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

This topic has 5 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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On a certain date, Hannah invested $5,000 at x percent

Post Mon Jul 31, 2017 6:43 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    Post Mon Jul 31, 2017 11:30 am
    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

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    Post Mon Jul 31, 2017 9:27 pm
    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 have:

    $5000 invested @ the rate of x%, and a different sum, say $P invested @ the rate of y%.

    We have to find out the value of P.

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

    => [(5000*x*1)/100 + (P*y*1)/100] = 900

    There are three variables, we cannot get the value of P. Insufficient.

    Statement 2: Hannah invested the $5,000 at 6 percent simple annual interest.

    Clearly insufficient as this gives the value of x = 6%, but we cannot get the value of P. Insufficient.

    Statement 1 & 2 combined:

    From (1), we have

    [(5000*x*1)/100 + (P*y*1)/100] = 900

    Plugging-in the value of x = 6 from (2) cannot get us the unique value of P. Insufficient.

    The correct answer: E

    Hope this helps!

    Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

    -Jay
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    Post Mon Jul 31, 2017 9:28 pm
    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 have:

    $5000 invested @ the rate of x%, and a different sum, say $P invested @ the rate of y%.

    We have to find out the value of P.

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

    => [(5000*x*1)/100 + (P*y*1)/100] = 900

    There are three variables, we cannot get the value of P. Insufficient.

    Statement 2: Hannah invested the $5,000 at 6 percent simple annual interest.

    Clearly insufficient as this gives the value of x = 6%, but we cannot get the value of P. Insufficient.

    Statement 1 & 2 combined:

    From (1), we have

    [(5000*x*1)/100 + (P*y*1)/100] = 900

    Plugging-in the value of x = 6 from (2) cannot get us the unique value of P. Insufficient.

    The correct answer: E

    Hope this helps!

    Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Singapore | London | Dubai | and many more...

    Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

    Post Mon Jul 31, 2017 9:28 pm
    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 have:

    $5000 invested @ the rate of x%, and a different sum, say $P invested @ the rate of y%.

    We have to find out the value of P.

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

    => [(5000*x*1)/100 + (P*y*1)/100] = 900

    There are three variables, we cannot get the value of P. Insufficient.

    Statement 2: Hannah invested the $5,000 at 6 percent simple annual interest.

    Clearly insufficient as this gives the value of x = 6%, but we cannot get the value of P. Insufficient.

    Statement 1 & 2 combined:

    From (1), we have

    [(5000*x*1)/100 + (P*y*1)/100] = 900

    Plugging-in the value of x = 6 from (2) cannot get us the unique value of P. Insufficient.

    The correct answer: E

    Hope this helps!

    Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

    -Jay
    _________________
    Manhattan Review GMAT Prep

    Locations: New York | Singapore | London | Dubai | and many more...

    Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

    Post Wed Aug 09, 2017 11:25 am
    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

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