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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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Sajjad1994
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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Sajjad1994
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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Sajjad1994
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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Sajjad1994
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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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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Parvez786
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.

Thank you!
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