SSC CGL Reasoning · Formula sheet

Analogy formulas

12 formulas, 1 reference table and 40 common traps for SSC CGL Reasoning Analogy, grouped by subtopic.

Word Analogy

General-knowledge pairs SSC has asked

Link	Word	Its pair
SI unit	Energy	Joule
SI unit	Frequency	Hertz
SI unit	Electric current	Ampere
SI unit	Illuminance	Lux
SI unit	Force	Newton
Capital	Portugal	Lisbon
Capital	New Zealand	Wellington
Capital	Ethiopia	Addis Ababa
Capital	Australia	Canberra
Capital	Turkey	Ankara
National animal	India	Royal Bengal tiger
National bird	India	Peacock
National bird	Australia	Emu
Chief river	Egypt	Nile
Chief river	Myanmar	Irrawaddy
Known for	Kaziranga National Park	One-horned rhinoceros
Known for	Gir National Park	Asiatic lion
Known for	Periyar (Kerala)	Elephants
Tournament	Duleep Trophy	Cricket
Tournament	Durand Cup	Football
Tournament	Aga Khan Cup	Hockey
Study of	Botany	Plants
Study of	Conchology	Shells
Study of	Dermatology	Skin
Study of	Ophthalmology	Eyes

Common traps

Picking the near synonym when the pair is opposite

In 'Fast : Slow :: Loud : ?', the option Noisy is there because it sits close to loud. The pair is a pair of opposites, so the answer is Quiet.

Stopping at 'they are related'

Two words can be related in more than one way. Name the exact link (same, opposite or stronger) so that an option which fits only a looser link is ruled out.

The right words in the wrong order

If the given pair is Saw : Cut, the option Cut : Saw has the same two kinds of word but the wrong order. The answer pair must also put the tool first and the use second.

Workplace or product?

Teacher : School is a worker and a workplace; Teacher : Lesson is a worker and what he gives. Fix which link the given pair uses before you choose, because SSC often prints both kinds among the options.

The young of a different animal

A pup is the young of a dog, a foal of a horse, a calf of a cow. SSC puts the young of another animal among the options, so match the animal the question names, not any young one.

Kind of, or part of?

A rose is a kind of flower; a petal is a part of a flower. The two links look alike, so check which one the given pair uses before you pick.

The biggest city is not always the capital

Istanbul is Turkey's biggest city but its capital is Ankara; Sydney is Australia's biggest city but its capital is Canberra. SSC prints the famous city as a trap.

A unit of the wrong quantity

The newton is the unit of force and the joule the unit of energy. An option that pairs a quantity with another quantity's unit looks right at a glance, so read both halves of every pair.

Letter Analogy

Learn this subtopic in the notes

Letter positions, forward and backward

Reverse position

\text{position from Z} = 27 - n

$n$ the position from A (A = 1, Z = 26)

One shift for every letter

Shift with wrap-round

n' = n + k \qquad (\text{take away } 26 \text{ if } n' > 26)

$n$ the position of the letter
$k$ the shift: positive forward, negative backward

Opposite letters: pairs that add to 27

Opposite letter

n + n_{\text{opp}} = 27

$n_{\text{opp}}$ the position of the opposite letter

Common traps

Counting the starting letter

Moving 3 places on from P lands on S (Q, R, S). Counting P itself as the first step gives R, one short. Count only the letters you move onto, or add the numbers:

16 + 3 = 19

, which is S.

Mixing the two directions

A rule may use positions from A or positions from Z. If one letter fits only when you count from Z, test every other letter from Z too before you trust the rule.

Forgetting to wrap past Z

X moved 4 forward is B, not a letter beyond Z. When a position comes out above 26, take 26 away before you look the letter up.

Trusting one letter

A gap found from the first letter alone may not hold for the rest; the code may be a pattern. Check at least two letters of the given pair before you work out the answer.

Dropping the sign of a gap

From O to M is 2 back, not 2 forward. Write every gap with its sign; a pattern such as +2,

-2

is invisible if all the gaps are written as 2.

Treating vowels like the other letters

When the gaps agree for some letters and not others, check whether the odd ones are all vowels. A rule with one gap for vowels and another for consonants hides behind gaps that look random.

Opposite letters are not a reversed word

Reversing BIRD gives DRIB: the same letters in a new order. The opposite-letter code YRIW changes every letter. Check whether the code uses the word's own letters before you choose the rule.

One before the opposite

If a letter and its code add to 26 rather than 27, the rule is 'one before the opposite'. Test the sum on two letters; using the plain opposite then gives an answer one letter off throughout.

Letter Rearrangement

Learn this subtopic in the notes

Common traps

Reversing the whole word when only the halves turn

A half-reversed code and a fully reversed code contain the same letters, and SSC prints both. Test the rule on the given pair: the full reversal must give the code exactly.

Cutting a word of odd length in the wrong place

A seven-letter word may be cut 4 and 3, or 3, 1 and 3 with the middle letter kept. Read the cut from the given pair rather than guessing it.

Reading the order the wrong way round

The order 3, 1, 4, 2 means the code's first letter is the word's third letter. It does not mean the word's first letter moves to place 3. For many orders the two readings give different answers, and SSC prints both.

Reading the order from a word with a double letter

In a word such as COFFEE you cannot tell which F went where. Take the order from a word whose letters are all different, then apply it.

Shifting before reversing when the gaps rise

With rising gaps, 'reverse then +1, +2, +3' and '+1, +2, +3 then reverse' give different codes. Take the order of the steps from the given pair and keep it.

Giving up on random-looking gaps

Gaps such as +18,

-13

, +15 against the word usually mean the letters were moved first. Reverse the word and measure the gaps again before you try anything stranger.

Number Analogy

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Multiply or divide by one number

One multiplier

\text{second} = k \times \text{first}

$k$ the same multiplier in every pair (it may be a fraction)

Add or take away one number

One fixed difference

\text{second} = \text{first} + d

$d$ the same difference in every pair (negative when the second is smaller)

Two steps: multiply, then add

Multiplier and constant from two pairs

a = \frac{y_2 - y_1}{x_2 - x_1} \qquad b = y_1 - a\,x_1

$x_1, y_1$ the first given pair
$x_2, y_2$ the second given pair

Common traps

Deciding the rule from one pair

3 : 12 could be 'multiply by 4' or 'add 9'. When two pairs are given, the second one decides; when only one is given, test both rules on the options and keep the one that lands on exactly one of them.

Splitting the digits when the note forbids it

When SSC prints the note about whole numbers, a rule such as 'add the digits of 52' is not allowed. A digit sum used only to check divisibility is fine, because the rule itself still works on the whole number.

The same gap in the wrong direction

If the given pair goes down by 56, an option that goes up by 56 has the same gap but the wrong sign. Write the difference as second minus first every time.

Multiplying first out of habit

For 214 and 131 the ratio is about 0.61 and leads nowhere, while the difference, 83, is the whole rule. When the numbers are close, the difference is the first check, not the last.

Accepting an untidy line

Any two pairs fit some rule 'times a, plus b'. If a comes out as

\frac{37}{9}

, that is a sign the real rule is a square or a product, not a reason to use the fraction.

A one-pair question with two answers in mind

With one given pair, such as 15 : 31, both 'double and add 1' and 'add 16' fit. Work out each rule's answer and keep the one that is printed; if both are printed, the question is ambiguous.

Number Set Analogy

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Sets that climb by fixed steps

Equal steps

2b = a + c

$a, b, c$ the three numbers of the set, in order

One number from a sum or difference of the others

Linear rule inside a set

c = p\,a + q\,b + r

$a, b$ the two numbers the rule uses
$p, q, r$ small whole numbers, the same for every set

One number from a product or quotient of the others

Product rule

c = k \times a \times b

$k$ the same multiplier for every set (often 1, 2, 3, 4 or 5)

Common traps

Checking only the first step

An option can match the first gap and break the second. SSC builds most wrong options this way, so check both gaps of every option you keep.

Missing a falling set

A set that drops by 22 each time is still a fixed-step set. Write the gaps with their signs, or the pattern looks random.

Looking for the result only in the last place

In (6, 30, 4) the middle number is

3 \times (6 + 4)

. A search that tries only the third place misses it; check the largest number wherever it stands.

Swapping the first two numbers

For a rule such as 2a + b or a

-

b, the order of a and b matters: (5, 9) and (9, 5) give different results. Keep the positions the given sets use.

Multiplying the wrong two numbers

When the big number sits in the middle, the rule multiplies the first and the third. Multiplying the first two gives a rule that fits neither given set.

Keeping an option whose quotient is not whole

If the rule divides and an option's division leaves a remainder, that option fails at once. Use this to strike options out before doing any other working.

Square and Cube Rules

Learn this subtopic in the notes

Squares, square roots and a number times its neighbour

Neighbour product and next square

n(n + 1) = n^2 + n \qquad (n + 1)^2 = n^2 + 2n + 1

Cubes and cube roots

Two forms SSC uses

n^2(n + 1) = n^3 + n^2 \qquad n^3 - n = (n - 1)\,n\,(n + 1)

Squares inside a number set

Square identities

a^2 - b^2 = (a - b)(a + b) \qquad (a + b)^2 = a^2 + 2ab + b^2

Common traps

Reading a neighbour product as a square

11 \times 12 = 132

, not

11^2 = 121

. When a number sits just above a square by the square root itself, it is

n(n + 1)

, and the next term in the pattern is

(n + 1)(n + 2)

Squaring the next number instead of moving to the next square

'24 goes to 35' is

5^2 - 1

going to

6^2 - 1

. Working out

24^2

25^2

wastes the time; first ask whether each number is a square plus or minus a small amount.

Using the last-digit rule on a number that is not a cube

The last digit tells you the root only if the number is a perfect cube. 3,400 ends in 0 but is not

10^3

20^3

; check the size first (between

15^3

and

16^3

Taking k times a cube for a plain cube

1,458 is not a cube, but it is

2 \times 9^3

. If a big number is not on your list of cubes, divide it by 2, 3, 5 or 6 before you give up on a cube rule.

Treating the square of a sum as a sum of squares

(3 + 4)^2 = 49

, but

3^2 + 4^2 = 25

. The two rules give different results for every set, so test the given sets with the exact one.

Stopping at the first option that fits

Square rules are loose enough that two options sometimes fit. Check all four; if two still fit, look again for a stricter rule that the given sets also obey.

Analogy formulas

Word Analogy

General-knowledge pairs SSC has asked

Common traps

Letter Analogy

Letter positions, forward and backward

One shift for every letter

Opposite letters: pairs that add to 27

Common traps

Letter Rearrangement

Common traps

Number Analogy

Multiply or divide by one number

Add or take away one number

Two steps: multiply, then add

Common traps

Number Set Analogy

Sets that climb by fixed steps

One number from a sum or difference of the others

One number from a product or quotient of the others

Common traps

Square and Cube Rules

Squares, square roots and a number times its neighbour

Cubes and cube roots

Squares inside a number set

Common traps

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