February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 7334

If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
Updated on: 29 Nov 2017, 20:12
Question Stats:
44% (01:21) correct 56% (01:18) wrong based on 70 sessions
HideShow timer Statistics
If the radius of a circle is positive integer less than 50, what is the probability that the area of circle is an integer? (A) \(0\) (B) \(\frac{7}{50}\) (C) \(\frac{1}{7}\) (D) \(\frac{1}{3}\) (E) \(\frac{7}{22}\) Self made
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert
Originally posted by chetan2u on 29 Nov 2017, 19:52.
Last edited by chetan2u on 29 Nov 2017, 20:12, edited 2 times in total.
updated the choices



Senior Manager
Joined: 17 Oct 2016
Posts: 318
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 20:07
Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7. So area will be an integer when radii are 7,14,21,28,35,42,49. Now the sample set is 49 as the radius is less than 50. 50 cannot be included. So probability has to be 7/49=1/7. Am I right? Sent from my iPhone using GMAT Club Forum
_________________
Help with kudos if u found the post useful. Thanks



Math Expert
Joined: 02 Aug 2009
Posts: 7334

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 20:10
Sasindran wrote: Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7. So area will be an integer when radii are 7,14,21,28,35,42,49.
Now the sample set is 49 as the radius is less than 50. 50 cannot be included.
So probability has to be 7/49=1/7.
Am I right?
Sent from my iPhone using GMAT Club Forum Yes, you are absolutely correct. typo in 50, it was supposed to be 51. But since you have already answered it as 50, will edit the choices accordingly
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentageincreasedecreasewhatshouldbethedenominator287528.html
GMAT Expert



Senior Manager
Joined: 17 Oct 2016
Posts: 318
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 20:11
chetan2u wrote: Sasindran wrote: Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7. So area will be an integer when radii are 7,14,21,28,35,42,49.
Now the sample set is 49 as the radius is less than 50. 50 cannot be included.
So probability has to be 7/49=1/7.
Am I right?
Sent from my iPhone using GMAT Club Forum Yes, you are absolutely correct. typo in 50, it was supposed to be 51. But since you have already answered it as 50, will edit the choices accordingly Ok. Good question though. It tests the basic concept of pi=22/7 rather than 3.14. Sent from my iPhone using GMAT Club Forum mobile app
_________________
Help with kudos if u found the post useful. Thanks



Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 20:12
chetan2u wrote: If the radius of a circle is positive integer less than 50, what is the probability that the area of circle is an integer?
(A) 0 (B) 1/50 (C) 7/50 (D) 22/50 (E) 1
Self made As Radius of Circle is +ve Integer it can take values from  7,14,21,35,42,49 P = 7/49.. Am I Missing something here??
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Current Student
Joined: 15 Oct 2017
Posts: 17
Location: India
Concentration: Marketing, Finance
GPA: 2.72
WE: Engineering (Aerospace and Defense)

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 21:29
rahul16singh28 wrote: chetan2u wrote: If the radius of a circle is positive integer less than 50, what is the probability that the area of circle is an integer?
(A) 0 (B) 1/50 (C) 7/50 (D) 22/50 (E) 1
Self made As Radius of Circle is +ve Integer it can take values from  7,14,21,35,42,49 P = 7/49.. Am I Missing something here?? You're missing 28. That gives you 7/49 = 1/7



Manager
Joined: 08 Oct 2015
Posts: 241

If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 22:29
chetan2u wrote: Sasindran wrote: Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7. So area will be an integer when radii are 7,14,21,28,35,42,49.
Now the sample set is 49 as the radius is less than 50. 50 cannot be included.
So probability has to be 7/49=1/7.
Am I right?
Sent from my iPhone using GMAT Club Forum Yes, you are absolutely correct. typo in 50, it was supposed to be 51. But since you have already answered it as 50, will edit the choices accordingly The question does not say assume pi as 22/7, so what if we were to assume pi as 3.14? The only way to get an integer area would be if the radius had 2x5, at the least, as this would give us "100" as r^2 and 100 x 3.14= integer. Possible cases: 2 x 5, 2 x 5 x 3, 2 x 2 x 5, 2 x 2 x 2 x 5, and 2 x 5 x 5 ( if we are to assume less than 51), which is only 5 cases.



Senior Manager
Joined: 17 Oct 2016
Posts: 318
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 22:32
rahulkashyap wrote: chetan2u wrote: Sasindran wrote: Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7. So area will be an integer when radii are 7,14,21,28,35,42,49.
Now the sample set is 49 as the radius is less than 50. 50 cannot be included.
So probability has to be 7/49=1/7.
Am I right?
Sent from my iPhone using GMAT Club Forum Yes, you are absolutely correct. typo in 50, it was supposed to be 51. But since you have already answered it as 50, will edit the choices accordingly The question does not say assume pi as 22/7, so what if we were to assume pi as 3.14? The only way to get an integer area would be if the radius had 2x5, at the least, as this would give us "100" as r^2 and 100 x 3.14= integer. Besides 2 x 5, we could also have 2 x 2 x 5, 2 x 2 x 2 x 5, and 2 x 5 x 5 ( if we are to assume less than 51), which is only 4 cases. Please note that value of pi is 22/7 which is rounded off to 3.14. In fact the non rounded of value will be 3.14285714285714..... Sent from my iPhone using GMAT Club Forum mobile app
_________________
Help with kudos if u found the post useful. Thanks



Current Student
Joined: 15 Oct 2017
Posts: 17
Location: India
Concentration: Marketing, Finance
GPA: 2.72
WE: Engineering (Aerospace and Defense)

Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
Show Tags
29 Nov 2017, 22:33
rahulkashyap wrote: chetan2u wrote: Sasindran wrote: Area of the circle will be an integer when the radius is a multiple of 7 since pi value is 22/7. So area will be an integer when radii are 7,14,21,28,35,42,49.
Now the sample set is 49 as the radius is less than 50. 50 cannot be included.
So probability has to be 7/49=1/7.
Am I right?
Sent from my iPhone using GMAT Club Forum Yes, you are absolutely correct. typo in 50, it was supposed to be 51. But since you have already answered it as 50, will edit the choices accordingly The question does not say assume pi as 22/7, so what if we were to assume pi as 3.14? The only way to get an integer area would be if the radius had 2x5, at the least, as this would give us "100" as r^2 and 100 x 3.14= integer. Besides 2 x 5, we could also have 2 x 2 x 5, 2 x 2 x 2 x 5, and 2 x 5 x 5 ( if we are to assume less than 51), which is only 4 cases. The exact decimal value of pi isn't 3.14. It has 2.7 trillion decimal digits. 3.14 is only an approximation. Taking 22/7 as the value of pi is a better option.




Re: If the radius of a circle is positive integer less than 50, what is
[#permalink]
29 Nov 2017, 22:33






