Maths 率與比

8510.
The answer is : C. 8

Let a be the first term, and r be the common ratio.

T(2) : ar = -12 ...... [1]
T(5) : ar⁴ = 81/2 ...... [2]

[2]/[1] :
r³ = -81/24
r³ = -27/8
r = -3/2

Put r = 3/2 into [1] :
a(-3/2) = -12
a = 8


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86. 42.
The answer is : D. 20 : 15 : 12

Let d be the distance.

A's speed : B' speed : C's speed
= d/3 : d/4 : d/5
= (1/3)×60 : (d/4)×60 : (d/5)×60
= 20 : 15 : 12


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88. 44.
The answer is : A. 1 : 2

Let W and d be the weight and diameter of the gold coin respectively.

W ∝ d²
W1 : W2 = d1² :d2²
1 : 4 = d1² : d2²
d1 : d2 = 1 : 2