I27-21

Question

A species of tree grows in a unique pattern such that its height in a given year follows a sequence defined as:
 
•  H_{n} = H_{n-1} + 2 * H_{n-2} 
 
where  H_{1} = 3  meters and  H_{2} = 5  meters, and  H_{n}  is the height of the tree in meters at the end of year  n .
 
The tree produces flowers in odd years (e.g., 1, 3, 5, 7, ...). The number of flowers produced in year  2n+1  is equal to the value of  H_{2n+1} * n .
 
Based on the above information, select for  H_{6}  the height of the tree in year 6 and for Flowers the total amount of flowers produced from year 1 to 6.

Bunuel · Answer

Official Solution:

The question first asks us to find  H_{6} .
 
Let’s list do the calculations for the first few terms:
 
-  H_{3} = H_{2} + 2 * H_{1} = 5 + 2 * 3 = 11 
 
-  H_{4} = H_{3} + 2 * H_{2} = 11 + 2 * 5 = 21 
 
-  H_{5} = H_{4} + 2 * H_{3} = 21 + 2 * 11 = 43 
 
-  H_{6} = H_{5} + 2 * H_{4} = 43 + 2 * 21 = 85 
 
Now the question asks us to find the total number of flower produced from year 1 to 6.
 
Let’s write out a table with the number of flowers made each year.
    Year   1   2    3   4   5   6      Flowers produced    H_{1} * 0    0    H_{3} * 1    0    H_{5} * 2    0

Or:
    Year   1   2   3   4   5   6      Flowers produced   0   0   11   0   86   0

That means the total number of flowers will be 86 + 11 = 97.
 
Our answer will be:  H_{6} - 85  and Flowers - 97.

Correct answer:

H_{6}   "85"

Flowers  "97"

AryakiSekera · Answer

This question took me 7 minutes to solve. Please help figure out a faster way to solve it and links to similar questions for practice would be much appreciated

Bunuel · Answer

Sequences

THEORY:

Sequences Made Easy - All in One Topic! 
 Math : Sequences & Progressions 
 Time to Tackle Geometric Progressions!

QUESTIONS:

Special Numbers and Sequences Problems  
 PS Questions

For other subjects:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope this helps.

nandini14 · Answer

Can you explain the flower calculation bit in detail?

Bunuel · Answer

The tree produces flowers only in odd years, and the number of flowers in year 2n+1 is given by H(2n+1) * n.

From year 1 to 6, the odd years are 1, 3, and 5:
 
Year 1: n = 0, flowers = H1 * 0 = 0
 Year 3: n = 1, flowers = H3 * 1 = 11 * 1 = 11
 Year 5: n = 2, flowers = H5 * 2 = 43 * 2 = 86

Total flowers = 0 + 11 + 86 = 97.

SwethaReddyL · Answer

Hi  Bunuel , why is n = 0 for the year 1? please explain this part

Bunuel · Answer

Please check the post just above yours  HERE . Hope it helps.

anknown123 · Answer

where can I get more these type of questions ?

Bunuel · Answer

If by “these types of questions” you mean Two-Part Analysis questions, you can find more in our TPA forum here:  https://gmatclub.com/forum/two-part-analysis-tpa-455/

Year	1	2	3	4	5	6
Flowers produced	\(H_{1} * 0\)	0	\(H_{3} * 1\)	0	\(H_{5} * 2\)	0

Year	1	2	3	4	5	6
Flowers produced	\(H_{1} * 0\)	0	\(H_{3} * 1\)	0	\(H_{5} * 2\)	0

I27-21

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My Rewards

\(H_{6}\)	Flowers
		67
		79
		85
		86
		97
		100

\(H_{6}\)	Flowers
		67
		79
		85
		86
		97
		100