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# In a list of numbers, each number after the first is exactly 1/3 the n

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
In a list of numbers, each number after the first is exactly 1/3 the n  [#permalink]

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04 Feb 2018, 20:14
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:16) correct 21% (01:32) wrong based on 52 sessions

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In a list of numbers, each number after the first is exactly 1/3 the number immediately preceding it. If the fifth number in the list is 3, what is the second number in the sequence?

(A) 1/9

(B) 1/3

(C) 1

(D) 27

(E) 81

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Re: In a list of numbers, each number after the first is exactly 1/3 the n  [#permalink]

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04 Feb 2018, 20:25
E

Let’s say x is the first number.
We have 5th number =x*3^(-4) =3
Solving for x,
X=243

Hence second number =81

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Re: In a list of numbers, each number after the first is exactly 1/3 the n  [#permalink]

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04 Feb 2018, 20:38
E - can work backwards quickly in this case .

1/3X = 3 (where x is the fourth term), then X = 9. Continue to work backwards with this method, you'll find the 3rd term = 27 and the second term is 81.
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Re: In a list of numbers, each number after the first is exactly 1/3 the n  [#permalink]

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19 Mar 2018, 21:02
Bunuel wrote:
In a list of numbers, each number after the first is exactly 1/3 the number immediately preceding it. If the fifth number in the list is 3, what is the second number in the sequence?

(A) 1/9

(B) 1/3

(C) 1

(D) 27

(E) 81

a5 = (a4)/3 = 3

a4 = 9

a4 = (a3) / 3 = 9

a3 = 27

a3 = (a2) /3 = 27

a2 = 81 = E the answer

thanks
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Re: In a list of numbers, each number after the first is exactly 1/3 the n  [#permalink]

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20 Mar 2018, 10:00
Bunuel wrote:
In a list of numbers, each number after the first is exactly 1/3 the number immediately preceding it. If the fifth number in the list is 3, what is the second number in the sequence?

(A) 1/9

(B) 1/3

(C) 1

(D) 27

(E) 81

$$5^{th}$$ Number = 3
$$4^{th}$$ Number = 9
$$3^{rd}$$ Number = 27
$$2^{nd}$$ Number = 81, Answer must be (E)
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Re: In a list of numbers, each number after the first is exactly 1/3 the n &nbs [#permalink] 20 Mar 2018, 10:00
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