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Retired Moderator Joined: 29 Apr 2015
Posts: 815
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Ten years ago, Dorothy deposited a certain amount of money in account  [#permalink]

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11 00:00

Difficulty:   55% (hard)

Question Stats: 63% (02:15) correct 37% (02:11) wrong based on 123 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.

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).
Intern  Joined: 17 Jun 2014
Posts: 15
GMAT 1: 760 Q51 V42
GPA: 3.3
WE: Engineering (Manufacturing)
Re: Ten years ago, Dorothy deposited a certain amount of money in account  [#permalink]

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2
Here's my solution.

Attachments math solution.PNG [ 33.8 KiB | Viewed 2820 times ]

CEO  S
Joined: 20 Mar 2014
Posts: 2548
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Ten years ago, Dorothy deposited a certain amount of money in account  [#permalink]

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2
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.

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.
CEO  S
Joined: 20 Mar 2014
Posts: 2548
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Ten years ago, Dorothy deposited a certain amount of money in account  [#permalink]

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colorbrandon wrote:
Here's my solution.

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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_________________ Re: Ten years ago, Dorothy deposited a certain amount of money in account   [#permalink] 19 Mar 2019, 01:11
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