GMAT Club Forum https://gmatclub.com:443/forum/ 

The radius of a circle is r yards. Is the area of the circle at least https://gmatclub.com/forum/theradiusofacircleisryardsistheareaofthecircleatleast281620.html 
Page 1 of 1 
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 
Hi rephrase pi*r^2 >= r or r>=(1/pi)yards or r>=(3/pi)ft A r>1 ft and 1 > 3/Pi Answer to question Yes. Sufficient B 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 Feet Thus, 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 > 2f Simplify πf^2 > 2f f > 2/π f > 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. INSUFFICIENT I 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 = \(\frac{1}{3}\) yard Case 1: \(r = \frac{1}{3}\) yard In this case, area \(= πr^2 = π(\frac{1}{3})^2 = \frac{π}{9} =\) more than \(\frac{1}{3} \)square yard Since 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 yard Case 2: r = 1 yard In this case, area \(= πr^2 = π1^2 = π =\) more than 3 square yards Since 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 = \(\frac{2}{9}\) yard In this case, area \(= πr^2 = π(\frac{2}{9})^2 = \frac{4}{81}π =\) less than 2/9 square yard Since 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. 
Page 1 of 1  All times are UTC  8 hours [ DST ] 
Powered by phpBB © phpBB Group http://www.phpbb.com/ 