Data Sufficiency

Ten years ago, Dorothy deposited a certain amount of money in account A at 3% simple annual interest rate. At the same time, Marla deposited another amount in account B at 4% simple annual interest rate. If there were no withdrawals or deposits during the ten years since the deposits, is the current interest in A greater than that in B?

(1) The amount invested in A was $1000 more than that invested in B.

(2) The investment in account A obtained an interest of $300 last year.


A)statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
B)statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked;
D)EACH statement ALONE is sufficient to answer the question asked;
E)statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Can anyone know how to pick number for this question.??Is there any strategy for picking number so that I can use it in future.

when I am picking principal for account B $1000 then current interest in A greater than that in B.

When I am picking principal for account B $10000 then current interest in B greater than that in A.

How I will understand I have to try with number $10000 instead of trying with $5000 after trying with $1000?

This is just a continuation of above question.

For statement 1

when I am picking principal for account B $1000 then current interest in A greater than that in B.

When I am picking principal for account B $10000 then current interest in B greater than that in A.

How I will understand I have to try next with number $10000 instead of trying with $5000 after trying with $1000?

OA C

Soumita Ghosh wrote:Ten years ago, Dorothy deposited a certain amount of money in account A at 3% simple annual interest rate. At the same time, Marla deposited another amount in account B at 4% simple annual interest rate. If there were no withdrawals or deposits during the ten years since the deposits, is the current interest in A greater than that in B?

(1) The amount invested in A was $1000 more than that invested in B.

(2) The investment in account A obtained an interest of $300 last year.

Let A = the amount invested in A and B = the amount invested in B.
We need to know whether 3% of A (the annual interest earned by A) is greater than 4% of B (the annual interest earned by B):
3A > 4B
A > (4/3)B.

Question stem rephrased: Is A > (4/3)B?

Statement 1: The amount invested in A was $1000 more than that invested in B.
Try EXTREMES.

Case 1: B = .01, A = 1000.01
In this case, the 1000 difference between A and B is clearly MORE than (1/3)B.
Thus, A > (4/3)B.

Case 2: B = 10^100, A = 10^100 + 1000.
In this case, the 1000 difference between A and B is clearly LESS than (1/3)B.
Thus, A < (4/3)B.

Statement 2: The investment in account A obtained an interest of $300 last year.
No information about B.
INSUFFICIENT.

Statements combined:
The information in statement 2 is sufficient to determine the value of A.
According to statement 1, B is $1000 less than A.
Since both values can be determined, we have sufficient information to calculate whether A > (4/3)B.

The correct answer is C.

The question stem asks for the RATIO of two values: whether A > (4/3)B.
Statement 1 gives the DIFFERENCE between the two values.

An important take-away:
The DIFFERENCE between two values is NOT sufficient information to determine the RATIO of the two values.
The reverse is also true:
The RATIO of two values is NOT sufficient information to determine the DIFFERENCE between the two values.

If we understand this take-away, we can see -- immediately, without plugging in values -- that statement 1 here is not information to answer the question stem.