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word problem

by sud21 » Thu Jan 12, 2012 2:57 am
Six years ago, a person deposited a certain amount of money in account A at 3% simple annual interest rate, and other amount in account B at 4% simple annual interest rate, respectively. If there was no any withdraw or deposit during the six years, is the current interest in A greater than that in B?
1). The amount invested in A was $1000 more than that in B
2). The investment in account A obtained an interest of $10 last year.
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Source: — Data Sufficiency |
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by sam2304 » Thu Jan 12, 2012 4:44 am
Six years ago, a person deposited a certain amount of money in account A at 3% simple annual interest rate, and other amount in account B at 4% simple annual interest rate, respectively. If there was no any withdraw or deposit during the six years, is the current interest in A greater than that in B?
1). The amount invested in A was $1000 more than that in B
Ia = (P+1000)*6*3/100 = (P+1000)18/100 ~= P+1000/5
Ib = P*6*4/100 ~= P/4

When P = 4, Ia = 250, Ib = 1 Ia > Ib
when P = 10000, Ia ~= 2200, Ib = 2500 Ib > Ia

INSUFF

One more approach is
Ia = P+1000/5 = P/5 + 200
Ib = P/4
Ia > Ib =>
P/5 + 200 > P/4
200 > P/4 - P/5
P < 4000. So the condition will hold true for P < 4000 and false for > 4000.
2). The investment in account A obtained an interest of $10 last year.
I = PNR/100
5 = P*5*3/100
P = 100/3

We get the P for A but no info about P in account B, so INSUFF.

Combining both we get investment for A = 100/3 and investment for B becomes -ve. Not sure if this is right or if i am going wrong somewhere.

Hence INSUFF.

IMO E.
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