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motel

This topic has 1 expert reply and 2 member replies
Ankitaverma Senior | Next Rank: 100 Posts Default Avatar
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motel

Post Wed Nov 20, 2013 1:49 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    One night a certain motel rented 3/4 th of its rooms, including 2/3rd of its air-conditioned rooms. If 3/5th of its rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?
    (A) 20%
    (B) 33*1/3%
    (C) 35%
    (D) 40%
    (E) 80%

    Q/A-E

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    Post Wed Nov 20, 2013 2:39 pm
    Ankitaverma wrote:
    One night a certain motel rented 3/4 th of its rooms, including 2/3rd of its air-conditioned rooms. If 3/5th of its rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?
    (A) 20%
    (B) 33*1/3%
    (C) 35%
    (D) 40%
    (E) 80%
    This question is a great candidate for the Double Matrix method, whichcan be used for most questions featuring a population in which each member has two characteristics associated with it.

    Here, we have a population of motel rooms, and the two characteristics are:
    - air conditioning or no air conditioning
    - rented or not rented

    So, we can set up our matrix like this:
    ttp://postimg.org/image/4ag1zmx0f/" target="_blank">

    Now since we're asked to find a certain PERCENTAGE, let's choose a nice value for the total number of motel rooms.
    Notice that the question includes the fractions 3/4, 2/3 and 3/5. So, let's choose a number that works well with all of these fractions.
    Since 60 is the least common denominator of 3/4, 2/3 and 3/5, let's say that there are 60 motel rooms altogether.
    ttp://postimg.org/image/5fa450jhb/" target="_blank">

    Now that we're set up, we can use the given information to determine the number of rooms to place in each of the four boxes.

    If 3/5 of its rooms were air-conditioned
    So, 3/5 of the 60 rooms are air conditioned. 3/5 of 60 = 36, which means 36 rooms have AC and the remaining 24 rooms do not have AC...
    ttp://postimg.org/image/bexv8o49r/" target="_blank">

    ...motel rented 3/4 of its rooms
    3/4 of 60 = 45, so 45 rooms are rented and the remaining 15 rooms are not rented.
    ttp://postimg.org/image/x3wrcj6hr/" target="_blank">

    ...a certain motel rented ....2/3 of its air-conditioned rooms
    So of the 36 rooms with AC, 2/3 were rented.
    2/3 of 36 = 24. So, 24 rooms had AC AND were rented.
    ttp://postimg.org/image/56cjf36ov/" target="_blank">

    Now that we know the number of rooms in 1 box, and we know the sums of the rows and columns, we can fill in the remaining boxes.
    ttp://postimg.org/image/w2winepi7/" target="_blank">

    Question: what percent of the rooms that were not rented were air-conditioned?
    There were 15 unrented rooms and 12 of them were air conditioned.
    12/15 = 4/5 = 80% = E

    ---------------------------------------
    To learn more about the Double Matrix method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Then try these additional practice questions that can be solved using the Double Matrix Method:
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
    - http://www.beatthegmat.com/ds-quest-t187706.html
    - http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html
    - http://www.beatthegmat.com/sets-t269449.html#692540
    - http://www.beatthegmat.com/in-costume-for-halloween-t269355.html#692116

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    Brent

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    ganeshrkamath Master | Next Rank: 500 Posts
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    Post Wed Nov 20, 2013 7:36 pm
    Ankitaverma wrote:
    One night a certain motel rented 3/4 th of its rooms, including 2/3rd of its air-conditioned rooms. If 3/5th of its rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?
    (A) 20%
    (B) 33*1/3%
    (C) 35%
    (D) 40%
    (E) 80%

    Q/A-E
    Let T be the total number of rooms in the motel.
    Total number of air-conditioned rooms = (3/5)T

    The motel rented out (3/4)T rooms
    The motel did not rent out T/4 rooms.

    2/3 of its air-conditioned rooms were rented out = 2/3*3/5*T = (2/5)T
    1/3 of its air-conditioned rooms were not rented out = 1/3*3/5*T = (1/5)T

    Percentage of rooms not rented out and air-conditioned = ((1/5)T) / (T/4) * 100
    = 80%

    Choose E

    Cheers

    _________________
    Every job is a self-portrait of the person who did it. Autograph your work with excellence.

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    GMAT Score: 750 V40 Q51 AWA 5 IR 8
    http://www.beatthegmat.com/first-attempt-750-in-2-months-t268332.html#688494

    nikhilgmat31 Legendary Member Default Avatar
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    Post Thu Oct 08, 2015 2:13 am
    Question is pretty simple but including 2/3rd of its air-conditioned rooms statement is little complex.

    2/3 of rooms rented or 2/3 of AC rooms.

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