Exactly 6 years ago, James opened 2 salary accounts, with no

Question

Exactly 6 years ago, James opened 2 salary accounts, with no further deposits nor withdrawals since then. Each account has earned simple interest, one at 3% per year and the other at 4% per year. Which account has more money now?

(1) When James opened the accounts, the account earning 3% interest contained $1,000 more than the account earning 4%.
(2) Last year, the account earning 3% earned exactly $150 in interest.

Bunuel · Answer

Exactly 6 years ago, James opened 2 salary accounts, with no further deposits nor withdrawals since then. Each account has earned simple interest, one at 3% per year and the other at 4% per year. Which account has more money now?

Say the amount invested at 3% was $x and the amount invested at 4% was $y.

(1) When James opened the accounts, the account earning 3% interest contained $1,000 more than the account earning 4%. x=y+1,000. Check extreme cases: if y=0 and x=1,000, then the amount invested at 4% ($0) would still have $0 after 6 years, thus the amount invested at 3% ($1,000) would naturally have more money. But if y=1,000,000 and x=1,001,000, then even after one year the amount invested at 4% would have more money than the amount invested at 3% (1,000,000+40,000=1,040,000 and 1,001,000+30,000+30=1,031,030). Not sufficient.

(2) Last year, the account earning 3% earned exactly $150 in interest. Since accounts earn  simple  interest, then each account earns the same amount each year --> x*0.03=$150 --> we can find x but still not sufficient.

(1)+(2) Since from (2) we know the value of x, then from x=y+1,000 we can find the value of y, hence we can answer the question. Sufficient.

Answer: C.

Hope it's clear.

gmatbull · Answer

Bunuel, your explanations were indeed helpful.

Meanwhile from "(2) Last year, the account earning 3% earned exactly $150 in interest."
Shouldn't it be x(0.03)*5 = $150? 
The accounts were opened 6 yrs ago, and last yr would mean the account would have been 
active for 5yrs...Other than that the explanations are crystal clear.

Thanks.

fukirua · Answer

I was also confused with "simple interest" term. I don't know what exactly GMAT means by that but in real world it means that interest acquires only at the end of the term. Thus it should be x(0.03)^5=150.
But anyhow it doesn't influence our solution. We don't have to calculate this X from the second statement, we just know that  X is some definite  number, which will help us to put it into first statement. I personally  stopped here .

Bunuel · Answer

The accounts earn  simple  interest, thus each year the accounts earn the same amount. Thus, if last year (for one, fifth year), the account earning 3% earned exactly $150 in interest, then x*0.03=$150.

Hope it's clear.

chibimoon · Answer

Hi there

My question is how do you know when to use the extreme number such as y=1,000,000 and x=1,001,000, whereas I would just use x = 2000 and y = 1000 and would still get the result that by the end of 6 years the 3% account would earn more.

bumpbot · Answer

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Exactly 6 years ago, James opened 2 salary accounts, with no

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