Chapter 3 · Topic 3.2 · Prelims + Mains2 of 4
Logical Reasoning & Analytical Ability: Coding, relations and directions
Key points
- Coding and symbols.
- Blood relations and directions.
Prelims box: facts and traps
- CSAT 2018, Q22: If RAMON is written as 12345 and DINESH as 675849, then HAMAM will be written as Prelims 2018 From RAMON = 12345: A = 2, M = 3.
- CSAT 2019, Q74: If $ means 'divided by'; @ means 'multiplied by'; # means 'minus', then the value of 10#5@1$5 is 10 # 5 @ 1 $ 5 becomes 10 − 5 × 1 ÷ 5.
- CSAT 2017, Q19: Consider the following: Prelims 2017 P + R: P is the son of R. R − Q: R is the wife of Q. So Q is R’s husband and P’s father.
- CSAT 2012, Q26: Given that, Prelims 2012 E is B’s daughter and D is E’s brother, so D is B’s child.
- Trap (UPSC Prelims 2012): “A is the brother of B” is incorrect. “C is the father of A” is incorrect. “D is the brother of E” is incorrect. “E is the daughter of B. Then the uncle of D is” is incorrect.
- Trap: Most wrong options come from working left to right.
Coding-decoding and symbol questions
Coding questions give one or two coded words and ask for another. Write the letter-to-digit (or letter-to-letter) pairs in a small table, then read off the new word. For letter shifts, write the alphabet position of each letter.
CSAT 2025, Q57: If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded? Prelims 2025 From FRANCE = 654321 and GERMANY = 9158437: Y = 7, E = 1, M = 8, N = 3. YEMEN = 7 1 8 1 3. Answer (d), 71813.
If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded ?
- 54321
- 81913
- 71913
- 71813
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Answer: (d) · UPSC official key
CSAT 2018, Q22: If RAMON is written as 12345 and DINESH as 675849, then HAMAM will be written as Prelims 2018 From RAMON = 12345: A = 2, M = 3. From DINESH = 675849: H = 9. HAMAM = 9 2 3 2 3. Answer (b), 92323.
If RAMON is written as 12345 and DINESH as 675849, then HAMAM will be written as
- 92233
- 92323
- 93322
- 93232
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Answer: (b) · UPSC official key
CSAT 2026, Q67: If ZERO is encoded as ADSN, then how do you encode STOP? Prelims 2026 Z to A is +1, E to D is −1, R to S is +1, O to N is −1: the moves alternate. S +1 = T, T −1 = S, O +1 = P, P −1 = O. Answer (b), TSPO.
If ZERO is encoded as ADSN, then how do you encode STOP?
- SPOT
- TSPO
- TSOP
- POST
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Answer: (b) · UPSC provisional key (final key awaited)
CSAT 2024, Q75: If a + b means a − b; a − b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 − 100 × 50 ÷ 25? (Operations are to be replaced simultaneously) Replace every sign at once: 10 − 30 × 100 ÷ 50 + 25. Multiply and divide first: 30 × 100 ÷ 50 = 60. Then 10 − 60 + 25 = −25. Answer (d).
If a + b means a − b; a − b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 − 100 × 50 ÷ 25? (Operations are to be replaced simultaneously)
- 15
- 0
- −15
- −25
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Answer: (d) · UPSC official key
CSAT 2019, Q74: If $ means ‘divided by’; @ means ‘multiplied by’; # means ‘minus’, then the value of 10#5@1$5 is 10 # 5 @ 1 $ 5 becomes 10 − 5 × 1 ÷ 5. Multiply and divide first: 5 × 1 ÷ 5 = 1. 10 − 1 = 9. Answer (d).
If $ means ‘divided by’; @ means ‘multiplied by’; # means ‘minus’, then the value of 10#5@1$5 is
- 0
- 1
- 2
- 9
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Answer: (d) · UPSC official key
i ORDER OF OPERATIONS After replacing symbols, always do × and ÷ before + and −. Most wrong options come from working left to right.
Blood relations and direction sense
Blood relations: draw a small family tree, with generations in rows and a plus or minus sign for male or female when it is known. Directions: draw North at the top; for distance, add the north-south moves and the east-west moves separately.
CSAT 2026, Q44: P has a son and a daughter. S is the mother of T. S is R’s spouse. Q and R are children of P. Then how is Q related to S? Prelims 2026 S is a mother and R’s spouse, so R is a man: P’s son. Then Q is P’s daughter, so Q is R’s sister, and R is S’s husband. Answer (d).
P has a son and a daughter. S is the mother of T. S is R’s spouse. Q and R are children of P. Then how is Q related to S?
- Q is a sister of S
- Q is a daughter of S
- Q is the mother of S
- Q is a sister of the husband of S
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Answer: (d) · UPSC provisional key (final key awaited)
CSAT 2017, Q19: Consider the following: Prelims 2017 P + R: P is the son of R. R − Q: R is the wife of Q. So Q is R’s husband and P’s father. Answer (c).
Consider the following : A + B means A is the son of B. A − B means A is the wife of B. What does the expression P + R − Q mean?
- Q is the son of P.
- Q is the wife of P.
- Q is the father of P.
- None of the above
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Answer: (c) · UPSC official key
CSAT 2012, Q26: Given that, Prelims 2012 E is B’s daughter and D is E’s brother, so D is B’s child. A is B’s brother, so A is D’s uncle. Answer (a).
Given that, 1. A is the brother of B. 2. C is the father of A. 3. D is the brother of E. 4. E is the daughter of B. Then the uncle of D is
- A
- B
- C
- E
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Answer: (a) · UPSC official key
CSAT 2024, Q57: A person walks 100 m Westward, then turns left and walks 100 m. He then takes 225° turn clockwise. In which direction is he walking now? Prelims 2024 Facing West, a left turn means facing South. Turning clockwise from South: 90° West, 180° North, 225° is halfway between North and East. Answer (d), North-East.
A person walks 100 m Westward, then turns left and walks 100 m. He then takes 225° turn clockwise. In which direction is he walking now?
- South-West
- South-East
- North-West
- North-East
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Answer: (d) · UPSC official key
CSAT 2016, Q58: A person walks 12 km due north, then 15 km due east, after that 19 km due west and then 15 km due south. How far is he from the starting point? Prelims 2016 North-south: 12 north, 15 south, so 3 km south. East-west: 15 east, 19 west, so 4 km west. A 3-4-5 right triangle: 5 km. Answer (a).
A person walks 12 km due north, then 15 km due east, after that 19 km due west and then 15 km due south. How far is he from the starting point ?
- 5 km
- 9 km
- 37 km
- 61 km
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Answer: (a) · UPSC official key
CSAT 2014, Q68: Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is North and east make a right angle at A. 5 × 5 + 12 × 12 = 25 + 144 = 169 = 13 × 13. Answer (b), 13 km.
Location of B is north of A and location of C is east of A. The distances AB and AC are 5 km and 12 km respectively. The shortest distance (in km) between the locations B and C is
- 60
- 13
- 17
- 7
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Answer: (b) · UPSC official key
Mains box: analysis and answer points
- Coding questions give one or two coded words and ask for another.
- Write the letter-to-digit (or letter-to-letter) pairs in a small table, then read off the new word.
- For letter shifts, write the alphabet position of each letter.
- Likely next angle: × ÷ first
Practice
Practice MCQs (8)
P is the sister of Q. Q is the son of R, who is a woman. How is R related to P?
Answer (c) & explanation
Step 1: Q is the son of R, and R is a woman, so R is Q's mother. Step 2: P is Q's sister, so P and Q share the same parents. Step 3: Hence R is P's mother.
A is the father of B. C is the mother of A. How is C related to B?
Answer (b) & explanation
Step 1: A is B's father. Step 2: C is A's mother, so C is the mother of B's father. Step 3: The father's mother is the grandmother (paternal).
If BAG is coded as 2-1-7, then FACE is coded as
Answer (c) & explanation
Step 1: B is the 2nd letter, A the 1st and G the 7th, so each letter is replaced by its alphabet position. Step 2: F = 6, A = 1, C = 3, E = 5. Step 3: FACE is coded as 6-1-3-5.
In a certain code, 'A + B' means A is the mother of B; 'A − B' means A is the brother of B; 'A × B' means A is the husband of B; and 'A ÷ B' means A is the daughter of B. Which one of the following expressions shows that P is the grandmother of S?
Answer (d) & explanation
Step 1: Decode (d): P + R means P is R's mother; R + S means R is S's mother. Step 2: So P is the mother of S's mother, that is, S's (maternal) grandmother. Step 3: Check the rest: (a) makes P S's mother, (b) makes P a husband (male), (c) makes P and S siblings.
L is the father of J. M is the sister of L, and N is the husband of M. How is N related to J?
Answer (b) & explanation
Step 1: M is the sister of J's father, so M is J's aunt (father's sister). Step 2: N is M's husband. Step 3: The husband of one's aunt is one's uncle.
In a code language, DOG = 26 and CAT = 24. What number does BIRD stand for in that language?
Answer (d) & explanation
Step 1: Test the sum of alphabet positions: DOG = 4 + 15 + 7 = 26 and CAT = 3 + 1 + 20 = 24; both match. Step 2: BIRD = 2 + 9 + 18 + 4. Step 3: The total is 33.
Town P is 6 km to the west of town Q. Town R is 8 km to the north of town P. How far is R from Q, and in which direction?
Answer (a) & explanation
Step 1: Place Q at (0, 0). P is 6 km west: (−6, 0). Step 2: R is 8 km north of P: (−6, 8). Step 3: From Q, R is 6 km west and 8 km north: distance √(36 + 64) = 10 km, towards the north-west.
Village B is 5 km due south of village A, and village C is 12 km due east of village A. What is the straight-line distance between B and C, and in which direction is B from C?
Answer (b) & explanation
Step 1: Place A at (0, 0). B is 5 km south: (0, −5). C is 12 km east: (12, 0). Step 2: B − C = (−12, −5): B is 12 km west and 5 km south of C. Step 3: Distance = √(144 + 25) = √169 = 13 km, and the direction of B from C is south-west.
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In 150 words, explain the significance of Logical Reasoning & Analytical Ability with one recent example.
Flashcards (5)
After replacing symbols, what comes first?
× and ÷ before + and −.
ZERO → ADSN; STOP → ?
TSPO (+1, −1 alternating).
Direction tip for distance?
Add N-S and E-W moves separately, then use the right triangle.
Two common right triangles in CSAT?
3-4-5 and 5-12-13.
Facing West, turn left: facing?
South.
Next topic · 3.3 →Logical Reasoning & Analytical Ability: Ranking, series and critical reasoning