If tuvw = 108

Question

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

Kurtosis · Accepted Answer

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

generis · Answer

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

dcummins · Answer

Clearly tuvw are factors of 108. To find the greatest possible value of t-w we need to maximise t and minimise w

Lets look at the factors of 108
1-108
2-54 
3-36
4-27
6-18
9-12

We need 4 factors and W is our minimum 
Choose w=1
 1 -108
2-54 
3-36
4-27
6-18
9-12

In the right hand column choose a value for t, you can test numbers but you'll see that 18 is the only one that works as 
So 18-1 = 17
 1 -108
2-54 
3-36
4-27
6- 18 
9-12
We can process eliminate the answers by asking whether we can obtain a given value.

Basshead · Answer

The prime factorization of  108 = 2^2 * 3^3 .

We're told  w < v < u < t . Using the factors, we need to create 4 different integers.

We can get the numbers  1 < 2 < 3 < 18

18 - 1 = 17 .

Answer is C.

CrackverbalGMAT · Answer

To  MAXIMIZE  the difference ,we need to minimize w.
w is a factor of 108 and the minimum such a factor is 1.Hence w=1.
108=3*3*3*2*2*1
 So  w=1 (smallest) 
Next smallest  v=2 
and  u=3  in the same way.
So, w, v, u are minimized and t is maximized if w=1,v=2,u=3.
This means  t=18  
  
 So t-w  =18-1=17 (C)

ALTERNATELY  ,you can also use options in the following way:
  Eliminate (a)  because t-w cannot be 1 (As t>u>v>w and belong to integers)
  Now add 1 to the options and see which of them is a factor of 108. 
  Eliminate   (b),(d) and (e) 
 Only (c) which is 17 when added to 1 gives 18 that is a factor of 108.
  Hence (c) 
Hope this helps! Keep studying!:)

Abhishek009 · Answer

108 = 1*2^2*3^3

So,  t = 18  ,  u = 3  ,  v = 2  &  w = 1

Hence,  t - w = 18 - 1 => 17 , Answer will be (C)

If tuvw = 108

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If tuvw = 108

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