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Ten years ago, Dorothy deposited a certain amount of money in account

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Ten years ago, Dorothy deposited a certain amount of money in account [#permalink]

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New post 29 Jul 2015, 09:02
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Difficulty:

  65% (hard)

Question Stats:

58% (01:38) correct 42% (01:19) wrong based on 128 sessions

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Ten years ago, Dorothy deposited a certain amount of money in account A at 3% simple annual interest rate. At the same time, Marla deposited another amount in account B at 4% simple annual interest rate. If there were no withdrawals or deposits during the ten years since the deposits, is the current interest in A greater than that in B?

(1) The amount invested in A was $1000 more than that invested in B.
(2) The investment in account A obtained an interest of $300 last year.



[Reveal] Spoiler:
OE

According to Stat. (1),

A $1000 head start for account A is fine, but without knowing the Principals, it is impossible to judge the weight this addition will have over 10 years. If the amounts invested in A and B were 1100 and 100 dollars, respectively, the interest in A would be larger than B after 10 years, whereas if the initial investments were 101,000 versus 100,000, B's higher interest rate over 10 years will compensate for the $1000 deficit. (4000$ a year in B, 3030$ in A).

Stat.(1)->IS->BCE.

According to Stat. (2),

it is possible to calculate the principal for A, but you do not know anything about the investment in B.

Stat.(2)->IS->CE.

According to Stat. (1+2),

from Stat (2), if the interest in A last year was 300$, and you know that it is 3% of the investment, then the investment in A was 10000$. From Stat (1), you can now calculate the principal for account B: 10000-1000 = 9000$. Using the interest rate and time in the question stem, it is now possible to calculate both interests earned and compare the two. regardless of the actual numbers, you will have a definite answer whether the interest in A is greater than B (It's not, and the answer is a definite 'no' answer, but you don't really need to calculate it - just know that you CAN calculate it).
[Reveal] Spoiler: OA

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Re: Ten years ago, Dorothy deposited a certain amount of money in account [#permalink]

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New post 29 Jul 2015, 09:30
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Here's my solution.

[Reveal] Spoiler:
Answer, C

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Re: Ten years ago, Dorothy deposited a certain amount of money in account [#permalink]

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New post 29 Jul 2015, 10:12
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reto wrote:
Ten years ago, Dorothy deposited a certain amount of money in account A at 3% simple annual interest rate. At the same time, Marla deposited another amount in account B at 4% simple annual interest rate. If there were no withdrawals or deposits during the ten years since the deposits, is the current interest in A greater than that in B?

(1) The amount invested in A was $1000 more than that invested in B.
(2) The investment in account A obtained an interest of $300 last year.



[Reveal] Spoiler:
OE

According to Stat. (1),

A $1000 head start for account A is fine, but without knowing the Principals, it is impossible to judge the weight this addition will have over 10 years. If the amounts invested in A and B were 1100 and 100 dollars, respectively, the interest in A would be larger than B after 10 years, whereas if the initial investments were 101,000 versus 100,000, B's higher interest rate over 10 years will compensate for the $1000 deficit. (4000$ a year in B, 3030$ in A).

Stat.(1)->IS->BCE.

According to Stat. (2),

it is possible to calculate the principal for A, but you do not know anything about the investment in B.

Stat.(2)->IS->CE.

According to Stat. (1+2),

from Stat (2), if the interest in A last year was 300$, and you know that it is 3% of the investment, then the investment in A was 10000$. From Stat (1), you can now calculate the principal for account B: 10000-1000 = 9000$. Using the interest rate and time in the question stem, it is now possible to calculate both interests earned and compare the two. regardless of the actual numbers, you will have a definite answer whether the interest in A is greater than B (It's not, and the answer is a definite 'no' answer, but you don't really need to calculate it - just know that you CAN calculate it).


Simple interest formula on P$ for n years @ r% interest = Pnr/100

Thus per the question, is 30A/100 > 40B/100 ---> 3A > 4B?

Statement 1, A=B+1000 ---> 3A-4B = 3B+3000-4B = 3000 - B > 0 ONLY IF B < 3000. As we dont know the exact value of B ---> not sufficient to answer is 3A> 4B.

Statement 2, Interest after 9 years = A*3*9/100= 27A/100 = 300 ---> A= 10000/9. No information about B ---> not sufficient.

Combining, A = 10000/9 and B = A -1000 = 1000/9, clearly 1 set of values for A and B and thus 1 set of value of 3A-4B ---> Sufficient to answer. C is the correct answer.
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Joined: 20 Mar 2014
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Re: Ten years ago, Dorothy deposited a certain amount of money in account [#permalink]

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New post 29 Jul 2015, 10:14
colorbrandon wrote:
Here's my solution.

[Reveal] Spoiler:
Answer, C


colorbrandon, the question is about simple interest and not compound interest. But luckily both the formulae would give you the same final answer.
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Re: Ten years ago, Dorothy deposited a certain amount of money in account [#permalink]

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New post 14 Jan 2018, 13:44
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Re: Ten years ago, Dorothy deposited a certain amount of money in account   [#permalink] 14 Jan 2018, 13:44
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