Data Sufficiency

Hello,

I am having some trouble with this question:

Linda put an amount of money into each of two new investment, A and B, that pay simple annual interest. If the annual interest rate of investment B is 3/2 times that of investment A, what amount did Linda put into investment A?

1. The interest for 1 year is $50 for investment A and $150 for investment B.
2. The amount that Linda put into investment B is twice the amount that she put into investment A.

OA: E

I tried starting as follows:

Let the amount of money in investment A and investment B be a and b resp.

We need to find 'a'

Also given, the interest earned in B = 1.5 times the interest earned in A

Statement 1:
Interest earned in A = $50/-
=> Interest earned in B = $75/-

I am thinking that this is in-sufficient since 'a' and 'b' could be anything.


Statement 2:
b = 2a

I am thinking that this is also in-sufficient


1 and 2:
Interest earned in A = $50/-
=> Interest earned in B = $75/-

and b = 2a

I am wondering how to show that this is in-sufficient.

Thanks a lot,
Sri

Rough


BI = 3/2 * AI

To find: AP

Statement 1:
50 = AP * AI * 1/100
5000 = AP * AI
We have no info about AI
INSUFFICIENT

Statement 2:
BP = 2 * AP
But we have no information about other BP.
INSUFFICIENT

Combining...
5000 = AP * AI
BP = 2 * AP
We have no command variables to reach to a numeric AP.
INSUFFICIENT
[spoiler]{E}[/spoiler]

Linda put an amount of money into each of two new investments, that pay simple annual interest. If the annual rate of investment B is 1.5 times that of investment A, what amount did Linda put into investment A?

1) The interest for 1 year is $50 for investment A and $150 for investment B.

2) The amount that Linda put in investment B is twice the amount she put in investment A.

OA E

The following cases satisfy the constraint that B's interest rate is 1.5 times A's interest rate:
Case 1: A = 100% interest, B = 150% interest
Case 2: A = 200% interest, B = 300% interest
To evaluate the statements, test both cases.

Statement 1: The interest for 1 year is $50 for investment A and $150 for investment B.
Case 1: 100% interest, B = 150% interest
Since A's interest ($50) is equal to 100% of the initial investment, the amount invested in A = $50.
Since B's interest ($150) is equal to 1.5 times the initial investment, the amount invested in B = $100.

Case 2: A = 200% interest, B = 300% interest
Since A's interest ($50) is equal to 200% of the initial investment, the amount invested in A = $25.
Since B's interest ($150) is equal to 3 times the initial investment, the amount invested in B = $50.

Since the amount invested in A is $50 in Case 1 but $25 in Case 2, INSUFFICIENT.

Both Case 1 and Case 2 also satisfy statement 2:
In each case, the amount invested in B is twice that invested in A.
Thus, when the two statements are combined, the amount invested in A could be $50 or $25.
INSUFFICIENT.

The correct answer is E.

theCodeToGMAT wrote:Rough


BI = 3/2 * AI

To find: AP

Statement 1:
50 = AP * AI * 1/100
5000 = AP * AI
We have no info about AI
INSUFFICIENT

Statement 2:
BP = 2 * AP
But we have no information about other BP.
INSUFFICIENT

Combining...
5000 = AP * AI
BP = 2 * AP
We have no command variables to reach to a numeric AP.
INSUFFICIENT
[spoiler]{E}[/spoiler]

Hi Rahul,

Thanks for your reply.

Does this mean that "Interest earned in B = 1.5 times the interest earned in A":
BI = 3/2 * AI

Also, I was not clear with Statement 1. Can you please explain it?

Thanks for your help,
Sri