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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2936
Given Kudos: 1286
GPA: 3.39
Out of $1000 with him, a man invested certain amount at 4% per annum a
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13 Jul 2026, 09:53
13 Jul 2026, 09:53
1
Expert Reply
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Question Stats:
55% (01:32) correct
44% (01:50) wrong based on 9 sessions
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Out of $1000 with him, a man invested certain amount at 4% per annum and rest at 6% per annum. The interest earned at the end of year was $48.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The amount invested at 4% rate per annum. |
The Amount invested at 6% rate per annum. |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2936
Given Kudos: 1286
GPA: 3.39
Re: Out of $1000 with him, a man invested certain amount at 4% per annum a
[#permalink]
15 Jul 2026, 20:19
15 Jul 2026, 20:19
Expert Reply
Explanation
Let the amount invested at 4% be \(x.\)
Then the amount invested at 6% is: \(1000−x\)
The total interest after one year is \($48,\) so:
\(0.04x+0.06(1000−x)=48\)
Solve:
\(0.04x+60−0.06x=48\)
\(60−0.02x=48\)
\(0.02x=12\)
\(x=600\)
So:
Amount at 4% = $600
Amount at 6% = $400
Comparing the quantities:
Quantity A: $600
Quantity B: $400
Quantity A is greater.
Answer: A
Let the amount invested at 4% be \(x.\)
Then the amount invested at 6% is: \(1000−x\)
The total interest after one year is \($48,\) so:
\(0.04x+0.06(1000−x)=48\)
Solve:
\(0.04x+60−0.06x=48\)
\(60−0.02x=48\)
\(0.02x=12\)
\(x=600\)
So:
Amount at 4% = $600
Amount at 6% = $400
Comparing the quantities:
Quantity A: $600
Quantity B: $400
Quantity A is greater.
Answer: A
Re: Out of $1000 with him, a man invested certain amount at 4% per annum a
[#permalink]
30 Jul 2026, 19:27
30 Jul 2026, 19:27
A faster way to do this one is to use the average interest. You can notice that the average interest rate on the 1000 dollars is effectively 1.048 which is less than 1.05.
Because 1.05 is would be the result if the money were split exactly evenly, you can tell that there must be more money in the 1.04 account than the 1.06 account without doing any further calculations.
Because 1.05 is would be the result if the money were split exactly evenly, you can tell that there must be more money in the 1.04 account than the 1.06 account without doing any further calculations.
