GMAT
题目
This year, a woman has a lucrative one-year position. During this year, she will give a fraction f of her salary to her husband, a private investor, to invest and they will live this year on the remainder. Through investments, her husband can turn each dollar she gives him into 1 + r, which will be deposited in a bank account. Their goal is to save & invest enough money so they can live off this money for two years following the end of the wife's position. Toward this end, they want to choose f such that the amount in the account at the end of the year is twice what they lived off this year. In terms of r, what should f be?
解析
设她的工资为 T
丈夫获得的金额为 f
剩余金额 = (T - f)
由于丈夫每投资1美元可获得(1 + r)美元，因此在年末，他的投资总额为f(1 + r)美元。
根据题意列出方程：
f(1 + r) = 2(T - f)
f(1 + r) = 2T - 2f
f(1 + r) + 2f = 2T
f(3 + r) = 2T
f = 2T/(r + 3)
因此，答案为选项D。
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