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27 Feb 2025, 01:30
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Difficulty:
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Question Stats:
78% (01:39) correct
22%
(02:18)
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based on 114
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Joern and Bin went on a year-long round-the-world backpacking tour starting January 1. Five days before the trip, each had opened a bank account. Then their insurance companies started to withdraw $300 from their accounts, respectively, on the first business day of each month. Assuming no other deposits or withdrawals, whose account had more money in it at the end of the year of travels?
(1) On April 15 during the tour, Bin's account had twice as much money as Joern's account.
(2) On June 15 during the tour, Bin's account had four times as much money as Joern's account.
(1) On April 15 during the tour, Bin's account had twice as much money as Joern's account.
(2) On June 15 during the tour, Bin's account had four times as much money as Joern's account.
27 Feb 2025, 02:04
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Account start 5 days before Jan 1
Every month 300 deducted
If Joern had a starting sum of J and Bin had a starting sum of B
After n months, the deduction, will be 300n each
Asked, whose account had more money at year end. Considering no other deposits or withdrawals and same deductions, whichever account had higher initial sum, they will end up with more money at the end of the year
Asked, which is greater J or B?
Statment 1
April 15 means 4 deductions(i.e. 1200) from both accounts
B'=2J' (amount after 1200 deduction from both)
So B > J
Sufficient
Statment 2
June 15 means 6 deductions(i.e. 1800) from both accounts
B'=4J' (amount after 1800 deduction from both)
So B > J
Sufficient
Every month 300 deducted
If Joern had a starting sum of J and Bin had a starting sum of B
After n months, the deduction, will be 300n each
Asked, whose account had more money at year end. Considering no other deposits or withdrawals and same deductions, whichever account had higher initial sum, they will end up with more money at the end of the year
Asked, which is greater J or B?
Statment 1
April 15 means 4 deductions(i.e. 1200) from both accounts
B'=2J' (amount after 1200 deduction from both)
So B > J
Sufficient
Statment 2
June 15 means 6 deductions(i.e. 1800) from both accounts
B'=4J' (amount after 1800 deduction from both)
So B > J
Sufficient
Bunuel
27 Feb 2025, 06:04
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Statement (1)
On April 15, Bin's account had twice as much money as Joern's account.
- After 4 months, Joern’s balance = J - 1200, and Bin’s balance = B - 1200
- Given: B - 1200 = 2(J - 1200)
- Solving: B = 2J - 1200
This provides a relationship between J and B but not their exact values.
Statement (1) alone is insufficient.
Statement (2)
On June 15, Bin’s account had four times as much money as Joern’s account.
- After 6 months, Joern’s balance = J - 1800, and Bin’s balance = B - 1800
- Given: B - 1800 = 4(J - 1800)
- Solving: B = 4J - 5400
This also provides a relationship between J and B but not their exact values.
Statement (2) alone is insufficient.
Combining (1) and (2)
We now have two equations:
1. B = 2J - 1200
2. B = 4J - 5400
Setting them equal:
2J - 1200 = 4J - 5400
4200 = 2J
J = 2100
Substituting into (1):
B = 2(2100) - 1200 = 3000
Final Balances After 12 Months:
- Joern’s final balance = 2100 - 3600 = 0
- Bin’s final balance = 3000 - 3600 = 0
Both have the same balance at year-end.
Statements together are sufficient.
Answer: C
On April 15, Bin's account had twice as much money as Joern's account.
- After 4 months, Joern’s balance = J - 1200, and Bin’s balance = B - 1200
- Given: B - 1200 = 2(J - 1200)
- Solving: B = 2J - 1200
This provides a relationship between J and B but not their exact values.
Statement (1) alone is insufficient.
Statement (2)
On June 15, Bin’s account had four times as much money as Joern’s account.
- After 6 months, Joern’s balance = J - 1800, and Bin’s balance = B - 1800
- Given: B - 1800 = 4(J - 1800)
- Solving: B = 4J - 5400
This also provides a relationship between J and B but not their exact values.
Statement (2) alone is insufficient.
Combining (1) and (2)
We now have two equations:
1. B = 2J - 1200
2. B = 4J - 5400
Setting them equal:
2J - 1200 = 4J - 5400
4200 = 2J
J = 2100
Substituting into (1):
B = 2(2100) - 1200 = 3000
Final Balances After 12 Months:
- Joern’s final balance = 2100 - 3600 = 0
- Bin’s final balance = 3000 - 3600 = 0
Both have the same balance at year-end.
Statements together are sufficient.
Answer: C
