Roland2rule wrote:On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?

(1) The total amount of interest earned by Hannah's two investments in one year was $900.
(2) Hannah invested the $5,000 at 6 percent simple annual interest.

a. Both statement are insufficient
b. statement 2 is sufficient
c. statement 1 and 2 are sufficient
d. statement 1 is insufficient and statement 2 is sufficient
e. None of the above
OA is a....

why is Statement 1 insufficient and 2 sufficient? Show it in mathematical language

Hi Roland2rule,

I just realized that your answer choices are totally off.

The 5 answer choices for Data Sufficiency questions are always the same:

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Where did you get your answer choices (in red above)?

Hi Roland2rule,

We're told that Hannah invested $5,000 at X percent simple annual interest and a DIFFERENT amount at Y percent simple annual interest. We're asked for the amount that Hannah invested at Y percent. This DS question can be solved by TESTing VALUES.

1) The total amount of interest earned by Hannah's two investments in one year was $900.

Based on the information in the prompt, we can create the following equation:

($5,000)(X/100) + ($Z)(Y/100) = 900

You can see that there are 3 variables, but just one equation - so there are likely lots of different possible values for Z. Here are two possibilities:

X = 6.... so ($5000)(6/100) = $300
Z = $10,000 and Y = 6... so ($10,000)(6/100) = $600
And the answer to the question is $10,000

X = 6.... so ($5000)(6/100) = $300
Z = $20,000 and Y = 3... so ($20,000)(3/100) = $600
And the answer to the question is $20,000
Fact 1 is INSUFFICIENT

(2) Hannah invested the $5,000 at 6 percent simple annual interest.

The same two examples that I listed in Fact 1 also 'fit' Fact 2 (and create the same two different results):

X = 6.... so ($5000)(6/100) = $300
Z = $10,000 and Y = 6... so ($10,000)(6/100) = $600
And the answer to the question is $10,000

X = 6.... so ($5000)(6/100) = $300
Z = $20,000 and Y = 3... so ($20,000)(3/100) = $600
And the answer to the question is $20,000
Fact 2 is INSUFFICIENT

Combined, we have no additional work to do - the two examples we have already 'fit' both Facts and produce two different answers.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich