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David used part of $100,000 to purchase a house. Of the remaining port

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David used part of $100,000 to purchase a house. Of the remaining port [#permalink]

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New post 27 May 2016, 03:09
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Question Stats:

74% (02:03) correct 26% (03:03) wrong based on 145 sessions

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David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?

(A) $96,000
(B) $94,000
(C) $88,000
(D) $75,000
(E) $40,000
[Reveal] Spoiler: OA

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Re: David used part of $100,000 to purchase a house. Of the remaining port [#permalink]

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New post 27 May 2016, 03:31
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Let the Price of house was x.

Then

\(\frac{1}{3}\)(10000-x) * \(\frac{4}{100}\) --> 1st investment

\(\frac{2}{3}\)(10000-x) * \(\frac{6}{100}\) --> 2nd investment


\(\frac{4}{300}\)(10000-x) *(1+3) = 320


(10000-x) = 20 * 300 = 6000

x = 94000

Option B is correct

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Re: David used part of $100,000 to purchase a house. Of the remaining port [#permalink]

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New post 14 Jun 2016, 11:57
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nalinnair wrote:
David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?

(A) $96,000
(B) $94,000
(C) $88,000
(D) $75,000
(E) $40,000


An alternative solution:

"Of the remaining portion" is split two ways - 1/3 & 2/3. The interest earned is an integer amount. So, we can pick some smart numbers for the remaining amount and calculate the interest rate. Use answer choices to pick a number that is divisible by 3.

Of all the answer choices, (A) and (D) do not offer a number divisible by 3. (E) can be eliminated easily because when you invest 1/3 of $60,000 ($20,000) @ 4% interest rate, you earn $800 interest, which is definitely more than $320. But, if you calculate 2/3 of $60,000 ($40,000) @ 6% interest rate, you earn $2400 interest. Total interest when $60,000 is the remaining amount: $800 + $2400 = $3200. We need $320. It means the remaining amount should be $6000. Therefore, (B) is the answer.

It may seem like a little bit lengthy approach, but with enough practice you can save yourself some trouble solving algebraic equations and save some time :wink:

Happy solving!

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Re: David used part of $100,000 to purchase a house. Of the remaining port [#permalink]

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New post 04 Oct 2017, 03:26
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Re: David used part of $100,000 to purchase a house. Of the remaining port   [#permalink] 04 Oct 2017, 03:26
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