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13 Mar 2026, 22:32
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
77% (02:31) correct
23%
(02:18)
wrong
based on 35
sessions
History
Date
Time
Result
Not Attempted Yet
Layla divides a sum of money between two accounts. Each month she spends half of the money remaining in the first account, while the balance of the second account remains unchanged. After 3 months, the combined balance of the two accounts equals 7/8 of the original amount.
Initially, what fraction of Layla’s money was in the second account?
A) 3/4
B) 5/6
C) 6/7
D) 7/8
E) 8/9
Initially, what fraction of Layla’s money was in the second account?
A) 3/4
B) 5/6
C) 6/7
D) 7/8
E) 8/9
16 Mar 2026, 01:53
Kudos
Bookmarks
Let's say Layla starts with a total of S dollars, and she puts a fraction f of it into the second account.
So:
- Second account = fS
- First account = (1 - f)S
Now, each month she spends HALF of what's left in the first account. That means each month, the first account gets multiplied by 1/2.
After month 1: first account = (1 - f)S × 1/2
After month 2: first account = (1 - f)S × 1/4
After month 3: first account = (1 - f)S × 1/8
The second account never changes, so it stays at fS.
Now we're told the combined balance after 3 months equals 7/8 of the original amount:
fS + (1 - f)S / 8 = (7/8)S
Divide everything by S:
f + (1 - f)/8 = 7/8
Multiply everything by 8 to clear the fractions:
8f + (1 - f) = 7
8f + 1 - f = 7
7f = 6
f = 6/7
Answer: C
Key Insight: When you repeatedly take half of something 3 times, you're left with (1/2)^3 = 1/8 of the original. So the first account shrinks to 1/8 of its starting value, while the second account stays the same. From there, it's just one equation with one unknown.
So:
- Second account = fS
- First account = (1 - f)S
Now, each month she spends HALF of what's left in the first account. That means each month, the first account gets multiplied by 1/2.
After month 1: first account = (1 - f)S × 1/2
After month 2: first account = (1 - f)S × 1/4
After month 3: first account = (1 - f)S × 1/8
The second account never changes, so it stays at fS.
Now we're told the combined balance after 3 months equals 7/8 of the original amount:
fS + (1 - f)S / 8 = (7/8)S
Divide everything by S:
f + (1 - f)/8 = 7/8
Multiply everything by 8 to clear the fractions:
8f + (1 - f) = 7
8f + 1 - f = 7
7f = 6
f = 6/7
Answer: C
Key Insight: When you repeatedly take half of something 3 times, you're left with (1/2)^3 = 1/8 of the original. So the first account shrinks to 1/8 of its starting value, while the second account stays the same. From there, it's just one equation with one unknown.
