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 Author: EncounterGMAT [ 14 Nov 2018, 11:25 ] Post subject: The radius of a circle is r yards. Is the area of the circle at least The radius of a circle is r yards. Is the area of the circle at least r square yards? (1 yard = 3 feet)(1) The diameter of the circle is more than 2 feet.(2) If the radius of the same circle is f feet, the area of the circle is more than 2f square feet.

 Author: ShankSouljaBoi [ 14 Nov 2018, 12:06 ] Post subject: Re: The radius of a circle is r yards. Is the area of the circle at least Hirephrase--- pi*r^2 >= r or r>=(1/pi)yards or r>=(3/pi)ftA r>1 ft and 1 > 3/Pi Answer to question Yes. SufficientB r > 2/pi . Clearly Insufficient.A

 Author: uvwxyz [ 14 Nov 2018, 16:31 ] Post subject: Re: The radius of a circle is r yards. Is the area of the circle at least I don't understand this question.Could someone explain?

 Author: EncounterGMAT [ 15 Nov 2018, 05:59 ] Post subject: Re: The radius of a circle is r yards. Is the area of the circle at least yoyowei wrote:I don't understand this question.Could someone explain?Firstly notice what the question stem is asking for. Is πr^2 ≥ r? [ Note: π=pi]We can simplify it more. πr ≥ 1 => Is r ≥ 1/π? The question is stated in yards, but the statements use feet, so we'll have to convert them. Given: 1 Yard= 2 FeetThus, r ≥ 3/π (now it's in feet)The value of 3/π is approximately$$\frac{3}{3.14}$$ which is around 0.955, i.e., a little less than 1, so we'll consider it as 1.So ultimately, we need to find whether r≥1?(1) Given: Diameter>2 feet => 2r>2 =>r>1 SUFFICIENT(2) Given: r=2ft and πr^2 > 2fSimplify πf^2 > 2f f > 2/πf > 2/3.14 (~0.65) f could be smaller than 3/π feet, i.e, 1 but it could also be larger. Nothing about f is mentioned in the question if you notice. INSUFFICIENTI hope you'll get it now.

 Author: fskilnik [ 16 Nov 2018, 07:09 ] Post subject: The radius of a circle is r yards. Is the area of the circle at least topper97 wrote:The radius of a circle is r yards. Is the area of the circle at least r square yards? (1 yard = 3 feet)(1) The diameter of the circle is more than 2 feet.(2) If the radius of the same circle is f feet, the area of the circle is more than 2f square feet.This is MUCH harder than I expected. Excellent question (kudos)!$$\pi {r^2}\,\,\mathop \ge \limits^? \,\,\,r\,\,\,\,\left[ {{\rm{yard}}{{\rm{s}}^{\rm{2}}}} \right]\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{r\,\, > \,\,0} \,\,\,\,\,\,\,\pi r\,\,\,\mathop \ge \limits^? \,\,\,1\,\,\,\,\,\left[ {{\rm{yards}}} \right]$$$$\left( 1 \right)\,\,\,2r\,\,{\rm{yards}}\,\,\, > \,\,\,2\,\,{\rm{ft}}\,\,\left( {{{\,1\,\,{\rm{yard}}\,} \over {3\,\,{\rm{ft}}}}} \right)\,\,\,\,\,\,\left[ {{\rm{yards}}} \right]\,\,\,\,\,\, \Leftrightarrow \,\,\,\,r > \,\,{1 \over 3}\,\,\,\,\left[ {{\rm{yards}}} \right]\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{ \cdot \,\,\pi } \,\,\,\,\,\,\pi r > 1\,\,\,\,\,\left[ {{\rm{yards}}} \right]\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle$$$$\left( 2 \right)\,\,\,\pi {f^2}\,\, > \,\,2f\,\,\,\,\left[ {{\rm{fee}}{{\rm{t}}^{\rm{2}}}} \right]\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{f\,\, > \,\,0} \,\,\,\,\,\pi f > 2\,\,\,\,\,\,\left[ {{\rm{feet}}} \right]\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\pi f\,\,{\rm{ft}}\,\,\,\left( {{{\,1\,\,{\rm{yard}}\,} \over {3\,\,{\rm{ft}}}}} \right) > \,\,\,2\,\,\,\left( {{{\,1\,\,{\rm{yard}}\,} \over {3\,\,{\rm{ft}}}}} \right)\,\,\,\,\,\,\left[ {{\rm{yard}}} \right]\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,{{\pi f} \over 3} > {2 \over 3}\,\,\,\,\left[ {{\rm{yard}}} \right]$$$${{\pi f} \over 3} > {2 \over 3}\,\,\,\,\left[ {{\rm{yard}}} \right]\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{r\,\, = \,\,{f \over 3}\,\,!!} \,\,\,\,\,\pi r > {2 \over 3}\,\,\,\,\left[ {{\rm{yard}}} \right]\,\,\,\,\,\,\,\,\,\left\{ \matrix{\\ \,{\rm{Take}}\,\,\pi r = {3 \over 4}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\ \,{\rm{Take}}\,\,\pi r = 1\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.

 Author: GMATGuruNY [ 03 Apr 2020, 10:51 ] Post subject: Re: The radius of a circle is r yards. Is the area of the circle at least EncounterGMAT wrote:The radius of a circle is r yards. Is the area of the circle at least r square yards? (1 yard = 3 feet)(1) The diameter of the circle is more than 2 feet.(2) If the radius of the same circle is f feet, the area of the circle is more than 2f square feet.Statement 1:Test the threshold value: d = 2 feet, implying that r = 1 foot = $$\frac{1}{3}$$ yardCase 1: $$r = \frac{1}{3}$$ yardIn this case, area $$= πr^2 = π(\frac{1}{3})^2 = \frac{π}{9} =$$ more than $$\frac{1}{3}$$square yardSince the area is greater than r square yards. the answer to the question stem is YES.Test a greater value: d = 6 feet, implying that r = 3 feet = 1 yardCase 2: r = 1 yardIn this case, area $$= πr^2 = π1^2 = π =$$ more than 3 square yardsSince the area is greater than r square yards. the answer to the question stem is YES.Since the answer is YES whether r is at or above the threshold, SUFFICIENT.Statement 2:Since the circle has a radius of f feet, the area of the circle is $$πf^2$$ square feet.Since the area must be greater than 2f, we get:$$πf^2 > 2f$$$$πf > 2$$$$f > \frac{2}{π}$$Here, the radius must be greater than $$\frac{2}{π}$$ feet.Case 1 also satisfies Statement 2.In Case 1, the answer to the question stem is YES.Case 3: $$r = \frac{2}{3}$$ feet = $$\frac{2}{9}$$ yardIn this case, area $$= πr^2 = π(\frac{2}{9})^2 = \frac{4}{81}π =$$ less than 2/9 square yardSince the area is LESS than r square yards. the answer to the question stem is NO.Since the answer is YES in Case 1 but NO in Case 3, INSUFFICIENT.

 Author: bumpbot [ 21 Jan 2023, 06:45 ] Post subject: Re: The radius of a circle is r yards. Is the area of the circle at least 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.

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