To calculate the area of the garden, given the ratios

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon Mar 17, 2014 10:36 pm

Hello,

Can you please tell me if my solution is correct here:

The ratio of the length of rectangular garden A to its width is 3:2. The length and width of rectangular garden B have the same ratio as the length and width of garden A. If garden A has perimeter 30, which is half the perimeter of garden B, what is the area of garden B?

(A) 27
(B) 54
(C) 108
(D) 216
(E) 864

OA: D

I tried to solve this as follows:

For Garden A: length/width = 3/2 = 3x/2x

Perimeter of Garden A = 30 => 30 = 2( 3x + 2x )
=> 30 = 2 (5x)
=> 30 = 10x
=> x = 3

Hence, length of Garden A = 3x = 3(3) = 9
and width of Garden A = 2x = 2(3) = 6

Perimeter of Garden B = 60. I was a bit confused about the ratio of the length and width of Garden B.

Is it correct here to take length/width = 3y/2y ?
=> 60 = 2 ( 3y + 2y )
=> 60 = 2 ( 5y )
=> y = 6

Hence, Area of garden B = (3y)(2y) = (3.6)(2.6) = 18.12 = 216

I am just wondering if the information about Garden A is even needed here since we aren't really using it in our calculations? We just need the ratio information i.e. 3:2 and the perimeter. Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Problem Solving | Mon Mar 17, 2014 10:36 pm

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Mar 17, 2014 11:32 pm

Your logic (and steps) are correct!

We do "need" the information about Garden A, however. To get the area of Garden B, we "need" to know the length and width of the garden. (There are other ways, but this seems to be the easiest way here.) Without the sides of Garden A and the relationship between Garden A and Garden B, we wouldn't have the lengths of the Garden B, so we couldn't otherwise solve the problem.

You're right that are probably more straightforward ways to write the question, but the testwriters can make the process long and awkward if they so choose

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Mar 18, 2014 8:09 pm

Hi Sri,

The GMAT Quant section will include many "story problems" as a way to test your ability to take information and re-organize it. The math involved in these questions won't necessarily be "hard" (and sometimes it will be really easy). Here's a way to approach this question that might help you to avoid some of the longer math steps.

We're told two facts about rectangle A:

1) The ratio of the length to the width is 3:2

L:W
3:2

2) The perimeter = 30

2L + 2W = 30
L + W = 15

From the first fact, we know that the Length is a multiple of 3 and the Width is the same multiple of 2. This means...

L=9 and W=6

Next, we're told that the length to width in rectangle B is ALSO 3:2. This is convenient info, since the last fact offered is that the perimeter of rectangle A is HALF the perimeter of rectangle B.

All we have to do is DOUBLE the side lengths to double the perimeter (and to get the dimensions for rectangle B):

L=18 and W=12

The area of garden B is D

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

Contact Rich at [email protected]

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Mar 19, 2014 9:30 am

gmattesttaker2 wrote:If garden A has perimeter 30, which is half the perimeter of garden B, what is the area of garden B?

Perimeter of Rectangle A - 30

Perimeter of Rectangle B - 60

gmattesttaker2 wrote:The ratio of the length of rectangular garden A to its width is 3:2.

Let the length and breadth be 3x and 2x

So, 30 = 2( 2x + 3x)

Or, 10x = 30

Or, x =3

So Sides of Rectangle A are -

Length = 9

Breadth = 6

The length and width of rectangular garden B have the same ratio as the length and width of garden A.

Let's assume Length of Rectangle B is 3x and Breadth be 2x

So , 60 = 2(3x + 2x)

Or, 60 = 10x

Or, x = 6

Hence Length of Rectangle B is = 18 and Breadth = 12

Area of Rectangle B = Length X Breadth => 12 * 18 = 216

So answer is (D)

PS: This problem is just like a jig saw Puzzle , you gotta arrange the pieces accordingly.

Abhishek

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Wed Mar 19, 2014 9:43 pm

Matt@VeritasPrep wrote:Your logic (and steps) are correct!

We do "need" the information about Garden A, however. To get the area of Garden B, we "need" to know the length and width of the garden. (There are other ways, but this seems to be the easiest way here.) Without the sides of Garden A and the relationship between Garden A and Garden B, we wouldn't have the lengths of the Garden B, so we couldn't otherwise solve the problem.

You're right that are probably more straightforward ways to write the question, but the testwriters can make the process long and awkward if they so choose

Hello Matt,

Thanks a lot for the explanation and for the clarification.

Best Regards,
Sri

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Wed Mar 19, 2014 9:44 pm

[email protected] wrote:Hi Sri,

The GMAT Quant section will include many "story problems" as a way to test your ability to take information and re-organize it. The math involved in these questions won't necessarily be "hard" (and sometimes it will be really easy). Here's a way to approach this question that might help you to avoid some of the longer math steps.

We're told two facts about rectangle A:

1) The ratio of the length to the width is 3:2

L:W
3:2

2) The perimeter = 30

2L + 2W = 30
L + W = 15

From the first fact, we know that the Length is a multiple of 3 and the Width is the same multiple of 2. This means...

L=9 and W=6

Next, we're told that the length to width in rectangle B is ALSO 3:2. This is convenient info, since the last fact offered is that the perimeter of rectangle A is HALF the perimeter of rectangle B.

All we have to do is DOUBLE the side lengths to double the perimeter (and to get the dimensions for rectangle B):

L=18 and W=12

The area of garden B is D

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

Hello Rich,

Thanks a lot for the explanation and for your detailed solution.

Best Regards,
Sri

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Mar 21, 2014 4:53 am

gmattesttaker2 wrote:Hello,

Can you please tell me if my solution is correct here:

The ratio of the length of rectangular garden A to its width is 3:2. The length and width of rectangular garden B have the same ratio as the length and width of garden A. If garden A has perimeter 30, which is half the perimeter of garden B, what is the area of garden B?

(A) 27
(B) 54
(C) 108
(D) 216
(E) 864

Garden B:
p = 60 (twice A's perimeter).
L:W = 3:2 (same as A's ratio).

If L=3 and W=2, p = 3+2+3+2 = 10.
Since the actual perimeter (60) is 6 times as great, L and W each must increase by a factor of 6:
L = 6*3 = 18.
W = 6*2 = 12.
Area = 18*12 = 216.

The correct answer is D.

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