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If tuvw = 108

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If tuvw = 108 [#permalink]

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New post 06 Dec 2017, 05:51
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A
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C
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E

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85% (01:26) correct 15% (02:13) wrong based on 54 sessions

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If tuvw = 108, and t, u, v, and w are all positive integers such that t > u > v > w, what is the greatest possible value for t - w?

A. 1
B. 16
C. 17
D. 18
E. 19
[Reveal] Spoiler: OA

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Re: If tuvw = 108 [#permalink]

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New post 06 Dec 2017, 07:05
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Factorize 108 = 1 * 2^2 * 3^3

t > u > v > w --> w = 1; v = 2; u = 3; t = 2 * 3^2 = 18

t - w = 18 - 1 = 17

Answer: C
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If tuvw = 108 [#permalink]

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New post 06 Dec 2017, 08:36
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adkikani wrote:
If tuvw = 108, and t, u, v, and w are all positive integers such that t > u > v > w, what is the greatest possible value for t - w?

A. 1
B. 16
C. 17
D. 18
E. 19

List the prime factors of 108: 2*2*3*3*3

To maximize the difference between the greatest number and the smallest number, make \(t\) as big as possible by making \(w\), \(v\) and \(u\) as small as possible -- remembering t > u > v > w

Let \(w\) = 1
Let \(v\) = 2
Let \(u\) = 3

From prime factor list, the remaining numbers are 2, 3, and 3
Let \(t\) = (2 * 3 * 3) = 18
(t - w) = (18 - 1) = 17

Answer C
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If tuvw = 108   [#permalink] 06 Dec 2017, 08:36
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