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# If tuvw = 108

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Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 585
Location: India
WE: Engineering (Other)

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06 Dec 2017, 05:51
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Difficulty:

15% (low)

Question Stats:

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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SC Moderator
Joined: 13 Apr 2015
Posts: 1540
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
Re: If tuvw = 108 [#permalink]

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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

VP
Joined: 22 May 2016
Posts: 1259

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06 Dec 2017, 08:36
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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

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

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