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.

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.

GMATGuruNY 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.

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.

Hey Guru!
I took the following values:-
Ra=100% and Rb=150%, which gave me Pa=50 and Pb=100.
Ra=500% and Rb=750%, which gave me Pa=10 and Pb=30.
therefore I concluded Statement 1 is insufficient.
However, according to the values, which I choose, I was convinced that statement 2 would give me a unique value for the principles.

But when I looked at your explanations,I found that you choose the correct values or perfect numbers to plug.
Is there any specific way to substitute values?
In this Q, please give me the line of thinking for you to choose the apt values?

[email protected] 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.

Hey Guru!
I took the following values:-
Ra=100% and Rb=150%, which gave me Pa=50 and Pb=100.
Ra=500% and Rb=750%, which gave me Pa=10 and Pb=30.
therefore I concluded Statement 1 is insufficient.
However, according to the values, which I choose, I was convinced that statement 2 would give me a unique value for the principles.

The value in red has been miscalculated.
For an interest rate of 750% to yield $150 in interest, the amount invested in B must be not $30 but $20:
750% of $20 = (7.5)(20) = $150.
Thus, both of your cases -- $50 in A and $100 in B, $10 in A and $20 in B -- also satisfy statement 2:
In each case, the amount in invested in B is twice that invested in A.
Since the amount invested in A can be different values, statement 2 is INSUFFICIENT.