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A business allocates $7.2 million between two investments. It invests

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Sajjad1994
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A business allocates $7.2 million between two investments. It invests [#permalink] New post   10 Oct 2023, 10:21
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Data Insights (DI) Butler 2023-24 [Question #23, Date: Oct-09-2023] [Click here for Details]


A business allocates $7.2 million between two investments. It invests the smaller portion in currencies and the remainder in real estate. The combined return on the investments for the first year is $846,000. If the investment in real estate exceeds the currency investment by $3 million, find the rate of return on each investment.
Rate of return on real estate Rate of return on currencies
2.2%
3.8%
7.5%
9.1%
11.75%
13.5%
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Official Answer
Rate of return on real estate: 13.5%
Rate of return on currencies: 7.5%
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Piyush786767
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   11 Oct 2023, 05:46
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11.75
11.75
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Nsingh06
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   12 Oct 2023, 06:20
Can someone please share the solution for this?
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   12 Oct 2023, 23:08
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Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   18 Oct 2023, 03:12
Sajjad1994 wrote:
Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.



Hi, why can't both investment provide returns of 11.75%? Its not mentioned in the question stem that interest rate for both investments have to be different.
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   21 Oct 2023, 08:30
Sajjad1994 wrote:
Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.


There's no mention of allocation for the Currency and Real Estate is done with equal weightage. So, why 2x comes here in the equation? Sajjad1994 bb Bunuel or any other person / expert?
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   22 Oct 2023, 03:18
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Nikkz99 wrote:
Sajjad1994 wrote:
Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.


There's no mention of allocation for the Currency and Real Estate is done with equal weightage. So, why 2x comes here in the equation? Sajjad1994 bb Bunuel or any other person / expert?


x = investment 1

as we know, the second investment is 3 million greater than first investment hence second investment would equal to x + 3 million and sum of both investment would equal to x + x + 3 million and x + x + 3 million = 2x+ 3 million.
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   22 Oct 2023, 03:20
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varad98 wrote:
Sajjad1994 wrote:
Official Explanation

Because the total of the two investments and the difference between them are both known, it is possible to determine that the smaller investment (x) is $2.1 million and the larger (x + $3 million) is $5.1 million: x + x + $3 million = $7.2 million, so 2x = $4.2 million, and x = $2.1 million.

The combined return is 11.75% of the total amount, suggesting that the interest rates are among the higher choices, so begin by finding 13.5% of $5.1 million = $688,500. Subtract that from the total return of $846,000 to get $157,500. Divide $157,500 by $2.1 million to find that the second interest rate was 7.5%.


Hi, why can't both investment provide returns of 11.75%? Its not mentioned in the question stem that interest rate for both investments have to be different.


The official explanation is correct, but the language of the question is ambigious, so bear it as it is.
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   15 Dec 2023, 09:26
Sajjad1994 bb Bunuel - why can't both be 11.75 .
11.75 % return on each investment gives 846,000 as the total return.
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Re: A business allocates $7.2 million between two investments. It invests [#permalink] New post   16 Dec 2023, 13:25
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Parvez786 wrote:
Sajjad1994 bb Bunuel - why can't both be 11.75 .
11.75 % return on each investment gives 846,000 as the total return.


Because the statement of the question was said as such. Read the last line of the question. Also, read the OE.

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Re: A business allocates $7.2 million between two investments. It invests [#permalink]
16 Dec 2023, 13:25
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