UPSC CSE · CSAT · Reasoning and judgment · TOPIC LESSON
Make relations, routes and symbol rules explicit before drawing conclusions.
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BEFORE YOU START
Original educational lesson. Work through the examples before revealing the practice answers. This original common-core lesson supports its declared paper scope. Optional subjects, qualifying language papers and the interview are outside this resource.
LEARN THROUGH ORIGINAL PRACTICE
All teaching examples, cases, prompts and model answers are original. Official exam questions and answer keys are not reproduced. This common-core lesson does not imply complete historical paper coverage or an official score.
01 / UNDERSTAND & APPLY
Translate each family statement into a labelled edge. Parent of points from parent to child; spouse of is a different relation; sibling of does not point from one generation to another. A chain with two parent edges establishes grandparenthood, but not a gendered term unless gender is supplied.
Names, surnames and occupations are not reliable premises for gender or kinship. If P is Q’s sister, P is female under the term’s stipulated use; Q’s gender remains open. If siblings are said to share one parent, do not silently add the second. Some tasks explicitly use full siblings, and that additional condition should be recorded.
Read the direction of the question. “How is A related to B?” asks A’s role relative to B, which can be the reverse of the relationship you most recently traced.
ORIGINAL PRACTICE · 1
A is C’s grandparent.
Two parent-to-child links span two generations. Grandfather or grandmother would require gender information that is absent.
ORIGINAL PRACTICE · 2
P is R’s aunt; whether she is on the maternal or paternal side is undetermined.
Sister supplies P’s female sibling role. The parent Q’s gender is not given, so the chain does not identify a maternal or paternal aunt.
02 / UNDERSTAND & APPLY
A family network should distinguish names, gendered roles and relationship types. A parent edge is not a spouse edge; two people can be stated as parents of the same child without a separate premise about marriage. Do not draw a spouse link unless it is supplied or explicitly defined by the task.
Use generation levels to organize the diagram, but let the facts determine the edges. An unclear line can create a false conclusion that two siblings share both parents. If the problem supplies that both have the same named parents, show both links and cite that fact.
A diagram can expose missing information rather than solve every relationship uniquely. That is a useful outcome: state the most specific warranted relation and identify the absent premise instead of filling the gap with a familiar family pattern.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL WORKED EXAMPLE
Arun is the father of Bela and Deepa. Isha is the mother of Bela and Deepa. Bela is the mother of Chitra, and Deepa is Bela’s sister. These are the supplied parentage facts; no marriage relationship is stated. How are Deepa and Arun related to Chitra?
Answer Deepa is Chitra’s maternal aunt and Arun is Chitra’s maternal grandfather.
03 / UNDERSTAND & APPLY
For a flat map, take east as positive horizontal x and north as positive vertical y unless another convention is supplied. West and south are negative directions. “A is east of B” places A to B’s east; it does not place B east of A. Keep the reference object visible.
A turn is relative to the traveller’s current heading. From north, right means east; from east, right means south; from south, left means east. Page-left is not always the walker’s left. Record the new heading after each turn before adding the next segment.
An absolute direction such as north is different from a relative location such as ahead of a person. The latter needs that person’s facing direction. If the heading is missing, explain the ambiguity rather than choose a compass direction.
ORIGINAL PRACTICE · 1
East.
Facing south, the walker’s left points east on a north-up map. Treating left as west regardless of heading would confuse person-relative and page-relative directions.
04 / UNDERSTAND & APPLY
Path length adds every travelled segment, including backtracking. Displacement is the vector from the starting point to the final point. Its magnitude is the straight-line distance between them, which cannot exceed the travelled path length. A return journey can have positive distance and zero displacement.
For perpendicular east-west and north-south components, the displacement magnitude is the square root of the sum of their squares. Add signed components first: north 6 followed by south 6 cancels in position, although both segments still contribute to path length.
State units and keep the origin fixed. A route diagram should label segment lengths, directions and endpoints; a dashed start-to-finish line represents displacement, not an extra segment walked.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL WORKED EXAMPLE
A walker starts at O, walks 6 m north, turns right and walks 8 m, turns right and walks 6 m, then turns left and walks 2 m. Find the total distance and final displacement.
Answer The walker travels 22 m and ends 10 m east of the start. The 6 m north and 6 m south cancel in displacement but not in path length.
ORIGINAL PRACTICE · 1
Path length 17 m; displacement magnitude 13 m.
The path adds 5+12. The perpendicular endpoint components give √(5²+12²)=√169=13 m. Adding the segments does not give the straight-line separation.
ORIGINAL PRACTICE · 2
Displacement 3 m north; path length 11 m.
The horizontal components−4 and+4 cancel. The three travelled segments still sum 4+3+4=11 m.
05 / UNDERSTAND & APPLY
Assign coordinates to one known point, then translate each relative statement. If the library is 4 km east of the school, setting the school at(0,0) places the library at(4,0). A clinic 3 km north of that library is at(4,3), not(0,3).
“Northeast” can mean a quadrant rather than an exact 45-degree bearing. The vector(4,3) has both positive east and north components but unequal magnitudes. Unless the question asks for and supports an exact bearing, state the quadrant and components rather than impose a diagonal direction.
Without distances, direction may be known while magnitude remains unknown. Conversely, knowing separation alone does not establish direction. Keep these targets distinct.
ORIGINAL WORKED EXAMPLE
The library is 4 km east of the school. The clinic is 3 km north of the library. On the stated flat-map model, how far and in what general direction is the clinic from the school?
Answer The clinic is 5 km from the school in the northeast quadrant, with components 4 km east and 3 km north.
06 / UNDERSTAND & APPLY
A coding task is determinate when the allowed rule is stated or the constraints within a stated family select it. A few input-output examples by themselves permit many mathematical rules. Prefer an explicitly given shift, reversal or substitution convention over an unsupported claim that the simplest visible pattern is the only possible one.
For alphabet shifts, specify the alphabet and wrap-around. With the 26-letter English alphabet, forward 3 sends X to A, Y to B and Z to C. Decoding reverses the shift. Multi-step operations may not commute: reverse-then-shift is a defined order, and another rule may require something else.
Check the whole word and the boundary letters. A method that works for ordinary letters but fails at Z has not implemented the stated cyclic alphabet.
ORIGINAL WORKED EXAMPLE
Use the 26-letter English alphabet cyclically. Encode each letter by moving forward three places, wrapping after Z. Encode YARD and decode FDW.
Answer YARD encodes as BDUG, and FDW decodes as CAT.
ORIGINAL PRACTICE · 1
BQQ.
Z wraps to B after two steps; each O becomes Q. The rule is supplied, so this is not a guess from examples.
ORIGINAL PRACTICE · 2
UBD.
Reverse CAT to TAC. Then T→U, A→B and C→D. Applying only the shift or only the reversal would leave the process incomplete.
07 / UNDERSTAND & APPLY
A one-to-one substitution means each distinct word has one code and different words have different codes. If code groups are unordered, shared membership can identify a mapping, but the displayed order of codes does not tell you word order. State that convention before using intersections.
Compare groups that share exactly one word and, under the one-to-one assumption, one code. Assign that shared pair, then remove it from each group to recover the remaining mapping. Check all statements afterwards. If two words always occur together and no other information separates them, their individual mappings may remain ambiguous.
ORIGINAL WORKED EXAMPLE
A one-to-one word code is used, and order within each displayed group is irrelevant. “red clay” is coded “ka mi”; “red brick” is “ka su”; “soft brick” is “lo su”. Find the four word codes.
Answer red=ka, clay=mi, brick=su and soft=lo.
08 / UNDERSTAND & APPLY
Finish a relations task by checking edge direction and missing gender; a route task by checking headings and signed components; a code task by checking its rule family, one-to-one conditions and wrap convention. A neat answer can still be unsupported if it answers a more specific question than the premises allow.
When information is insufficient, identify the additional fact that would help. A grandparent’s gender would select grandfather or grandmother. A traveller’s initial heading would anchor relative turns. A restriction to linear rules could make a small coding dataset more informative. Stating the missing condition is more useful than silently guessing it.
ORIGINAL PRACTICE · 1
No. Doubling gives 8, but the two examples do not uniquely determine the rule.
For example, f(x)=2x+(x−2)(x−3) gives 4 at 2 and 6 at 3, yet gives 10 at 4. Both rules match the supplied examples. A stated family such as f(x)=kx would justify the doubling inference after checking the examples.
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