Data Sufficiency

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

Answer is B.
Can someone please explain? even if same dimensions, won't ratios be distorted with real numbers?

tutonaranjo wrote:
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

Answer is B.
Can someone please explain? even if same dimensions, won't ratios be distorted with real numbers?

1) The perimeter doesnt state anything about the length and breadth. So INSUFF

2) The three small rectangles have the same dimensions. It is also obvious in the figure that the length of one side of the smaller rectangle is twice the breadth. Hence we can insert figures like L=2 and B=1. So we get the larger rectangle length as 3 and breadth as 2. The proportion will always remain 2/3. Hence SUFF

Answer therefore B.

Hope this clears ur doubts.

got it.... could not see the length = 2edge
thanks!

The second statement is not clear.Also,how are you getting your answer on the basis of the diagram?Are'nt we supposed to NOT rely on it unless mentioned that the figure is according to scale??

I think picking numbers for Statement (2) makes the job easier.

same question as the guy before me:
"The second statement is not clear.Also,how are you getting your answer on the basis of the diagram?Are'nt we supposed to NOT rely on it unless mentioned that the figure is according to scale??"

Just assign numbers, as per your wish. You can get the ratio. You can assign two different sets of values yet get the same ratio.

Hence, (B).

alexdallas wrote:same question as the guy before me:
"The second statement is not clear.Also,how are you getting your answer on the basis of the diagram?Are'nt we supposed to NOT rely on it unless mentioned that the figure is according to scale??"

ok,,still confused about my question

Hmm.. maybe this will clear things up slightly. So the thing is, while we can't assume that diagrams are drawn to scale, we can definitely "assume" that intersections are held. ie, we know that KL and ML intersect at point L (as obvious as this may sound). Also, we know that there are intersections on the boundaries and one in the interior of the diagram.

There is honestly one way to draw the diagram (unless you're just a smart alec or something) such that the intersections are all made correctly and the dimensions are all correct.

If I were you, I would never just substitute numbers in for geometry problems (to solve the ENTIRE problem... if you're trying to find a counterexample, go for it!). Instead, I would set the shorter side to length a and the longer side to length b.

In this case, we see that length ML is of size 2a and length KN is of size b. So, b = 2 * a. Now, we are trying to find KN/MN = b / (a + b). Let's try and solve an easier problem..

If we knew MN/KN, we'd be okay.. just take the reciprocal! So, can we do this? Well,

MN/KN = (a+b)/b = (a/b) + 1

But b = 2a, so MN/KN = 3/2, so KN/MN = 2/3. Does this make sense? If this seems really contrived, let me know and I'll try to make it a bit less contrived.

maybe im the only one that doesnt get it

"In this case, we see that length ML is of size 2a ".
how do we know that the 2 segments that make up ML are equal?
It cannot be based on the image,,,then how do we deduce that?

tks...

alexdallas wrote:maybe im the only one that doesnt get it

"In this case, we see that length ML is of size 2a ".
how do we know that the 2 segments that make up ML are equal?
It cannot be based on the image,,,then how do we deduce that?

tks...

Try constructing an image where all the intersections hold and all dimensions are correct (I think you may be over-thinking this problem ). It's true that you can't assume that things aren't to scale in the GMAT, but in this case, you can see it as valid.

Hey Alex,

Even I too had a long struggle before figuring it out

Premise 2 clearly states that - "The three small rectangles have the same dimesion"

Now jus look into the diagram. For the top two parallel rectagles , it obvious that the length and breadth are equal.

Now for the the rectangle whose base is KN , the dimension is the addition breadth of the above two parallel rectangles. We can conclude from the premise that KN(length) = LM = 2 times (Breadth) of the smaller rectangles.

Simple things can even take long time in figuring it out...

Good that you kept repeatedly asking without settling seeing the figure. Its dangerous in GMAT to conclude answers from figures as they are not drawn to the scale !

alexdallas wrote:maybe im the only one that doesnt get it

"In this case, we see that length ML is of size 2a ".
how do we know that the 2 segments that make up ML are equal?
It cannot be based on the image,,,then how do we deduce that?

tks...

:roll: :roll: :roll: :roll: :roll: :roll: :roll: :roll: :roll:

uptowngirl92 wrote:The second statement is not clear.Also,how are you getting your answer on the basis of the diagram?Are'nt we supposed to NOT rely on it unless mentioned that the figure is according to scale??

You're 100% right - we never make assumptions in data sufficiency and we can't rely on diagrams unless we're explicitly given information.

However, 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.

KN/MN could be 1/3 or 2/3....

2) The 3 small rectangle have same dimension or L1*B1
Let Dimesion of LMNK be L*B
Area of LMNK = 3 times the small rect KN
L*B = 3 L1*B1
MN*KN = 3 KN*B1
MN = 3 B1
MN-B1 = KN
KN = 2 B1
KN/MN=2/3
Suff