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

Question

https://gmatclub.com/forum/download/file.php?id=26830 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. ds.jpg 2015-06-05_1517.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=26830 
 What is the ratio KN/MN?

(1) The perimeter of rectangle KLMN is 30 meters. Clearly insufficient as numerous combinations of sides will make a perimeter of 30.

(2) The 3 small rectangles have the same dimensions --> let the shorter sides of small rectangles be  x  and longer side be  y , so  KN=LM=y  and  MN=x+y . Also two smaller sides add up to bigger side, so  x+x=2x=y  (LM, or KN, which is  y  equal to the sum of 2 shorter sides).  \frac{KN}{MN}=\frac{y}{x+y}=\frac{2x}{x+2x}=\frac{2}{3} . Sufficient.

Answer: B.

rxs0005 · Answer

ah ... right ...

thank you i missed that part where

"Also two smaller sides add up to bigger side"

EMPOWERgmatRichC · Answer

Hi All,

This is a great 'pattern-matching' question, and you can TEST VALUES to prove that the pattern exists.

Since this is a DS question, we can't trust that the picture is drawn to scale. While it certainly appears that the 3 smaller rectangles are the same size, we don't know that for sure.

We're asked for the ratio of KN to MN...

Fact 1: The perimeter of rectangle KLMN is 30 meters.

This gives us the dimensions of the larger rectangle, but we don't know the dimensions of its 2 sides.

IF...
KN = 3 and MN = 10, then the answer to the question is 3/10

IF...
KN = 5 and MN = 16, then the answer to the question is 5/6
Fact 1 is INSUFFICIENT

Fact 2: The three small rectangles have the same dimensions.

Now THIS is an interesting piece of information. Since the small rectangles are all exactly the same, we can see that in each of those smaller rectangles....TWICE the SHORT side = LONG side

IF...
Long side = 2 and Short side = 1, then the answer to the question is 2/3

IF...
Long side = 4 and Short side = 2, then the answer to the question is 4/6 = 2/3

IF...
Long side = 3 and Short side = 1.5, then the answer to the question is 3/4.5 = 2/3

The answer is ALWAYS 2/3
Fact 2 is SUFFICIENT

Final Answer:  B

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

anairamitch1804 · Answer

Statement (2) gives us a lot, including what we need to answer the question.

2) The three small rectangles have the same dimensions.

First, we now know that all 3 shapes are rectangles. Second, we know that they're identical rectangles.

Let's label all the short sides w and the long sides l.

From the diagram, we can now see that 2w is the same as l (since LM = KN), so we know the relationship between w and l.

So, let's go back to the original question:

What's KN/MN?

KN = l and MN = l + w

Subbing in l = 2w, we get:

KN = 2w and MN = 2w + w = 3w

and

KN/MN = 2w/3w = 2/3... sufficient.

tanvi9 · Answer

Can you please explain why is it not working for :
Long side= 1.5, short side =1. then the answer is 1.5/2.5=3/5 ? Am I missing something?

EMPOWERgmatRichC · Answer

Hi tanvi9,

Based on the information in Fact 2 - the 3 small rectangles are IDENTICAL, so if you add 2 "short sides", the total equals 1 "long side." In your example, you set a 'short side' = 1 and a 'long side' = 1.5.... but that does NOT fit what we were told (1.5 is NOT equal to 1+1).

IF....
you set the short side = 1, then the long side = 2
you set the long side = 1.5, then the short side = 0.75

With either of those examples, you'll end up with the same answer that I did (the answer to the question is still 2/3).

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

tanvi9 · Answer

Oh God

that was stupid! Thanks Rich!

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards