Question

Which of the following options is true?

• A. The person from Chennai is older than the person from Kochi.
• B. The oldest teacher is from Mumbai.
• C. The person from Mumbai is older than at least one of the engineers.
• D. The person from Kochi got down at Mughal Sarai, and was an engineer.
• E. The person who got down at New Delhi is older than Y, who in turn is older than the person from Hyderabad.
• A. Only Y.
• B. The person Y and the traveller from Chennai.
• C. The person Y and the travellers from Kochi and Hyderabad.
• D. The travellers from Kochi and Hyderabad.
• J. The teacher from Mumbai, the traveller from Kochi and the younger engineer.
• A. She got down at Koderma.
• B. She is 36 years old.
• C. She got down at Mughal Sarai.
• D. She is from Kochi.
• O. None of the above

Answer 1

The Correct Option is D

Step 1: Decode direct facts and fix ages.
From (1): Kochi and Chennai <36; $Z$ is the doctor and the youngest.
From (7): Teacher from Kochi is $31+4=35$ years; the 31-year-old doctor is not from Mumbai.
$\Rightarrow$ Set $Z=\text{Doctor}, \ \text{Age}=31$. Kochi’s profession = Teacher, Age $=35$. 

Step 2: Identify the Kolkata & Mughal Sarai link and the doctor’s city.
From (2): Oldest person is from Kolkata and has the same profession as the person who got down at Mughal Sarai. That profession cannot be Doctor (doctor is only 31) and engineers are compared separately. $\Rightarrow$ The common profession must be Teacher. So Kolkata is a Teacher and the oldest. Since the doctor (31) is not from Mumbai and Kolkata is a teacher, the consistent assignment is: $Z$ (Doctor, 31) from Hyderabad. 

Step 3: Pin destinations using (3) and age window for $Y$.
From (6): $Y$ (at Mughal Sarai) has Age $<34$. But Mughal Sarai’s profession is Teacher. Kochi is 35, so Mughal Sarai must be the Mumbai Teacher. $\Rightarrow Y$: Mumbai, Teacher, Age $31<x<34$, Destination = Mughal Sarai. From (3): Among {Bangalore, Chennai, Hyderabad, Mumbai}, the eldest → Koderma, youngest → Kanpur; New Delhi person is older than Mughal Sarai person. - $Z$ (Hyderabad, 31) is youngest → destination Kanpur. - Eldest → Bangalore → destination Koderma. - New Delhi person must be older than $Y$ → Chennai → New Delhi. 

Step 4: Resolve engineers using (4) and (5).
(5): Middle teacher’s age = Engineer from Chennai’s age. Teachers: Kochi (35), Mumbai ($31<x<34$), Kolkata (oldest). Middle = 35. $\Rightarrow$ Engineer(Chennai) Age = 35. (4): Engineer(Bangalore) older than Engineer(Chennai) → Engineer(Bangalore) $>35$. 

Step 5: Consolidated table (key points).
 

• $Z$: Hyderabad, Doctor, Age = 31, Destination = Kanpur (youngest).
• Kochi: Teacher, Age = 35.
• Kolkata: Teacher, Oldest ($>35$).
• $Y$: Mumbai, Teacher, Age $31<x<34$, Destination = Mughal Sarai.
• Bangalore: Engineer, Age $>35$, Destination = Koderma.
• Chennai: Engineer, Age = 35, Destination = New Delhi.

Step 6: Test the options.
(A) Chennai (35) older than Kochi (35)? No, same age. ✗
(B) Oldest teacher from Mumbai? No, oldest teacher is from Kolkata. ✗
(C) Mumbai ($31<x<34$) older than an engineer? Engineers are 35 and $>35$, so Mumbai is younger. ✗
(D) Kochi at Mughal Sarai & engineer? Mughal Sarai is Mumbai, not Kochi; Kochi is a teacher. ✗
(E) New Delhi person (Chennai, 35) $>$ $Y$ (Mumbai, $31<x<34$) $>$ Hyderabad ($Z$, 31). Chain holds exactly. ✓ 

 

\[ \boxed{\text{(E) is true}} \]

Answer 2

Step 1: Bring forward the fixed grid from Q.
From earlier deductions:
  $\bullet$ $Z$ (Hyderabad) is the Doctor, Age $=31$ (youngest), Destination $=$ Kanpur.
  $\bullet$ Teachers: Kochi ($35$), Mumbai ($31 < x < 34$ and $Y$, at Mughal Sarai), Kolkata (oldest, $>35$).
  $\bullet$ Engineers: Chennai ($35$, younger engineer, New Delhi) and Bangalore ($>35$, older engineer, Koderma).
$\Rightarrow$ Current ages are $\ge 31$ for everyone.

Step 2: Interpret the fresh graduate and military rule.
- A fresh graduate must have joined when $<30$ years old. Since everyone has $\ge 1$ year of service, their current age is $\ge 30$; with our grid, the smallest is $31$.
- For people in the same profession, any traveler with military background is at least $5$ years older than a traveler (of the same profession) who joined as a fresh graduate.
$\Rightarrow$ Within each profession group, the younger member(s) are the only candidates to be fresh grads; the older member(s) can be military if they are $\ge 5$ years older than a fresh grad of that profession. 

Step 3: Apply by profession.
Teachers (Mumbai $x$, Kochi $35$, Kolkata $>35$):
- The youngest teacher is Mumbai ($x$ with $31 < x < 34$). This naturally fits fresh graduate.
- Any military-background teacher must be at least $x+5$ years old. Kolkata is the oldest ($>35$) and can satisfy $\ge x+5$ (e.g., if $x=32$, military $\ge 37$).
- Kochi is $35$; depending on $x$, Kochi can also be a fresh grad (e.g., $x=32$ gives $x+5=37$, so Kochi at $35$ is not military).
$\Rightarrow$ Mumbai teacher is a fresh grad; Kochi teacher may also be fresh grad; Kolkata teacher can be the military-background senior. 

Engineers (Chennai $35$, Bangalore $>35$):
- The younger engineer is Chennai ($35$) $\Rightarrow$ candidate for fresh graduate.
- The older engineer (Bangalore) must be at least $5$ years older to qualify as military background $\Rightarrow$ can be $\ge 40$ (consistent with $>35$ and “oldest among the four-city set” from Q53). 

Doctor (Hyderabad $31$):
- Single-person profession, so the “$\ge 5$ older than fresh grad” comparison cannot force a military-vs-fresh pairing.
- With only one doctor, we cannot deduce fresh grad status from the rule; options that hinge on Hyderabad being fresh grad therefore over-commit. 

Step 4: Validate options.
(A) Only $Y$ (Mumbai teacher). → Too narrow, since Kochi (teacher, $35$) can also be a fresh grad. ✗
(B) $Y$ and Chennai. → Misses Kochi. ✗
(C) $Y$, Kochi, and Hyderabad. → Hyderabad (Doctor) cannot be concluded. ✗
(D) Kochi and Hyderabad. → Excludes $Y$, who is clearly a fresh grad. ✗
(E) Mumbai teacher ($Y$), Kochi (teacher), and the younger engineer (Chennai). → This matches the “youngest within profession $\Rightarrow$ fresh grad” logic in all multi-member professions and leaves the seniors (Kolkata teacher, Bangalore engineer) to satisfy the “military $\ge 5$ years older” condition. ✓ 

 

$\boxed{\text{(E) is the correct set of fresh graduates}}$

Answer 3

Step 1: Recall the profession distribution from earlier questions.
- Doctor: Hyderabad ($Z$, 31 years, youngest). Only one doctor, so no comparison possible. ✗
- Engineers: Chennai (35 years), Bangalore ($>35$, older). Only two engineers, so everyone is either youngest or oldest; no middle possible. ✗
- Teachers: Mumbai ($31 < x < 34$, $Y$ at Mughal Sarai), Kochi (35), Kolkata ($>35$, oldest). This group has three teachers. ✔ 

Step 2: Apply the condition for W.
W is described as “neither the youngest nor the oldest among the travelers from her profession.”
- Among doctors: not possible (only one).
- Among engineers: not possible (only two).
- Among teachers: youngest = Mumbai, oldest = Kolkata, so the middle = Kochi (35 years). 

Step 3: Identify W.
Therefore, W must be the middle teacher → the one from Kochi (35 years old). 

Step 4: Validate the options.
(A) Koderma → destination of Bangalore engineer, not W. ✗
(B) 36 years old → W is 35, not 36. ✗
(C) Mughal Sarai → destination of Y (Mumbai teacher). ✗
(D) From Kochi → correct, as deduced. ✓
(E) None of the above → wrong, since (D) is valid. ✗ 

 

\[ \boxed{\text{Correct Answer: D (She is from Kochi)}} \]