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On July 1, 2017, a certain tree was 128 centimeters tall. Ea

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On July 1, 2017, a certain tree was 128 centimeters tall. Ea

by Brent@GMATPrepNow » Tue Jun 12, 2018 4:24 am

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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
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Another approach

by swerve » Tue Jun 12, 2018 11:22 am
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.

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by Brent@GMATPrepNow » Thu Jun 14, 2018 4:52 am
Brent@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)
Let's create a growth table and look for a pattern

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
Brent Hanneson - Creator of GMATPrepNow.com
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