When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at then end of the 4th year. By how many feet did the height of the tree increase each year?
a) 3/10
b) 2/5
c) 1/2
d) 2/3
e) 6/5
我就快考GMAT了，但有D數仲未搞得通，請有心人指教!謝!
[不恥下問系列]又有GMAT數學題不懂之4
2009-06-21 10:10 pm
回答 (2)
2009-06-21 10:56 pm
✔ 最佳答案
Let h ft be the height of the tree increased each year.Height of the tree at the end of the 6th year = (4 + 6h) ft
Height of the tree at the end of the 4th year = (4 + 4h) ft
(4 + 6h) - (4 + 4h) = (1/5)(4 + 4h)
5(4 + 6h) - 5(4 + 4h) = 4 + 4h
20 + 30h - 20 - 20h = 4 + 4h
6h = 4
h = 2/3
The answer is d).
2009-06-21 10:39 pm
等差數列 Arithmetric Sequence
一定一定要記得: T(n) = a + (n-1)*d
今次講緊 height, 姑且以 H(n) 表示 height after n years
一開始，H(0) = 4
第二件事：H(6) = H(4)*(1 + 1/5) = 6/5 * H(4)
設每年 rise R 咁多
H(1) = H(0) + R
H(2) = H(1) + R + R
H(3) = H(1) + R + R + R
see?
H(4) = H(1) + 4*R = 4 + 4*R
H(6) = 4 + 6*R
咁代返落 H(6) = H(4) * (6/5) 度，
咪變左 R ge equation lor~
你自己solve 下先，再對答案
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(4 + 6*R ) = (4 + 4*R) * ( 6/5 )
5*( 4 + 6R ) = 6*( 4 + 4R )
20 + 30R = 24 + 24 R
6R = 4
R = 2/3
therefore, it rises 2/3 feet each year.
一定一定要記得: T(n) = a + (n-1)*d
今次講緊 height, 姑且以 H(n) 表示 height after n years
一開始，H(0) = 4
第二件事：H(6) = H(4)*(1 + 1/5) = 6/5 * H(4)
設每年 rise R 咁多
H(1) = H(0) + R
H(2) = H(1) + R + R
H(3) = H(1) + R + R + R
see?
H(4) = H(1) + 4*R = 4 + 4*R
H(6) = 4 + 6*R
咁代返落 H(6) = H(4) * (6/5) 度，
咪變左 R ge equation lor~
你自己solve 下先，再對答案
.
.
.
.
.
.
.
.
.
.
(4 + 6*R ) = (4 + 4*R) * ( 6/5 )
5*( 4 + 6R ) = 6*( 4 + 4R )
20 + 30R = 24 + 24 R
6R = 4
R = 2/3
therefore, it rises 2/3 feet each year.
參考: 加油加油，有唔識再問我地喎~
收錄日期: 2021-04-13 16:41:02
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