Reasoning Extensions: Jumbling, Similarities and Differences, Maps, Conclusions and Decision Making

This chapter answers the reasoning items in the Level-1 and NTPC computer-based tests that the general reasoning chapters only partly cover: jumbling of words and letters, similarities and differences, maps, conclusions and decision making, and basic ordering puzzles. Syllabus wording changes between notifications, so check the current one; the topics here are those that commonly appear in these papers. It teaches letter-level operations and arrangement counts, testable-property comparison, a coordinate method for maps with scale and Pythagoras, rule-gate decisions, what really follows from a statement, and elimination for ordering puzzles. Level-1 and NTPC candidates both use it, and it is built for speed under negative marking.

Jumbled Words: Rebuilding a Word from Its Letters

A jumbled word is a real word whose letters have been shuffled. The task is either to name the word or to answer a question about it, such as its third letter or its vowels. Speed comes from not trying random orders. Count the letters, split vowels from consonants, then look for a familiar ending (-ING, -TION, -ER, -ED, -MENT, -LY) and a familiar beginning (STR-, TR-, PL-, CH-). Fix those chunks, and the leftover letters usually fall into place.

Jumbled lettersClue usedWord
RTNIATR- start, vowels AI insideTRAIN
GNLIDIBU-ING ending, then B-U-I-L-DBUILDING
YAWLIAR-WAY ending pattern, R-A-I-LRAILWAY
⚠️ Exam trap
Many shuffles have more than one valid word (for example LEAST can become STEAL, SLATE or STALE). A well-set exam item either lists only one valid word among the options or fixes a further condition, such as the starting letter. Always test the answer you pick against every letter given: the same count and the same letters, with none left over.

Letter Operations: Sorting, Swapping, Adjacent Pairs and Arrangements

Four operations repeat. (1) Alphabetical rearrangement: write the letters in A-to-Z order (repeated letters stay together), then read the position asked, from left or right. RAILWAY sorts to A A I L R W Y, so its 4th letter from the left is L. (2) Same-position count: compare the original and sorted strings place by place. PLATFORM becomes A F L M O P R T, and only R is unchanged, so the count is 1. (3) Swap instructions: carry them out one at a time on a numbered row; JUNCTION with places 1 and 8 swapped and then places 2 and 7 swapped becomes N O N C T I U J. (4) Adjacent pairs: count neighbouring letters in the word that are also neighbours in the alphabet, in either order. In STATION the pairs S-T and O-N qualify, so the count is 2.

WordOperationResult
RAILWAYSorted A to ZA A I L R W Y
STATIONAdjacent-in-alphabet pairsST, ON = 2
SIGNALVowels I and A together5! x 2 = 240

Counting arrangements. All n letters distinct give n! orders. If a letter repeats r times, divide by r!. To keep chosen letters together, glue them into one block, arrange the blocks, then multiply by the orders inside the block. SIGNAL has 6 distinct letters; gluing I and A makes 5 units, so 5! = 120 orders, and the block itself can read IA or AI, giving 120 x 2 = 240.

🧠 Memory hook
Number the places 1, 2, 3 ... under the word before any swap. Most errors come from counting a place from the wrong end or swapping the letters instead of the places after an earlier swap has moved them.

Similarities and Differences: Name the Property Before You Compare

These items ask what is common to two or three things, or which one differs. The method is to list each item's properties in a short row, then pick the property that every item shares (similarity) or that exactly one item lacks (difference). A property must be testable: 'is prime', 'is a perfect square', 'moves on rails', 'has equal diagonals'. A vague label such as 'looks similar' never decides an answer.

What a rhombus and a rectangle share is only the last column.
ShapeAll sides equalEqual diagonalsDiagonals bisect each other
RhombusYesNoYes
RectangleNoYesYes
SquareYesYesYes

Number and letter groups. For numbers, test in this order: prime or composite, square or cube, odd or even, divisibility by 3, 7, 11. In 51, 57, 91, 97 the first three are composite (3 x 17, 3 x 19, 7 x 13) and 97 is prime, so 97 differs. For letter groups, write each letter's step to the next: BDF, HJL, NPR all step +2, while TVW steps +2 then +1. For pairs, find the rule that turns the left number into the right one and spot the pair that breaks it: 12 to 144, 9 to 81, 7 to 49 are squares, while 6 to 38 is not, because 6 squared is 36.

⚠️ Exam trap
'Differs' can be answered by two rules. In 27, 64, 125, 144 the cubes make 144 odd, but 27, 125 are odd numbers while 64, 144 are even. Always pick the rule that isolates exactly one item and check the rule against the other options before you mark.

Maps and Map-Based Direction Questions

Map and direction items appear in these papers (Maps). The questions give the layout in words (X is 4 km west of Y, Z is south of X) and ask for a distance, a direction or a route. Treat the page as a coordinate grid: north is up, east is right. Put the starting point at (0, 0), east and north positive, west and south negative. Every statement then becomes a pair of numbers, and the answer is read off.

MoveChange in (east, north)
Walk north d(0, +d)
Walk south d(0, -d)
Walk east d(+d, 0)
Walk west d(-d, 0)

Turns depend on the way you face. Facing north, a right turn leads east; facing east, a right turn leads south; facing south, a left turn leads east. Example: a trolley goes 5 km north, turns right for 12 km, turns right for 5 km, then turns left for 3 km. The legs are north 5, east 12, south 5, then (facing south, left is east) east 3. The net result is 15 km east and 0 north, so it stands 15 km due east of the start, even though it walked 25 km.

Straight-line distance uses the right-angled triangle, a^2 + b^2 = c^2. Station A is 8 km east of B and C is 6 km north of B: AC = 10 km (the 3-4-5 family scaled by 2). With A 10 km north of B and C 24 km east of B, the midpoint D of AC is at (12, 5), and BD = 13 km (the 5-12-13 triple). Map scale: actual distance = map distance x scale denominator. On a 1 : 5,000,000 map, 4.8 cm stands for 4.8 x 5,000,000 cm = 24,000,000 cm = 240 km (100,000 cm = 1 km).

🎯 Why it works
Coordinates remove the guesswork. A phrase such as 'S is east of R and directly south of Q' fixes two numbers at once: S shares R's north-south value and Q's east-west value. Two such clues pin a point without any drawing.

Conclusions and Decision Making: Rules, Cut-offs and What Really Follows

Decision-making items give a rule set (age band, qualification, deadline, cost) and ask which case satisfies all the rules. Treat every rule as a gate. Test each candidate against each gate in turn and drop at the first failure; exactly one should survive. Watch the words: 'at least' includes the number itself, 'more than' excludes it, 'between 20 and 35' is stated inclusive only if the stem says so, and 'if ... then' binds only the people it describes.

Rule set (fictional)CandidateVerdict
Age 20 to 35 inclusive; graduate; if age above 30 then at least 3 years of experience; no pending caseAge 34, graduate, 4 years, no casePasses every gate
Same rulesAge 32, graduate, 2 years, no caseFails: age over 30 needs 3 years

Choosing among options works the same way: strike out any option that breaks a hard limit (a deadline), then take the best of the remainder on the stated measure. If a journey must finish within 8 hours, a 9-hour option is out however cheap; among the 5-hour and 7-hour options the cheaper one wins.

Conclusions. A conclusion follows only if it is forced by the statement. From 'All tracks in section X are electrified. Some electrified tracks are double lines', the conclusion 'Some double lines are electrified tracks' follows (a particular statement can be reversed), but 'Some tracks in section X are double lines' does not, since the double lines may all lie elsewhere. For assumptions, ask what must already be true for the statement to make sense. 'Passengers are asked to book through the official app to avoid touts' assumes passengers can use the app. It does not assume that touts can never use it, nor that every passenger stops using counters: both are far stronger than the statement needs.

⚠️ Exam trap
Strong words such as all, never, only, every, cannot make an assumption or conclusion fail. A safe conclusion uses the same strength as the statement or weaker ('some', 'may').

Puzzle Basics: Ordering Puzzles by Elimination

An ordering puzzle places people or events on slots (days, ranks, seats) under a few clues. Draw the slots in a row, then convert each clue to a fixed fact or a relation. Fixed facts first ('T is on Monday'), then chains ('S immediately before R' makes a two-slot block SR), then inequalities ('P after R'). Combine chains into a longer chain and see where it can sit.

Worked example. Five officers P, Q, R, S, T each take one of Monday to Friday. Clues: S is immediately before R; P is after R; T is immediately after Q; Q is before S. Block SR must be followed by P, so the chain S-R-P needs three days. Chain Q-T comes before S. Five days leave one fit: Q Monday, T Tuesday, S Wednesday, R Thursday, P Friday. Wednesday is S. Whenever a puzzle is well made, the clues leave exactly one such arrangement, and a quick check against every clue confirms it.

🧠 Memory hook
Verify the finished arrangement against every clue, including the ones you used early. A single unchecked 'immediately' or 'before' is where the slip hides. If two arrangements survive, you have misread a clue.

Key takeaways

  • Jumbling is a search for chunks: fix the ending and beginning, test the result against every letter, and remember some shuffles have two valid words.
  • Number the places before swaps; arrangements of n letters are n!, divided by r! for a repeated letter, and a glued block is arranged inside as well.
  • For similarities and differences, name a testable property for each item, then pick the property shared by all or lacking in exactly one.
  • Maps are coordinates: north up, east right, turns depend on facing, distance by a^2 + b^2 = c^2, and actual distance = map distance x scale denominator.
  • Decision rules are gates: test each case against every gate, read 'at least' and 'more than' exactly, and drop a case at its first failure.
  • A conclusion or assumption must be forced by the statement; strong words (all, never, only) usually make it fail, and ordering puzzles yield to chains first, then inequalities.

Practice questions (20)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. The letters of the word RAILWAY are arranged in alphabetical order from A to Z. Which letter is fourth from the left?

    1. I
    2. L
    3. R
    4. A
    Show answer

    Answer: B — L

    Sorted, RAILWAY reads A, A, I, L, R, W, Y, so the fourth letter from the left is L. The repeated A is counted twice, which is why R is the tempting wrong answer: it is the fourth letter only if the second A is dropped.

  2. In the word PLATFORM, the letters are rearranged in alphabetical order. How many letters keep the same position as in the original word?

    1. None
    2. Two
    3. One
    4. Three
    Show answer

    Answer: C — One

    The sorted order is A, F, L, M, O, P, R, T against the original P, L, A, T, F, O, R, M. Only R sits in the seventh place in both, so the count is one. 'None' tempts because seven of the eight places change, but the seventh place matches.

  3. How many pairs of adjacent letters in the word STATION are also adjacent to each other in the alphabet, in either order?

    1. 2
    2. 1
    3. 3
    4. 0
    Show answer

    Answer: A — 2

    The adjacent pairs are S-T, T-A, A-T, T-I, I-O and O-N. S-T are consecutive letters (S, T) and O-N are consecutive (N, O); T-A, A-T, T-I and I-O are not. The count is two. Counting I-O as a pair is the usual slip, because I and O are separated by J to N.

  4. In the word JUNCTION the letters at places 1 and 8 are swapped, and then the letters at places 2 and 7 are swapped (places counted from the left, on the word as it stands after the earlier swap). Which letter is fourth from the right in the final arrangement?

    1. C
    2. N
    3. I
    4. T
    Show answer

    Answer: D — T

    JUNCTION has J U N C T I O N. Swapping places 1 and 8 gives N U N C T I O J; swapping places 2 and 7 gives N O N C T I U J. From the right the letters read J, U, I, T, so the fourth is T. Taking C is the slip of counting from the left.

  5. In how many different ways can the six letters of the word SIGNAL be arranged so that the two vowels stand next to each other?

    1. 120
    2. 240
    3. 360
    4. 720
    Show answer

    Answer: B — 240

    Glue the vowels I and A into one block. The block and four consonants make 5 units, arranged in 5! = 120 ways, and the block can read IA or AI, so 120 x 2 = 240. The figure 120 forgets the two orders inside the block, and 720 is the count with no condition.

  6. The words of the sentence THE TRAIN LEAVES FROM PLATFORM NINE are arranged in dictionary (alphabetical) order. Which word comes third?

    1. NINE
    2. LEAVES
    3. PLATFORM
    4. FROM
    Show answer

    Answer: A — NINE

    In dictionary order the words are FROM, LEAVES, NINE, PLATFORM, THE, TRAIN, so the third is NINE. LEAVES is second; it is the usual pick when FROM is overlooked or counted as the third.

  7. Four numbers are given: 51, 57, 97, 91. Three of them share a property that the remaining one lacks. Which number is the odd one out?

    1. 51
    2. 57
    3. 97
    4. 91
    Show answer

    Answer: C — 97

    51 = 3 x 17, 57 = 3 x 19 and 91 = 7 x 13 are composite, while 97 has no divisor other than 1 and itself, so it is prime and differs. The number 91 is the usual wrong pick because many learners wrongly believe it is prime.

  8. Four letter groups are given: BDF, HJL, NPR and TVW. Which one does not follow the rule shared by the other three?

    1. BDF
    2. HJL
    3. NPR
    4. TVW
    Show answer

    Answer: D — TVW

    In BDF, HJL and NPR each letter is two places after the one before it (B, D, F; H, J, L; N, P, R). In TVW the step from T to V is two but from V to W is one, so TVW breaks the pattern. The other three are all consistent, so none of them can be the odd one.

  9. Consider a rhombus and a rectangle. P: both have all four sides equal. Q: both have equal diagonals. R: both are parallelograms. S: in both, the diagonals bisect each other. Which statements are true of both shapes?

    1. R and S only
    2. Q and R only
    3. P and R only
    4. P, Q and S only
    Show answer

    Answer: A — R and S only

    Every rhombus and every rectangle is a parallelogram, so R is true, and parallelogram diagonals bisect each other, so S is true. A rectangle's sides need not be equal, which fails P, and a rhombus's diagonals need not be equal, which fails Q.

  10. The pairs (12, 144), (9, 81), (7, 49) and (6, 38) are given. Three pairs follow one rule that the remaining pair breaks. Which pair breaks it?

    1. (9, 81)
    2. (6, 38)
    3. (12, 144)
    4. (7, 49)
    Show answer

    Answer: B — (6, 38)

    The rule is that the second number is the square of the first: 12 squared is 144, 9 squared is 81 and 7 squared is 49. The square of 6 is 36, not 38, so (6, 38) breaks the rule. The pair (12, 144) is the tempting alternative only because 144 is large; it fits exactly.

  11. Station A is 8 km due east of station B, and station C is 6 km due north of station B. What is the straight-line distance between A and C?

    1. 14 km
    2. 12 km
    3. 10 km
    4. 2 km
    Show answer

    Answer: C — 10 km

    The three stations form a right angle at B with legs 8 km and 6 km, so AC = sqrt(8 x 8 + 6 x 6) = sqrt(100) = 10 km. The sum 14 km is the walking distance via B, not the straight line, and is the tempting wrong choice.

  12. A trolley starts from a point and runs 5 km north, turns right and runs 12 km, turns right again and runs 5 km, then turns left and runs 3 km. How far, and in which direction, is it from the starting point?

    1. 17 km east
    2. 12 km east
    3. 5 km north-east
    4. 15 km east
    Show answer

    Answer: D — 15 km east

    The legs are north 5, east 12 (right of north), south 5 (right of east) and east 3 (left of south). North and south cancel and east totals 12 + 3 = 15, so it is 15 km due east. The figure 17 km adds 12 and 5 and ignores that the 5 km south cancels the 5 km north.

  13. Town P is 4 km due west of town Q. Town R is 3 km due south of P. Town S is due east of R and due south of Q. In which direction and at what straight-line distance is R from Q?

    1. South-west, 5 km
    2. South-west, 7 km
    3. North-west, 5 km
    4. South-east, 5 km
    Show answer

    Answer: A — South-west, 5 km

    Put Q at (0, 0): P is at (-4, 0) and R is 3 km south of P at (-4, -3). So R is 4 km west and 3 km south of Q, which is south-west, and the distance is sqrt(16 + 9) = 5 km. The value 7 km is the walking distance 4 + 3, not the straight line.

  14. On a railway map drawn to a scale of 1 : 5,000,000, two stations are 4.8 cm apart. What is the actual distance between them?

    1. 24 km
    2. 240 km
    3. 2,400 km
    4. 120 km
    Show answer

    Answer: B — 240 km

    Actual distance = 4.8 cm x 5,000,000 = 24,000,000 cm. Since 100,000 cm make 1 km, this is 240 km. The values 24 km and 2,400 km come from slipping a power of ten when converting centimetres to kilometres, and 120 km would need a scale of 1 : 2,500,000.

  15. Point A is 10 km due north of point B. Point C is 24 km due east of B. Point D is the midpoint of the straight line joining A and C. What is the distance BD?

    1. 12 km
    2. 17 km
    3. 13 km
    4. 26 km
    Show answer

    Answer: C — 13 km

    With B at (0, 0), A is (0, 10) and C is (24, 0), so D is (12, 5) and BD = sqrt(144 + 25) = 13 km. Also AC = 26 and in a right triangle the median to the hypotenuse is half of it, 13 km. The value 26 km is AC itself, which is the tempting wrong choice.

  16. A fictional selection rule: a candidate must be aged 20 to 35 years inclusive, must be a graduate, must have at least 3 years of experience if aged above 30, and must have no pending case. Which candidate qualifies?

    1. Age 32, graduate, 2 years of experience, no case
    2. Age 28, not a graduate, 5 years of experience, no case
    3. Age 24, graduate, no experience, one case pending
    4. Age 34, graduate, 4 years of experience, no case
    Show answer

    Answer: D — Age 34, graduate, 4 years of experience, no case

    The age-34 candidate is in the 20 to 35 band, is a graduate, has the 3 years required above age 30 (4 years), and has no case. The age-32 candidate has only 2 years, so fails the experience gate. The age-28 candidate is not a graduate, and the age-24 candidate has a pending case.

  17. Statement: All the tracks in section X are electrified. Some electrified tracks are double lines. P: Some tracks in section X are double lines. Q: Some double lines are electrified tracks. R: All electrified tracks are in section X. Which conclusion(s) follow?

    1. Only Q follows
    2. Only P follows
    3. P and Q follow
    4. Q and R follow
    Show answer

    Answer: A — Only Q follows

    A particular statement can be reversed, so some electrified tracks being double lines gives Q. P does not follow, as the double lines may be electrified tracks outside section X. R reverses 'All the tracks in section X are electrified', which is not allowed: electrified tracks may exist outside X.

  18. A parcel must reach a depot within 8 hours at the lowest cost. The modes are W (Rs 1,500, 3 hours), X (Rs 1,200, 5 hours), Y (Rs 900, 7 hours) and Z (Rs 700, 9 hours). Which mode should be chosen?

    1. Mode W
    2. Mode Y
    3. Mode X
    4. Mode Z
    Show answer

    Answer: B — Mode Y

    The 8-hour deadline is a hard limit, so Z (9 hours) is out even though it is cheapest. Among W, X and Y, which all arrive in time, Y costs least at Rs 900. Mode Z is the tempting answer because the cost alone looks best, but it misses the deadline.

  19. Five officers P, Q, R, S and T each take duty on a different day from Monday to Friday. S is on the day immediately before R. P is after R. T is on the day immediately after Q. Q is before S. Who is on duty on Wednesday?

    1. T
    2. R
    3. S
    4. P
    Show answer

    Answer: C — S

    The chain S-R-P needs three days, and the pair Q-T comes before S, so the only fit is Q Monday, T Tuesday, S Wednesday, R Thursday, P Friday. Wednesday is therefore S. T is the tempting answer for those who place the Q-T pair after S, which the clue that Q is before S forbids.

  20. Statement: The railway office has asked passengers to buy tickets through its official app to avoid touts. P: Passengers are able to use the app. Q: Touts can never buy tickets through the app. R: Every passenger will stop buying tickets at counters. Which is an implicit assumption?

    1. Only Q
    2. Q and R
    3. P, Q and R
    4. Only P
    Show answer

    Answer: D — Only P

    The request makes sense only if passengers can use the app, so P is implicit. Q is far too strong: the request aims to reduce touts, not to claim they can never get tickets. R is also too strong, since the office only asks and does not assume that every passenger will comply.