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24 Dec 2024, 09:00
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m: 55
b: 90
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:29) correct
28%
(02:55)
wrong
based on 728
sessions
History
Date
Time
Result
Not Attempted Yet
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
An investor has two cryptocurrency wallets, Main and Backup. The Main wallet holds m% of its maximum capacity, while the Backup wallet holds b% of its maximum capacity. Both wallets have identical maximum capacities.
Due to new regulations, the investor must optimize storage by transferring tokens from the Backup wallet to the Main wallet until the Main wallet reaches its maximum capacity. After this transfer, the Backup wallet contains exactly half of its previous percentage.
If the Backup wallet initially held a higher percentage than the Main wallet, select for m the possible value of m, and select for b the possible value of b that would be jointly consistent with the given information. Make only two selections, one in each column.
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An investor has two cryptocurrency wallets, Main and Backup. The Main wallet holds m% of its maximum capacity, while the Backup wallet holds b% of its maximum capacity. Both wallets have identical maximum capacities.
Due to new regulations, the investor must optimize storage by transferring tokens from the Backup wallet to the Main wallet until the Main wallet reaches its maximum capacity. After this transfer, the Backup wallet contains exactly half of its previous percentage.
If the Backup wallet initially held a higher percentage than the Main wallet, select for m the possible value of m, and select for b the possible value of b that would be jointly consistent with the given information. Make only two selections, one in each column.
| m | b | |
| 30 | ||
| 45 | ||
| 50 | ||
| 55 | ||
| 60 | ||
| 90 |
ShowHide Answer
Official Answer
m: 55
b: 90
24 Dec 2024, 10:00
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Bunuel
GMAT Club's Official Explanation:
The amount transferred from the Backup wallet to the Main wallet must equal (100 - m).
This transfer from the Backup wallet was b/2.
Therefore:
b/2 = 100 - m
Simplifying: b + 2m = 200
Only b = 90 and m = 55 satisfy this equation.
General Discussion
24 Dec 2024, 09:26
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Given:
The Main wallet holds m% of its max capacity.
The Backup wallet holds b% of its max capacity.
After transferring tokens to the Main wallet until it is full (100%), the Backup wallet holds b/2% of its max capacity.
Steps:
The amount transferred to the Main wallet is: 100% - m% = amount transferred from Backup
The Backup wallet’s remaining amount is: b% - b/2% = b/2% (remaining in Backup)
Set up the equation: 100 - m = b/2
Multiply both sides by 2: 2(100 - m) = b
b = 200 - 2m
Test values for m:
If m = 30:
b = 200 - 2(30) = 140 (not an option)
If m = 45:
b = 200 - 2(45) = 110 (not an option)
If m = 50:
b = 200 - 2(50) = 100 (not an option)
If m = 55:
b = 200 - 2(55) = 90 (valid option)
If m = 60:
b = 200 - 2(60) = 80 (not an option)
If m = 90:
b = 200 - 2(90) = 20 (not an option)
Answer:
m = 55
b = 90
The Main wallet holds m% of its max capacity.
The Backup wallet holds b% of its max capacity.
After transferring tokens to the Main wallet until it is full (100%), the Backup wallet holds b/2% of its max capacity.
Steps:
The amount transferred to the Main wallet is: 100% - m% = amount transferred from Backup
The Backup wallet’s remaining amount is: b% - b/2% = b/2% (remaining in Backup)
Set up the equation: 100 - m = b/2
Multiply both sides by 2: 2(100 - m) = b
b = 200 - 2m
Test values for m:
If m = 30:
b = 200 - 2(30) = 140 (not an option)
If m = 45:
b = 200 - 2(45) = 110 (not an option)
If m = 50:
b = 200 - 2(50) = 100 (not an option)
If m = 55:
b = 200 - 2(55) = 90 (valid option)
If m = 60:
b = 200 - 2(60) = 80 (not an option)
If m = 90:
b = 200 - 2(90) = 20 (not an option)
Answer:
m = 55
b = 90
