On a certain date, Hannah invested $5,000 at x percent

Question

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.

Official Guide question
Answer: E

Rich.C@EMPOWERgmat.com · Answer

Hi jjjinapinch,

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

Contact Rich at [email protected]

Jay@ManhattanReview · Answer

jjjinapinch 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.

Official Guide question
Answer: E

We are given that Hannah invested $5,000 at x percent simple annual interest and invested another amount at y percent simple annual interest. We need to determine the amount that she invested at y percent simple annual interest. We can let this amount be n.

Statement One Alone:

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

Using statement one, we can set up the following equation:

5,000(x/100) + n(y/100) = 900

Multiplying the entire equation by 100, we have:

5,000x + ny = 90,000

Since we do not know the value of x or y, we cannot determine the value of n, and thus statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

From statement two, we know that x is 6, and thus we can determine how much interest Hannah made from her investment at x percent interest.

5,000 x 6/100 = $300

However, we still do not know how much money was invested at y percent simple annual interest. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From both statements, we have the following equation:

300 + n(y/100) = 900

Since we do not know the value of y, we still cannot determine a value for n.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Jay@ManhattanReview · Answer

jjjinapinch 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.

Official Guide question
Answer: E

We are given that Hannah invested $5,000 at x percent simple annual interest and invested another amount at y percent simple annual interest. We need to determine the amount that she invested at y percent simple annual interest. We can let this amount be n.

Statement One Alone:

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

Using statement one, we can set up the following equation:

5,000(x/100) + n(y/100) = 900

Multiplying the entire equation by 100, we have:

5,000x + ny = 90,000

Since we do not know the value of x or y, we cannot determine the value of n, and thus statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

From statement two, we know that x is 6, and thus we can determine how much interest Hannah made from her investment at x percent interest.

5,000 x 6/100 = $300

However, we still do not know how much money was invested at y percent simple annual interest. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From both statements, we have the following equation:

300 + n(y/100) = 900

Since we do not know the value of y, we still cannot determine a value for n.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Jay@ManhattanReview · Answer

jjjinapinch 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.

Official Guide question
Answer: E

We are given that Hannah invested $5,000 at x percent simple annual interest and invested another amount at y percent simple annual interest. We need to determine the amount that she invested at y percent simple annual interest. We can let this amount be n.

Statement One Alone:

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

Using statement one, we can set up the following equation:

5,000(x/100) + n(y/100) = 900

Multiplying the entire equation by 100, we have:

5,000x + ny = 90,000

Since we do not know the value of x or y, we cannot determine the value of n, and thus statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

From statement two, we know that x is 6, and thus we can determine how much interest Hannah made from her investment at x percent interest.

5,000 x 6/100 = $300

However, we still do not know how much money was invested at y percent simple annual interest. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From both statements, we have the following equation:

300 + n(y/100) = 900

Since we do not know the value of y, we still cannot determine a value for n.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Jeff@TargetTestPrep · Answer

jjjinapinch 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.

Official Guide question
Answer: E

We are given that Hannah invested $5,000 at x percent simple annual interest and invested another amount at y percent simple annual interest. We need to determine the amount that she invested at y percent simple annual interest. We can let this amount be n.

Statement One Alone:

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

Using statement one, we can set up the following equation:

5,000(x/100) + n(y/100) = 900

Multiplying the entire equation by 100, we have:

5,000x + ny = 90,000

Since we do not know the value of x or y, we cannot determine the value of n, and thus statement one alone is not sufficient to answer the question.

Statement Two Alone:

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

From statement two, we know that x is 6, and thus we can determine how much interest Hannah made from her investment at x percent interest.

5,000 x 6/100 = $300

However, we still do not know how much money was invested at y percent simple annual interest. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From both statements, we have the following equation:

300 + n(y/100) = 900

Since we do not know the value of y, we still cannot determine a value for n.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

On a certain date, Hannah invested $5,000 at x percent

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER