places

A missed blank shifts every letter after it by one place, and the block then seems not to repeat. Number the places once, slowly, before looking for the block.

Stopping once the first half fits

With two letters, a wrong option can match the first six places and fail later. Check every printed letter all the way to the end.

Hunting for an exact repeat that is not there

When the blocks almost repeat, do not give up on the block idea. Look for the single place that changes and check that it steps along the alphabet.

Difference Series

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Steady and evenly growing differences

Next term when the difference grows by a fixed step

tn+1=tn+dndn+1=dn+kt_{n+1} = t_n + d_n \qquad d_{n+1} = d_n + k
  • tnt_nthe term in place n
  • dnd_nthe difference after that term
  • kkthe fixed amount the difference grows by (0 for a steady series)

Common traps

Not checking the term after the blank

An answer that fits the differences before a middle blank can still break the one after it. Always add the next difference and land on the printed term.

Mixing up the sign of the difference

In a falling series the differences are negative. 70, 58, 47 has differences −12-12 and −11-11, so the next is −10-10 and the term is 37, not 57.

Counting 1 or 9 as a prime

1 is not a prime, and neither are 9, 15, 21 or 27. The primes after 7 are 11 and 13, so a difference row of 5, 7, 9 is not the primes.

Skipping a prime

After 31 come 37, 41, 43, 47: the gaps between primes are uneven, so list them, do not add a fixed step.

Putting the blank in the wrong series

In a woven series the 7th term belongs to the odd places. Count the places before you decide which rule to continue.

Multiplication Series

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A steady ratio

Term n of a geometric progression

Tn=a r n−1T_n = a\,r^{\,n-1}
  • aathe first term
  • rrthe common ratio
  • nnthe place of the term

Multiply, then add or take away a fixed amount

Times a fixed number, plus a fixed amount

tn+1=a tn+bt_{n+1} = a\,t_n + b
  • aathe fixed multiplier (about the ratio of next-door terms)
  • bbthe fixed amount added (negative if taken away)

The multiplier or the amount added changes

A multiplier that rises with each step

tn+1=(m+n) tn+cnt_{n+1} = (m + n)\,t_n + c_n
  • m+nm + nthe multiplier, one more at each step
  • cnc_nthe amount added at that step (steady, rising or taking turns)

Common traps

Raising the ratio to the power n

The 3rd term is ar2a r^2, not ar3a r^3: the first term has had no multiplication yet.

Checking the rule on one pair only

From 5 to 11 alone, both ×2+1\times 2 + 1 and ×3−4\times 3 - 4 work. Test the rule on a second pair; only one survives.

Forcing a fixed multiplier

In 1, 2, 6, 24 the ratios are 2, 3, 4. Trying a steady ×3\times 3 plus something leaves a messy row of leftovers. When the rough ratios climb, the multiplier climbs.

Using the wrong multiplier for the missing step

When the blank is in the middle, its step uses the multiplier for that place. Count the steps from the start so you do not use the one meant for the last pair.

Using differences on a series that takes turns

For 4, 12, 15, 45 the differences 8, 3, 30 look random. Look at each step's operation instead: a whole-number ratio at every other step is the giveaway.

Squares, Cubes and Primes

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One step away from a square or a cube

Common near-square and near-cube terms

n2±1n3±1n(n+1)n3−n=(n−1) n (n+1)n^2 \pm 1 \qquad n^3 \pm 1 \qquad n(n+1) \qquad n^3 - n = (n-1)\,n\,(n+1)
  • nnthe counting number behind each term

Primes, factorials and sums

Sums and factorials

1+3+⋯+(2n−1)=n21+2+⋯+n=n(n+1)2n!=n×(n−1)!1 + 3 + \dots + (2n - 1) = n^2 \qquad 1 + 2 + \dots + n = \frac{n(n+1)}{2} \qquad n! = n \times (n-1)!
  • nnhow many numbers are added, or the number whose factorial is taken

Common traps

Calling the list too early

64 is both 828^2 and 434^3, and 729 is both 27227^2 and 939^3. Read the neighbouring terms to decide whether the series is squares or cubes.

Plus one or minus one

24 is 52−15^2 - 1, while 26 is 52+15^2 + 1. Test the first two terms, not just one, before you decide which way the series goes.

Numbers that look prime

51 is 3×173 \times 17, 57 is 3×193 \times 19, 87 is 3×293 \times 29 and 91 is 7×137 \times 13. Add the digits to test for 3 (a digit sum divisible by 3 means the number is too) and try 7 before calling a number prime.

Alphanumeric and Pattern Series

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Common traps

Right letters, wrong number

SSC's options often share the correct letters and change only the number by one or two. Check every part of the term, not just the letters.

Continuing the wrong series

If the answer is the 5th term, it carries on the 1st and 3rd terms, not the 4th. Counting places first avoids picking the option that continues the other series.

Using one order for every step

If the first rearrangement does not turn term 2 into term 3, the rule is not wrong: the series may switch between two orders. Find both before you apply one.

Wrong Term Series

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Common traps

Blaming the term after the break

In 4, 7, 10, 14, 16 the differences are 3, 3, 4, 2: two of them are off. The term between them, 14, is wrong (it should be 13). The 16 after it is correct.

Changing the rule to fit the wrong term

If one term disagrees, do not invent a new rule that fits it. A rule that needs a new step at just one place is the sign that the term there is the wrong one.

Checking only one direction

A cluster can follow the steps inside it and still start with the wrong letter. Check the inside steps and the cluster-to-cluster steps before you choose.

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