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Pamela and Joe invested some money at annual simple interest

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Pamela and Joe invested some money at annual simple interest [#permalink]

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New post 17 Oct 2012, 02:08
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Pamela and Joe invested some money at annual simple interest rates of 6% and 7% respectively. At the end of 2 years they found that together they received a sum of $354 as interest.Find the total money invested by them.

(1) One fourth of Pamela’s initial investment is equal to one-fifth of the money invested by Joe.
(2) Joe invested $300 more than the sum invested by Pamela.
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Re: Pamela and Joe invested some money at annual simple interest [#permalink]

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Pamela and Joe invested some money at annual simple interest rates of 6% and 7% respectively. At the end of 2 years they found that together they received a sum of $354 as interest. Find the total money invested by them.

Say Pamela invested \($x\) and Joe invested \($y\).
At the end of the first year Pamela's interest would be \($0.06x\) and Joe' interest would be \($0.07y\).
At the end of the second year Pamela's interest would be \($2*0.06x\) and Joe' interest would be \($2*0.07y\).
Given: \(2*0.06x+2*0.07y=354\).
Question: \(x+y=?\)

(1) One fourth of Pamela’s initial investment is equal to one-fifth of the money invested by Joe. \(\frac{x}{4}=\frac{y}{5}\). We have two distinct linear equations (\(2*0.06x+2*0.07y=354\) and \(\frac{x}{4}=\frac{y}{5}\)), which means that we can solve for \(x\) and \(y\), therefore can find the value of \(x+y\). Sufficient.

(2) Joe invested $300 more than the sum invested by Pamela. \(x+300=y\). The same here: we have two distinct linear equations (\(2*0.06x+2*0.07y=354\) and \(x+300=y\)). Sufficient.

Answer: D.
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Re: Pamela and Joe invested some money at annual simple interest [#permalink]

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New post 19 Oct 2012, 10:59
I am kind of inclined to 'B'. Please say me why I'm wrong. In the options, option (1) says
"One fourth of Pamela’s initial investment is equal to one-fifth of the money invested by Joe."
The initial investment word gives me the suspicion that the assumption is they invest after the initial investments too. Otherwise why would we have "initial investment" and "money invested" as two separate words? Thanks in advance for your help. I know you can't be wrong, so just asking.
Re: Pamela and Joe invested some money at annual simple interest   [#permalink] 19 Oct 2012, 10:59
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