what is the value of t?

Question

In the figure,if POQ is 90deg.then what is the value of t? 1. The value of r is -root3 2. The y-coordinate of point P is 1

raghavsarathy · Answer

Statement 1 is insufficient because we are not told that the Y coordinate bisects angle O. Hence the value of T depends on the degree to which the triangle is tilted w.r.t the x axis.

Statement 2 is insufficient as we do not know the value of r.

Combining both statements. Drop a perpendicular to the x axis from P. We will know that the angle mad eby PO with x - axis = tan(x) = 1/sqrt(3)
Angle = 30

Angle made by PO witb Y - axis = 60

Not able to proceed after this. Help !

gmat740 · Answer

Please refer to the fig.

We know tanx = y-c0ordinate/x-c0ordinate

so here we get , 1/sq-rt(3) = tan 30 => x = 30(shown in fig)

now we have been given POQ is 90 and the entire fig is enclosed in a semi-cirle => total angle = 180
so we can find angle QOk = 60

Now again in triangle QOK,

We have tan 60 =sq-rt(3)/1 = y-coordinate/x-coordinate

so y-coordinate =u = sq-rt(3)
x-coordinate = t = 1

So OA => C
Apologizes for my horrible drawing skills

Hope this Helps.

raghavsarathy · Answer

Hi Karan

In your soln you have considered the value of u 1.

But how did you arrive at that ?

The lines PO and OQ subtend different angles with the X- axis. Hence we cannot consider the y-coordinate of point P and y-coordinate of point Q same.

gmat740 · Answer

raghavsarathy wrote:Hi Karan

In your soln you have considered the value of u 1.

But how did you arrive at that ?

The lines PO and OQ subtend different angles with the X- axis. Hence we cannot consider the y-coordinate of point P and y-coordinate of point Q same.

No, Raghav, I did not assume anything.

Look, the angle QOK = 60
and tan 60 = Y-coordinate/X-coordinate
And tan 60 = sq-rt(3) = sq-rt(3)/1

so we have a simple ratio
and correspondingly, sq-rt(3) = Y-cordinate
and 1 = X-cordinate

Hope this helps

raghavsarathy · Answer

gmat740 wrote:
and tan 60 = Y-coordinate/X-coordinate
And tan 60 = sq-rt(3) = sq-rt(3)/1

Hi Karan
Sorry to ge this topic again.. How do you know that the value of X-coordinate is 1 (The highlighted part)? It is not mentioned anywhere.

gmat740 · Answer

raghavsarathy wrote:gmat740 wrote: and tan 60 = Y-coordinate/X-coordinate And tan 60 = sq-rt(3) = sq-rt(3)/1 Hi Karan Sorry to ge this topic again.. How do you know that the value of X-coordinate is 1 (The highlighted part)? It is not mentioned anywhere. It is a simple ratio. So if the denominator is 1(X-coordinate), then the numerator will be sq-rt(3) However, since it is a ration, can always say that X-coordinate(denominator) can be 2. I would agree to that, only if the numerator becomes 2 times sq-rt(3). Becoz we have to keep the ratio of Numerator/denominator = Sq-rt(3) I took the simple ratio and got 1= denominator. lets say that there are two answers given which are x=1 and x=2, so now which one would you choose?? If you look P(r,s).The distance between P and O(center) = 2(there is formula for calculating distance between 2 points whose whose coordinates are given, I am not going into that detail) distance between P and O(center) is actually radius.So the max value of x-coordinate on the positive X side(Q-side) will be 2. However, when X=2, Y-coordinate =0. But we know the simple ratio has to be sq-rt(3). So definitely x=2 is not the answer. Hope this long post clears all your doubts

pandeyvineet24 · Answer

I think the Answer is D.

Both the statements are providing similar information. One provides the X corodinate of point P and other statement describes the Y coordinate of point P.

in both cases we can determine angle QOK as 60 degrees and the semicircle with a radius of 2.

yogami · Answer

I think the question is messed up. How do you guys assume that that is a semi-circle? If it was given that it was a semi circle then C is correct otherwise its E

vyomb · Answer

my answer is C. Pls confirm the OA.

gmat740 · Answer

pandeyvineet24 wrote:I think the Answer is D.

Both the statements are providing similar information. One provides the X corodinate of point P and other statement describes the Y coordinate of point P.

in both cases we can determine angle QOK as 60 degrees and the semicircle with a radius of 2.

I would love to know how will you get the same info using one of the statement.I would be glad to see the working.

I think the question is messed up. How do you guys assume that that is a semi-circle? If it was given that it was a semi circle then C is correct otherwise its E

Question is not at all messed up. In the figure It is clear that it is semi-circle.
On GMAT DAY if you find a closed fig. made with 3 closed lines and you say that the question never says anything,these 3 lines could make a Square

Then you will find your Quant score Very very High!

There are certain minor things which you have to assume by looking at the fig. and this is a semi-circle, you have to assume(untill and unless it doesnt look like a circle!

)

my answer is C.

Pls confirm the OA.

I am not the poster of this question but still I would say the OA is C. This is a GMAT prep Question.

Hope this Helps

pandeyvineet24 · Answer

gmat740 wrote:pandeyvineet24 wrote:I think the Answer is D. Both the statements are providing similar information. One provides the X corodinate of point P and other statement describes the Y coordinate of point P. in both cases we can determine angle QOK as 60 degrees and the semicircle with a radius of 2. I would love to know how will you get the same info using one of the statement.I would be glad to see the working. Karan, i know where i messed it up. The answer should be C. I assumed something which i should not have. my bad

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