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Perimeter

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sparkles3144 Really wants to Beat The GMAT! Default Avatar
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Perimeter Post Fri May 10, 2013 2:07 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    A rectangle has a perimeter of 28 inches. What are the dimensions of the rectangle?

    (1) The area of the rectangle is 40 inches squared.

    (2) The length is 6 inches more than the width

    I know how to solve this.
    However, I am wondering if I can assume that l and w are integers.
    It is not stated.

    Thanks!

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    Post Fri May 10, 2013 2:20 pm
    sparkles3144 wrote:
    A rectangle has a perimeter of 28 inches. What are the dimensions of the rectangle?

    (1) The area of the rectangle is 40 inches squared.

    (2) The length is 6 inches more than the width

    I know how to solve this.
    However, I am wondering if I can assume that l and w are integers.
    It is not stated.

    Thanks!
    No, we cannot assume that the lengths are integers.
    Here's one solution:

    Target question: What are the dimensions of the rectangle?

    Given: A rectangle has a perimeter of 28 inches.
    Let L = length of rectangle
    Let W = width of rectangle

    If the perimeter is 28, then 2L + 2W = 28
    We can simplify this by dividing both sides by 2 to get: L + W = 14

    Statement 1: The area of the rectangle is 40 inches squared.
    In other words, LW = 40

    Since we already know that L + W = 14, we can solve for W to get W = 14 - L
    Now take the equation LW = 40, and replace W with (14 - L) to get . . .
    L(14 - L) = 40
    Expand: 14L - L^2 = 40
    Rearrange to get: L^2 - 14L + 40 = 0
    Factor: (L - 4)(L - 10) = 0
    So, L = 4 or 10

    If L = 4, then W = 10, which means the dimensions are 4 by 10
    If L = 10, then W = 4, which means the dimensions are still 4 by 10
    In other words, the the dimensions must be 4 by 10
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: The length is 6 inches more than the width
    In other words, L = W + 6

    Since we already know that L + W = 14, we can solve for W to get W = 14 - L
    Now take the equation L = W + 6, and replace W with (14 - L) to get . . .
    L = (14 - L) + 6
    Rearrange: 2L = 20
    Solve: L = 10
    If L = 10, then W = 4, which means the dimensions are 4 by 10
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer = D

    Cheers,
    Brent

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    Post Fri Apr 01, 2016 10:13 am
    Hello Together,

    Please clarify as I believe answer should be option B not D because When solve statement 1 we get 2 values of W and L i.e when l = 10 then W = 4 and when W = 4 then l =10 since this statement does lock L and W to have one particular value I believe it is insufficient and Option B should be the right choice.

    Please reply as I am in too much of a fix

    Post Fri Apr 01, 2016 10:21 am
    Rohit_Prakash88@yahoo.in wrote:
    Hello Together,

    Please clarify as I believe answer should be option B not D because When solve statement 1 we get 2 values of W and L i.e when l = 10 then W = 4 and when W = 4 then l =10 since this statement does lock L and W to have one particular value I believe it is insufficient and Option B should be the right choice.

    Please reply as I am in too much of a fix
    Yes, we do get two different values for W (W = 4 or W = 10).
    However, the target question does not ask us to determine the value of W. The target question asks us to determine the dimensions of the rectangle.
    A rectangle with dimensions 4 x 10 is identical to a rectangle with dimensions 10 x 4

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our free video course along with Beat The GMAT's free 60-Day Study Guide

    GMAT Prep Now's 35-hour (500+ videos) course is 100% FREE. Use our free course in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Fri Apr 01, 2016 10:24 am
    Thanks a lot Smile . A key point I missed out and was scratching my head .. Thanks a lot for your guidance again

    Gurpreet singh Rising GMAT Star Default Avatar
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    Post Thu Jun 09, 2016 6:10 pm
    Hi Brent,

    In case the question stem had asked for the length instead of dimension will the statement 1 still be sufficient? since we are getting 2 values.
    Thanks
    Gurpreet


    Brent@GMATPrepNow wrote:
    sparkles3144 wrote:
    A rectangle has a perimeter of 28 inches. What are the dimensions of the rectangle?

    (1) The area of the rectangle is 40 inches squared.

    (2) The length is 6 inches more than the width

    I know how to solve this.
    However, I am wondering if I can assume that l and w are integers.
    It is not stated.

    Thanks!
    No, we cannot assume that the lengths are integers.
    Here's one solution:

    Target question: What are the dimensions of the rectangle?

    Given: A rectangle has a perimeter of 28 inches.
    Let L = length of rectangle
    Let W = width of rectangle

    If the perimeter is 28, then 2L + 2W = 28
    We can simplify this by dividing both sides by 2 to get: L + W = 14

    Statement 1: The area of the rectangle is 40 inches squared.
    In other words, LW = 40

    Since we already know that L + W = 14, we can solve for W to get W = 14 - L
    Now take the equation LW = 40, and replace W with (14 - L) to get . . .
    L(14 - L) = 40
    Expand: 14L - L^2 = 40
    Rearrange to get: L^2 - 14L + 40 = 0
    Factor: (L - 4)(L - 10) = 0
    So, L = 4 or 10

    If L = 4, then W = 10, which means the dimensions are 4 by 10
    If L = 10, then W = 4, which means the dimensions are still 4 by 10
    In other words, the the dimensions must be 4 by 10
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: The length is 6 inches more than the width
    In other words, L = W + 6

    Since we already know that L + W = 14, we can solve for W to get W = 14 - L
    Now take the equation L = W + 6, and replace W with (14 - L) to get . . .
    L = (14 - L) + 6
    Rearrange: 2L = 20
    Solve: L = 10
    If L = 10, then W = 4, which means the dimensions are 4 by 10
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer = D

    Cheers,
    Brent

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    Post Fri Jun 10, 2016 9:56 am
    Gurpreet singh wrote:
    Hi Brent,

    In case the question stem had asked for the length instead of dimension will the statement 1 still be sufficient? since we are getting 2 values.
    Thanks
    Gurpreet
    If I remember correctly, the GMAT actually considers the length to be the longer side of the rectangle. (I learned this the hard way, doing an OG problem back in 2009 when I was studying for the test; I was quite surprised.) I had never heard this anywhere before, so I'm still skeptical, but I'm quite sure I remember an OG DS problem that turned on this.

    By their logic, then, if I tell you I have a rectangle with dimensions 10 and 4, the length MUST be 10 and the width MUST be 4.

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    Post Fri Jun 10, 2016 10:15 am
    Matt@VeritasPrep wrote:
    Gurpreet singh wrote:
    Hi Brent,

    In case the question stem had asked for the length instead of dimension will the statement 1 still be sufficient? since we are getting 2 values.
    Thanks
    Gurpreet
    If I remember correctly, the GMAT actually considers the length to be the longer side of the rectangle. (I learned this the hard way, doing an OG problem back in 2009 when I was studying for the test; I was quite surprised.) I had never heard this anywhere before, so I'm still skeptical, but I'm quite sure I remember an OG DS problem that turned on this.

    By their logic, then, if I tell you I have a rectangle with dimensions 10 and 4, the length MUST be 10 and the width MUST be 4.
    Now I'm intrigued - Matt, do you know which edition of the OG that question shows up in? (I'm assuming it's 10th or earlier.)

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