Hello,
Can you please tell me how to solve this:
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
OA: 17
Thanks a lot,
Sri
If tuvw = 108, and t, u, v, and w are all positive integers
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To maximize the value of t - w, we must MAXIMIZE t and MINIMIZE wgmattesttaker2 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
First find the prime factorization of 108.
108 = (2)(2)(3)(3)(3)
We can also add a 1 to this product to get: 108 = (1)(2)(2)(3)(3)(3)
So, the smallest value in our product is 1.
So, w = 1
The next smallest value in our product is 2
So, v = 2
The next smallest value in our product is 3
So, u = 3
Now that we've MINIMIZED the values of w, v and u, we have MAXIMIZED the value of t
If w = 1, v = 2 and u = 3, then t = 18
So, t - w = 18 - 1 = [spoiler]17 = C[/spoiler]
Cheers,
Brent
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To Maximize the difference, W should be 1.gmattesttaker2 wrote:Hello,
Can you please tell me how to solve this:
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
OA: 17
Thanks a lot,
Sri
Add 1 to the answer choices and see which one is a factor of 108.
Looking at the options, A is ruled out because 1 cannot be the difference.
between B,C,D and E only C+1 is a factor of 108.
Pick C
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don't be afraid of failure and don't abandon it.
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Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
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The greatest value of t-w will be obtained for least value of w (which is 1 as factor of 108) and greatest value of t which we have to understand by factorising 108 into 4 distinct part such that their product is 108 and smallest factor is 1.
Since the smalles factor is 1 and then next is 2 and the next is 3 therefore the biggest factor which could be the value of t will be 108 / (1 x 2 x 3) = 18
Because, 108 = 1 x 2 x 3 x 18
Thefore t-w = 18 - 1 = 17 Answer
Since the smalles factor is 1 and then next is 2 and the next is 3 therefore the biggest factor which could be the value of t will be 108 / (1 x 2 x 3) = 18
Because, 108 = 1 x 2 x 3 x 18
Thefore t-w = 18 - 1 = 17 Answer
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