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ratio of rectangle sides

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Source: — Data Sufficiency |
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by Patrick_GMATFix » Sat Feb 08, 2014 9:45 am
statement 1 just tells us that 2(KN + MN) = 30. We can come up with a lot of values for KN and MN that would result in different ratios, so that statement is not helpful. Statement 2 is more interesting. If all the rectangles are the same, we can start to label sides using only two variables (for width and length) and perhaps even find out the ratio KN/MN. The full solution below is taken from the GMATFix App.

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by Brent@GMATPrepNow » Sat Feb 08, 2014 10:02 am
LulaBrazilia wrote:Image

In the figure above, what is the ratio KN/MN?

1) The perimeter of rectangle KLMN is 30 meters.

2) The three small rectangles have the same dimensions.
Target question: what is the ratio KN/MN?

Statement 1: The perimeter of rectangle KLMN is 30 meters.
This doesn't tell us much. Consider these two possible cases (among many)
case a:
Image
Here the ratio KN/MN = 1/14

case b:
Image
Here the ratio KN/MN = 7/8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The three small rectangles have the same dimensions.
Let x = length of shorter side of 1 rectangle:
Image

Since 3 rectangles have the same dimensions, we can add x to another side:
Image

Notice that that this means that side KN has length 2x.
Image

Since 3 rectangles have the same dimensions, we can add 2x to another side:
Image

At this point, we can see that side MN has length 3x
Image

From here, we can see that the ratio KN/MN = 2x/3x = 2/3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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