Data Sufficiency

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

josh80 wrote: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 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 twice 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.