The Age Of A Tree Is Determined By The Number Of Concentric Circles GMAT Problem Solving

Question: 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?

  1. 23
  2. 24
  3. 46
  4. 47
  5. 69

Approach Solution (1)

We will use the Arithmetic Progression (AP)
an = a + (n - 1) * d
an = 60 * 12 = 720 inches
a = 30
d = 30
Solving further for the value of n
n = 24

Correct option: B

Approach Solution (2)

an = 60 * 12 = 720 inches
So, d = 30
a = 30
Therefore,
720 = 30 + (n - 1) * 30
n = 24

Correct option: B

Approach Solution (3)

We can see that 30 inches = 30/12 = 5/2 feet
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 (the number of concentric rings) is:
(30 - 5/4) / (5/4) + 1 = (115/4) * (⅘) + 1 = 23 + 1 = 24

Correct option: B

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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