Data Sufficiency

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OA: D

[spoiler]In the explanation given, the distance between the two circles (line OQ) is taken to be the radius of the circles. On eyeballing, yes it appears that circumference of circle Q goes through center point O (and vice-versa). But as this is not explicit (i think) in the question, isn't it wrong to assume that distance OQ is the radius?? [/spoiler]


Source: Knewton.

Hi,
I can give you solution with A
Using 14pi as circumference we can get radius = 7
Here you can see OP = OR = QP = QR = OQ = 7
Area of OPQR = 2* two equilateral triangles = 2* sqrt(3)/4 * 7^2 = 2* QRO

Using B :breath of rectangle = 2* radius of circle = (using area 294 = 2*7^2*3) = 2*7 && 3*7
breath should be small and interms of 2*x so 2*7...
Now you again got radius = 7 and area of OPQR = 2* QRO

Hope this helps... this is tough on a given day and took me 5min

Hi StuartM,

The distance OQ is indeed the radius, as per the definition of the circle - " collection of all the points having the same distance from the center" - since the Point O is on the circle Q and vice-versa the OQ is the radius.


Statement 1:
Circumference of the circle Q is 14PI= 2*r*PI
Hence, r=7

PQ=PR=OQ=7 (we know two side of the quadrilateral i.e. PQ & PR)

draw a line between O and Q which makes the isosceles triangle OPQ, we can find the length of the OP and hence OR

Sufficient

Statement 2:
Insufficient

IMO A

Thanks for the reply, guys.

But my question is how can we assume line OP = radius? While it looks like that's the case from the diagram, it cannot be assumed from the question/statements, can it?

I agree with OA and so do with diagram.. there is no statment "Not to scale" and need to identify the words

quadrilatreal == all four points PQRO are connected
a line from centre to circumference is radius...

Hope this helps

Thanks, HSPA.

But there is such a statement for all DS questions.

OG12, p268: "Be very careful not to make unwarranted assumptions based on the images represented. Figures are not necessarily drawn to scale."

StuartM wrote:Thanks for the reply, guys.

But my question is how can we assume line OP = radius? While it looks like that's the case from the diagram, it cannot be assumed from the question/statements, can it?

That's an interesting question and one that I asked in a previous post because the directions do not explicitly state that "if a point appears to be on a line it actually is on that line." But the general consensus was that that had to be assumed.

O is stated to be the center and also one vertex of the desired polygon. P is another vertex and appears to also lie on the circle with center O. Therefore, by definition, OP is a radius of circle O. But yes, you have to assume that the point is actually on the circle because it appears to be on the circle.

Thanks, Idoolitt.

I think i've found the post you're referring to: https://www.beatthegmat.com/assumptions- ... tml#351287

Seems messed up that in DS we have to evaluate whether an assumption is warranted or not (especially when a little statement saying so would completely remove any doubt). But I guess we're at the mercy of the GMAT Gods so just have to grin and bear it.

Thanks, Brent. Really helpful.

Still seems a bit arbitrary - that if you assume two lines are parallel in a DS question, you can (will most likely) get the question wrong, yet if you don't assume two assume lines intersect at an exact point, you also get the question wrong!

C'est la vie. I assume that the world won't end tomorrow and all my GMAT study won't have been in vain!

One little question: When the instructions say that the figures are not accurate to the scale, does it mean that they are illusive (meaning the point on the line is not actually on the line)?

The point is, even if the figure is not drawn to the scale, the point that has been shown on a particular line, should be on that line irrespective of the scale. So, why do we need to assume anything when it is given in the question?

Once we get the radius in the second statement, both the statements become one and the same. The answer: D

isanju wrote:One little question: When the instructions say that the figures are not accurate to the scale, does it mean that they are illusive (meaning the point on the line is not actually on the line)?

The point is, even if the figure is not drawn to the scale, the point that has been shown on a particular line, should be on that line irrespective of the scale. So, why do we need to assume anything when it is given in the question?

The instructions actually don't say that they are not accurate to scale. It just says "figures are drawn as accurately as possible." So, for example, we know it's not safe to assume two lines that appear parallel are actually parallel but it is safe to assume that if a point appears to be on a line that is actually on that line.

Its just weird GMAT quirkiness that you need to know for the test.

ldoolitt wrote:
The instructions actually don't say that they are not accurate to scale. It just says "figures are drawn as accurately as possible." So, for example, we know it's not safe to assume two lines that appear parallel are actually parallel but it is safe to assume that if a point appears to be on a line that is actually on that line.

Its just weird GMAT quirkiness that you need to know for the test.

For DS, the instructions Do say that diagrams are not drawn to scale. From the Official Guide (p24 of 12th ed.):

Figures:

Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight are straight, and lines that appear jagged are also straight.

The position of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Based on the first point, we know that DS diagrams are not necessarily drawn to scale and we can't rely on the way that they appear.

Based on the third point, we know that points exist in the order shown; so, if a point appears on a line, it must be on that line (otherwise how could it be in order?).

Further, contrast the first point to two additional things that we're explicitly told for problem solving (p.20, 12th ed. Official Guide):

All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible.

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Stuart Kovinsky wrote:
Based on the first point, we know that DS diagrams are not necessarily drawn to scale and we can't rely on the way that they appear.

Oh yeah, that is true for the statements in DS questions. I was more thinking of PS questions and the question stem in DS questions which that statement says "conforms to the information given in the question." That was my fault for making that unclear statement but I agree with that.

Stuart Kovinsky wrote: Based on the third point, we know that points exist in the order shown; so, if a point appears on a line, it must be on that line (otherwise how could it be in order?).

I dunno, maybe it means x coordinate in order or y coordinate in order. At best its a weak inference. Obviously inductively we know that all points that appear to be on a line are on a line, since I've never encountered a problem for which that isn't true (which I guess makes this discussion moot). But deductively from the instructions I don't see how that can be inferred.

The instructions are like a CR problem!