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The age of a tree is determined by the number of concentric circles th

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Bunuel
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The age of a tree is determined by the number of concentric circles th [#permalink] New post   02 Jun 2019, 23:35
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The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69
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nick1816
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   02 Jun 2019, 23:58
Diameter of tree= 60 feet=60*12=720 inches
Age of tree= 720/30=24 years

Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 02:57
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60 FEET equals 720 inches.

After the smallest/ innermost concentric circle, each concentric circle is separated by 15 inches; (720-30)/15= 46 concentric circles after the inner most circle.

Therefore, total number of concentric circles = 46 + 1 = 47
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 03:32
720,690,630,........30
720=30+(n-1)30
n= 24
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The age of a tree is determined by the number of concentric circles th [#permalink] New post   Updated on: 04 Jun 2019, 01:07
Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69


we can use AP
an=a +(n-1)*d
an= 720 inches ; 60*12 ;
a=30
d=30
solve for n = 24
IMO B

Originally posted by Archit3110 on 03 Jun 2019, 08:33.
Last edited by Archit3110 on 04 Jun 2019, 01:07, edited 3 times in total.
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 08:34
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SaiPrasadPatnaik wrote:
720,690,630,........30
720=30+(n-1)30
n= 24


SaiPrasadPatnaik
formula used is wrong
an=a+(n-1)*d
d is 15 not 30
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 08:34
nick1816 wrote:
Diameter of tree= 60 feet=60*12=720 inches
Age of tree= 720/30=24 years

Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69


nick1816
you forgot to use the info given 15 inch gap it seems...
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 08:47
Now that I think of it, there are 15 inches on both sides of the circle, so 30 inches could also be correct. Man this is confusing.

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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 08:50
Sourav700 wrote:
Now that I think of it, there are 15 inches on both sides of the circle, so 30 inches could also be correct. Man this is confusing.

Posted from my mobile device


well by gap of 15 inches it means from center of 1st circle you can understand like this if first dia is 30 then 2nd circle has dia 30+15 ; 45; 3rd has 30+15+15; 60 and so on ...
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   03 Jun 2019, 08:52
By this logic, 47 is the correct answer, Archit3110

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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   04 Jun 2019, 00:57
Bro!! It says the gap is 15 cm. This means radius of next circle will increase by 15cm and diameter will increase by 30cm. Hence diameter of second circle is 60cm. Diameter of third circle will be 60+30=90cm and so on. Hence the circle whose radius is 720 is the 720/30=24th.

Look at the diagram, will help you easy to understand.
AB=CD+AD+DB=30+15+15=60cm


Archit3110 wrote:
Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69


we can use AP
an=a +(n-1)*d
an= 720 inches ; 60*12 ;
a=30
d=15
solve for n = 47
IMO D

Bunuel why is 47 not correct? what is the significance of 15 inch gap b/w each ring then?
nick1816 please explain your solution

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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   04 Jun 2019, 01:06
okay nick1816 , well my approach and thought was the gap of 15 inch was from center , i took d= 15 my bad ; d should be 30
an=720
d=30
a=30
so
720=30+(n-1)*30
n=24


nick1816 wrote:
Bro!! It says the gap is 15 cm. This means radius of next circle will increase by 15cm and diameter will increase by 30cm. Hence diameter of second circle is 60cm. Diameter of third circle will be 60+30=90cm and so on. Hence the circle whose radius is 720 is the 720/30=24th.

Look at the diagram, will help you easy to understand.
AB=CD+AD+DB=30+15+15=60cm


Archit3110 wrote:
Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69


we can use AP
an=a +(n-1)*d
an= 720 inches ; 60*12 ;
a=30
d=15
solve for n = 47
IMO D

Bunuel why is 47 not correct? what is the significance of 15 inch gap b/w each ring then?
nick1816 please explain your solution
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   06 Jun 2019, 17:55
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Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69


We see that 30 inches = 30/12 = 5/2 feet and 15 inches = 15/12 = 5/4 feet. However, if we use the gap of 15-inch as the difference between two consecutive rings, we should use the radius of each ring since the 15-inch gap is the difference between the radii of two consecutive rings. Therefore, the age of the tree (i.e., the number of concentric rings) is:

(30 - 5/4)/(5/4) + 1 = 115/4 x 4/5 + 1 = 23 + 1 = 24

Answer: B
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Re: The age of a tree is determined by the number of concentric circles th [#permalink] New post   06 Jun 2019, 18:13
Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69



GMAT actually mentions conversion. Here 1 feet = 12 inches.

So total radius of the trunk = 30 * 12 inches = 360 inches.

Inner most circle has radius = 15 inches.

So from the question, for every 15 inches it will gain 1 year age.

Age of the tree = 360/15 = 24.

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The age of a tree is determined by the number of concentric circles th [#permalink] New post   07 Jun 2021, 01:03
Diameter of the tree trunk in inches is:

60 feet * (12 inches per foot) = 720 inches

Radius of entire tree trunk = (1/2) (Diameter) = 360 inches



The inner most circle has a Diameter = 30 inches

The inner most circle’s radius = 15 inches.

If each gap between concentric circles is 15 inches, then the number of circles will be measured by the Radius of the entire trunk ——-> which is given by how many 15 inch gaps exist between circles AND the 15 inch radius of the inner most circle.


15 * (number of circles) = 360 inches = radius of entire trunk

15 * c = 360

c = 24

Number of circles = 24



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The age of a tree is determined by the number of concentric circles th [#permalink] New post   13 Nov 2021, 20:17
Bunuel wrote:
The age of a tree is determined by the number of concentric circles that mark the stem when the trunk of the tree is cut. A tall redwood tree cut whose tree trunk had a 60 feet diameter. If the innermost circle had a diameter that measured 30 inches and the concentric circles had a 15 inch gap between them, how many years old was the tree when it was cut?

A) 23
B) 24
C) 46
D) 47
E) 69



The question is completely flawed ...we don't account for the bark of a tree for counting its age, so the last radius should be ignored. The answer should be 23 if we account that, I don't think GMAT will give such a confusing question EVER.

https://www.wikihow.com/Determine-the-Age-of-a-Tree
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