CAT 2025 Slot 3 · DILR · Set 5: Calls Between Six Friends
The full set and all 4 questions (Q19–Q22) from CAT 2025 Slot 3, with answers and solutions.
Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.
Friend | Operator | Outgoing minutes to | Incoming minutes from | ||
Operator Xitel | Operator Yocel | Operator Xitel | Operator Yocel | ||
Anu | Xitel | 100 | 50 | 225 | |
Bijay | Xitel | 200 | 125 | ||
Chetan | Yocel | 50 | 175 | 250 | 150 |
Deepak | Yocel | 100 | 150 | 275 | 100 |
Eshan | Yocel | 100 | 100 | 375 | |
Faruq | Yocel | 0 | 100 | 150 | |
It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from:
i. Bijay to Eshan,
ii. Chetan to Anu and Chetan to Deepak,
iii. Deepak to Bijay and Deepak to Faruq,
iv. Eshan to Chetan and Eshan to Deepak.
Question 19 · Reasoning Based DI
What was the duration of calls (in minutes) from Bijay to Anu?
Answer & solution
Answer: 50
Anu and Bijay are the only Xitel users. Anu's incoming minutes from Xitel (50) can only come from Bijay.
So Bijay → Anu = 50 minutes.
Shortcut: with only two Xitel users, each one's Xitel column is a single call flow from the other.
Hence, the answer is 50.
Question 20 · Reasoning Based DI
What was the total duration of calls (in minutes) made by Anu to friends having mobile numbers from Operator Yocel?
Answer & solution
Answer: 525
Every incoming minute from Xitel for a Yocel user was made by Anu or Bijay.
Total incoming from Xitel to Yocel users = 250 (Chetan) + 275 (Deepak) + 100 (Eshan) + 100 (Faruq) = 725.
Bijay's outgoing to Yocel is 200, so Anu's outgoing to Yocel = 725 − 200 = 525.
Shortcut: minutes that Yocel users received from Xitel must equal minutes that Xitel users sent to Yocel.
Hence, the answer is 525.
Question 21 · Reasoning Based DI
What was the total duration of calls (in minutes) made by Faruq to friends having mobile numbers from Operator Yocel?
Answer & solution
Answer: 350
Work out the calls into each Yocel user from other Yocel users.
Deepak's incoming from Yocel (100): Chetan → Deepak and Eshan → Deepak are zero, so Faruq → Deepak = 100.
Eshan's outgoing to Yocel (100): Eshan → Chetan and Eshan → Deepak are zero, so Eshan → Faruq = 100.
Faruq's incoming from Yocel (150) = Chetan → Faruq + Eshan → Faruq (100) (Deepak → Faruq is zero), so Chetan → Faruq = 50.
Chetan's outgoing to Yocel (175) = Chetan → Eshan + Chetan → Faruq (Chetan → Deepak is zero), so Chetan → Eshan = 125.
Eshan's incoming from Yocel (375) = Chetan → Eshan (125) + Deepak → Eshan + Faruq → Eshan (200), so Deepak → Eshan = 50.
Deepak's outgoing to Yocel (150) = Deepak → Chetan + Deepak → Eshan (50), so Deepak → Chetan = 100.
Chetan's incoming from Yocel (150) = Deepak → Chetan (100) + Faruq → Chetan (Eshan → Chetan is zero), so Faruq → Chetan = 50.
Faruq's outgoing to Yocel = Faruq → Chetan (50) + Faruq → Deepak (100) + Faruq → Eshan (200) = 350.
Shortcut: start with the rows where all but one sender or receiver is ruled out (Deepak's incoming and Eshan's outgoing), and the rest follows step by step.
Hence, the answer is 350.
Question 22 · Reasoning Based DI
What was the duration of calls (in minutes) from Deepak to Chetan?
- A
100
- B
125
- C
50
- D
0
Answer & solution
Answer: Option A
From the chain of deductions: Eshan → Faruq = 100, so Chetan → Faruq = 50 (Faruq's incoming from Yocel is 150), so Chetan → Eshan = 175 − 50 = 125.
Eshan receives 375 from Yocel users: 125 from Chetan + 200 from Faruq + Deepak → Eshan, so Deepak → Eshan = 50.
Deepak's outgoing to Yocel is 150, and Deepak → Faruq is zero, so Deepak → Chetan = 150 − 50 = 100.
Shortcut: Eshan's incoming from Yocel pins Deepak → Eshan; subtract it from Deepak's Yocel total.
Hence, the answer is option 1.
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