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A company produces computers with 7 different speeds, and the ratio of

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A company produces computers with 7 different speeds, and the ratio of  [#permalink]

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New post 25 Oct 2016, 17:57
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A company produces computers with 7 different speeds, and the ratio of each speed to the next one is a fixed ratio. If the fastest computer is 5.4 GHz, while slowest speed is 0.2 GHz, what is the speed of the second slowest computer?

A) (3^1/2) (0.2)
B) (27^1/7) (0.2)
C) (5.2/7) + 0.2
D) (0.2)^2
E) 0.8

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Manager
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A company produces computers with 7 different speeds, and the ratio of  [#permalink]

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New post 25 Oct 2016, 18:30
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This is a question on Geometric Progression.
Nth term of a GP is \(a * r^{n-1}\), where a is the first term and r is the ratio between two consecutive terms.

7th term and first term are given
7th term = \(a * r^{6}\)
\(5.4 = 0.2 *r^{6}\)
\(r = 27 ^{1/6}\)

Second ratio = a *r
= \(0.2 * 27 ^{1/6}\)
=\(0.2 * (3^3) ^{1/6}\)
= \(0.2 * 3 ^{1/2}\)
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A company produces computers with 7 different speeds, and the ratio of  [#permalink]

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New post 25 Oct 2016, 20:32
duahsolo wrote:
A company produces computers with 7 different speeds, and the ratio of each speed to the next one is a fixed ratio. If the fastest computer is 5.4 GHz, while slowest speed is 0.2 GHz, what is the speed of the second slowest computer?

A) (3^1/2) (0.2)
B) (27^1/7) (0.2)
C) (5.2/7) + 0.2
D) (0.2)^2
E) 0.8


1st speed=0.2
Let x be ratio,then 1st/2nd=x
0.2/2nd =x------>2nd=0.2/x------(a)
.
.
.
7th=0.2/x^6=5.4
x^6=0.2/5.4=1/27----->1/3^3
x=1 / 3^(3*1/6)------->1/3^1/2
therefore 2nd speed(from (a)) =0.2/(1/3^1/2)-------->3^1/2*0.2

Ans A
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Re: A company produces computers with 7 different speeds, and the ratio of  [#permalink]

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New post 26 Oct 2016, 04:07
Tough question!
Could someone explain in detail?
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Re: A company produces computers with 7 different speeds, and the ratio of  [#permalink]

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Re: A company produces computers with 7 different speeds, and the ratio of   [#permalink] 13 Aug 2018, 05:44
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