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OG 2017 Ratio Question

This topic has 3 expert replies and 1 member reply
mv2019 Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
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OG 2017 Ratio Question

Post Wed Jul 13, 2016 10:14 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The only articles of clothing in a certain closet are shirts, dresses, and jackets. The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively. If there are more than 7 dresses in the closet, what is the total number of articles of clothing in the closet?

    (1) The total number of shirts and jackets in the closet is less than 30.

    (2) The total number of shirts and dresses in the closet is 26.

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    Post Wed Jul 13, 2016 10:24 am
    mv2019 wrote:
    The only articles of clothing in a certain closet are shirts, dresses, and jackets. The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively. If there are more than 7 dresses in the closet, what is the total number of articles of clothing in the closet?

    (1) The total number of shirts and jackets in the closet is less than 30.

    (2) The total number of shirts and dresses in the closet is 26.
    Number of shirts: 9x
    Number of dresses: 4x
    Number of jackets: 5x
    Total articles of clothing: 18x


    If there are more than 7 dresses, and the number of dresses is 4x, we know that x must be at least 2, giving us a minimum of 8 dresses. To the statements!

    S1: we know that 9x + 5x < 30, or that 14x < 30. We also know that x cannot be 1, as we'd have fewer than 7 dresses in that scenario. Therefore x must be 2. (If x = 3, then 14x would not be less than 30.) Total articles of clothing = 18*2 = 36. Sufficient.

    S2: 9x + 4x = 26. 13x = 26. x = 2. Same information. This is also sufficient. The Answer is D.

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    Danny@GMATAcademy Junior | Next Rank: 30 Posts Default Avatar
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    Post Wed Jul 13, 2016 10:32 am
    Here's a video explanation for this question: https://www.youtube.com/watch?v=5iFLsVP2MO0


    For more on the method used in the video above, see the videos below:

    Intro to the chart method for ratios: https://www.youtube.com/watch?v=WfHm5SF95vU
    Using the ratio chart in Data Sufficiency: https://www.youtube.com/watch?v=MA686n6S4z8

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    Thanked by: mv2019
    Post Wed Jul 13, 2016 11:33 am
    Hi mv2019,

    This DS question can be solved rather easily with a bit of 'brute force' and some simple arithmetic. To start, it's worth noting that you CANNOT have a 'fraction' of a piece of clothing. We're told that the ratio of shirts:dresses:jackets is 9:4:5, so the number of shirts MUST be a multiple of 9, the number of dresses MUST be an equivalent multiple of 4 and the number of jackets MUST be an equivalent multiple of 5. I'm going to put together a quick list of the first few potential possibilities...

    There COULD be...
    9 shirts/4 dresses/5 jackets
    18 shirts/8 dresses/10 jackets
    27 shirts/12 dresses/15 jackets
    36 shirts/16 dresses/20 jackets
    Etc.

    We're also told that there are MORE than 7 dresses. We're asked for the total number of articles of clothing.

    (1) The total number of shirts and jackets in the closet is less than 30.

    With this Fact, we can look at our notes and find whatever options fit this information (AND include MORE than 7 dresses). There's only one...

    18 shirts/8 dresses/10 jackets
    Fact 1 is SUFFICIENT.

    (2) The total number of shirts and dresses in the closet is 26.

    With this Fact, we can again look at the available options. There's only one...

    18 shirts/8 dresses/10 jackets
    Fact 2 is SUFFICIENT.

    Final Answer: D

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

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    Post Fri Jul 22, 2016 2:04 am
    S1:

    We know that Shirts + Jackets = 9*(some integer) + 5*(some integer) = 14*(some integer)

    Since this number < 30, we must have 14 or 28. But if we only have 14, then we'd have 4 dresses (ratio 9 : 4 : 5) ... and we've got more than 4 dresses! So the only possibility is 28, with 8 dresses and a ratio of 18 : 8 : 10. SUFFICIENT

    S2:

    Similar to the above, we'd have 9*some integer + 4*some integer = 26, so "some integer" = 2, and we're set: we know that the ratio multiplier is 2. SUFFICIENT

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