What was the total duration of calls (in minutes) made by Ananya to friends on the Vertex network?
Answer and solution
Correct answer: 350
Solution
Answer: 350
1. Incoming-from-Vertex totals for the four Vertex friends sum to 150+100+375+150=775.
2. Every Vertex-to-Vertex minute must also occur once in their combined outgoing-to-Vertex total.
3. Known outgoing totals are 175+150+100=425, so Ananya contributes 775−425=350 minutes.
Detailed setup and verification:
Restrict both totals to calls whose caller and receiver are Vertex users. Incoming 150+100+375+150=775 counts every such minute once. Outgoing 175+150+100+Ananya must therefore also total 775. Calls to AeroNet are outside this balance and must not be mixed in.
Subtract the known 425 outgoing minutes to get 350. Check 175+150+100+350=775. This determines Ananya’s aggregate even though her individual pairwise calls need not be uniquely determined by the table.
Verification: 3. Known outgoing totals are 175+150+100=425, so Ananya contributes 775−425=350 minutes.
Trap to avoid: Balance only Vertex→Vertex calls.
1. Incoming-from-Vertex totals for the four Vertex friends sum to 150+100+375+150=775.
2. Every Vertex-to-Vertex minute must also occur once in their combined outgoing-to-Vertex total.
3. Known outgoing totals are 175+150+100=425, so Ananya contributes 775−425=350 minutes.
Detailed setup and verification:
Restrict both totals to calls whose caller and receiver are Vertex users. Incoming 150+100+375+150=775 counts every such minute once. Outgoing 175+150+100+Ananya must therefore also total 775. Calls to AeroNet are outside this balance and must not be mixed in.
Subtract the known 425 outgoing minutes to get 350. Check 175+150+100+350=775. This determines Ananya’s aggregate even though her individual pairwise calls need not be uniquely determined by the table.
G Strategy shortcut
Method: Conserve within-network calls: total incoming 775 minus other outgoing 425=350.Verification: 3. Known outgoing totals are 175+150+100=425, so Ananya contributes 775−425=350 minutes.
Trap to avoid: Balance only Vertex→Vertex calls.
G Strategy: Method: Conserve within-network calls: total incoming 775 minus other outgoing 425=350. Verification: 3. Known outgoing totals are 175+150+100=425, so Ananya contributes 775−425=350 minutes. Trap to avoid: Balance only Vertex→Vertex calls.