Number and Letter Rules in Analogy and Classification

What you will learn

You will test number rules against supplied examples, classify numbers by a shared property, and use English-alphabet positions without changing the rule halfway through. Read the relationship lesson first. You need basic addition, multiplication and small squares/cubes; a short alphabet-position guide is included here.

A numerical analogy is not a proof that one formula is the only formula imaginable. A single pair can fit many rules. In these exercises, look for a simple consistent rule, check every supplied pair, and compare the answer options. Do not add a special exception just to fit one choice.

1 Prerequisite English alphabet positions

Use the English alphabet even when the question is displayed in Hindi. The letters themselves do not change between language versions.

A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13

N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26

A position difference of 3 means moving three places: C(3) → F(6). It does not mean there are three letters between C and F; only D and E lie between them.

Prerequisite check: What is Q’s position, and how many letters lie strictly between F and L?

Answer: Q=17. Between F(6) and L(12) there are 12−6−1=5 letters: G, H, I, J, K.

All letter shifts in this lesson stay between A and Z. Do not assume that moving past Z returns to A. A question that uses such wraparound must state it explicitly.

2 Test a number rule on every pair

Suppose two pairs are given: 4 → 17 and 6 → 37. Complete 9 → ?

A. 82 B. 81 C. 55 D. 19

Answer A, 82. Squaring and then adding one fits both pairs: 4²+1=17 and 6²+1=37. Apply the same two steps to 9: 9²+1=82.

81 stops after squaring and forgets the extra one. 19 comes from 2×9+1, but that rule gives 9 rather than 17 for the first input. A rule that works only for the target or one example is not enough.

Useful candidate relationships include addition/subtraction, multiplication/division, squares, cubes and short combinations. Which to test first depends on the supplied numbers. There is no mandatory “squares, then cubes, then ×2” order for every question.

3 Keep the order of operations

Given 3 → 10 and 5 → 16, complete 8 → ?

A. 24 B. 25 C. 26 D. 64

Answer B, 25. The rule 3n+1 fits both supplied pairs. For n=8, multiply first and then add one: 3×8+1=25. The rule 3(n+1) is different: it gives 12 for input 3, not 10.

Use a small table if mental calculation becomes uncertain: input, operation, output. Test the proposed rule on the original pairs before applying it to the missing value.

If the rule is supplied directly, follow it rather than inventing another. Under the rule “take the cube”, 3 → 27 and 5 → 125 are worked applications, not evidence that cubing is the only possible relation between those pairs.

4 Number classification Compare properties

When the stated property is “perfect square”, 9, 16, 25 and 35 form a clear question: 35 is different because 9=3², 16=4² and 25=5², while 35 is not a perfect square.

Do not substitute parity just because one number happens to be even. The stated criterion controls this exercise. In an uncued question, check that the proposed property really groups three entries and is relevant to the options.

Keep these distinctions clear:

• A prime number has exactly two positive divisors: 1 and itself
• 1 is neither prime nor composite
• 2 is prime, although it is even
• A square and a cube are different properties; some numbers, such as 64, satisfy both

If the criterion is “perfect cube”, 8, 27, 64 and 100 have 100 as the different entry. Calling 64 a square does not stop it from being 4³.

5 Letter transformations Track every position

Worked example: BD : EG :: HJ : ?

A. KL B. JM C. KM D. IM

Answer C, KM. Each letter moves three positions forward: B(2)→E(5) and D(4)→G(7). Therefore H(8)→K(11) and J(10)→M(13). Both positions must follow the rule.

A different question may use reversal. If the stated rule is “reverse the pair, then move each letter one position forward”, JL becomes LJ and then MK. Doing only the reversal gives LJ; shifting without reversing gives KM. These are different operations.

A two-step rule should be checked in the same order every time. For that stated rule, BD → DB → EC and FG → GF → HG provide two additional checks.

6 Letter classification Internal difference

Compare the difference between the two alphabet positions in each pair: AC, DF, GI, JN.

AC has difference 3−1=2; DF has 6−4=2; GI has 9−7=2; JN has 14−10=4. JN is different under this criterion.

“Position difference” and “letters in between” are not interchangeable. AC has position difference 2 but only one letter, B, between A and C. Use the quantity actually asked.

Before answering, write down the operation or property, check every given example, and then verify the selected option. A quick method is useful only when its conditions are satisfied.

Independent checks

Try all six before the key. The English alphabet and its positions are the same in both languages.

1. The pairs are 2 → 7 and 4 → 13. Using the same simple rule, 7 → ?

A. 21 B. 22 C. 28 D. 24

2. The pairs are 3 → 10 and 6 → 37. Which option completes 8 → ? under the same simple rule?

A. 16 B. 64 C. 65 D. 73

3. Using “perfect cube” as the criterion, which number differs?

A. 27 B. 64 C. 125 D. 150

4. Which pair has a different difference between its two English-alphabet positions?

A. AD B. CF C. HK D. MQ

5. CE : FH :: KM : ? Each letter uses the same forward shift; no wraparound is used.

A. NP B. MP C. NO D. PN

6. Rule: reverse the two letters, then move each one position forward. What does LM become?

A. MN B. NO C. OM D. NM

Explained key

1. B — 3n+1 fits both pairs: 3×2+1=7 and 3×4+1=13. It gives 3×7+1=22.
2. C — n²+1 fits both given pairs. For 8, it gives 64+1=65; 64 omits the final addition.
3. D — 27=3³, 64=4³ and 125=5³. 150 is not a perfect cube.
4. D — AD, CF and HK each have position difference 3. MQ has difference 17−13=4.
5. A — C→F and E→H are +3 shifts. K→N and M→P therefore give NP.
6. D — LM reverses to ML; M→N and L→M then give NM.

Source and scope

RRB CEN 09/2025, §14.1, p. 28 names analogies and classification in reasoning. The transformations, examples and questions here are original teaching exercises. They are not official previous-year questions or a full reasoning syllabus.

Analogy

A rule acts like the same calculation instruction applied to each input. If the instruction is “square, then add one”, 4 gives 17 and 6 gives 37. Keep both steps for 9, which gives 82. This demonstration explains consistency; it does not prove that finitely many pairs determine only one possible formula.

Quick reference

Number and letter rules quick reference

• State a simple rule and verify every supplied pair before using it
• Preserve the order of operations; 3n+1 and 3(n+1) differ
• A few examples do not prove uniqueness among all imaginable formulae
• Prime means exactly two positive divisors; 1 is neither prime nor composite
• A number may be both a square and a cube; use the stated classification criterion
• English alphabet: A=1 through Z=26; retain Latin letters in Hindi questions
• Position difference is not the number of letters strictly between two letters
• For positions a<b, letters strictly between = b−a−1
• Reversal and shifting are separate steps; keep their stated order
• No wraparound beyond A/Z unless explicitly stated