On July 1, 2017, a certain tree was 128 centimeters tall. Each year, the tree's height increases 50%.
Given this growth rate, the tree's height on July 1, 2023 will be how many centimeters greater than the tree's height on July 1, 2022?
A) (2^2)(3^4)
B) (2)(3^4)
C) (2)(3^5)
D) (4)(3^5)
E) (2)(3^6)
Answer: C
Difficulty level: 600 - 650
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On July 1, 2017, a certain tree was 128 centimeters tall. Ea
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Every year tree's height increases by 50%.
Height on July 1, 2018 = 128*1.5
Height on July 1, 2019 = 128*1.5^2
Similarly
Height on July 1, 2022 = 128*1.5^5
Height on July 1, 2023 = 128*1.5^6
Therefore, the difference in height of the tree from July 1, 2022, to July 1, 2023, can be calculated as below
= 128*1.5^6 - 128*1.5^5
= 128*1.5^5*0.51 = 2^7*3/2*3/2*3/2*3/2*3/2*1/2 = 2*3^5.
Hence, The correct answer is the option C.
Regards!
Height on July 1, 2018 = 128*1.5
Height on July 1, 2019 = 128*1.5^2
Similarly
Height on July 1, 2022 = 128*1.5^5
Height on July 1, 2023 = 128*1.5^6
Therefore, the difference in height of the tree from July 1, 2022, to July 1, 2023, can be calculated as below
= 128*1.5^6 - 128*1.5^5
= 128*1.5^5*0.51 = 2^7*3/2*3/2*3/2*3/2*3/2*1/2 = 2*3^5.
Hence, The correct answer is the option C.
Regards!
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let's create a growth table and look for a patternBrent@GMATPrepNow wrote:On July 1, 2017, a certain tree was 128 centimeters tall. Each year, the tree's height increases 50%.
Given this growth rate, the tree's height on July 1, 2023 will be how many centimeters greater than the tree's height on July 1, 2022?
A) (2^2)(3^4)
B) (2)(3^4)
C) (2)(3^5)
D) (4)(3^5)
E) (2)(3^6)
year | height in cm
2017: 128
2018: 128(1.5)
2019: 128(1.5)^2
2020: 128(1.5)^3
2021: 128(1.5)^4
2022: 128(1.5)^5
2023: 128(1.5)^6
The tree's height on July 1, 2023 will be how many centimeters greater than the tree's height on July 1, 2022?
Difference = 128(1.5)^6 - 128(1.5)^5
Factor out 128(1.5^5) to get: difference = 128(1.5^5)[1.5 - 1]
Simplify: difference = 128(1.5^5)[0.5]
Rewrite with fractions: difference = (2^7)(3/2)^5)(1/2)
Expand: difference = (2^7)(3^5)/(2^6)
Simplify: difference = (2)(3^5)
Answer: C
Cheers,
Brent