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What is the smallest possible sum of nonnegative integers a, b, anD
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21 Mar 2017, 05:06
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What is the smallest possible sum of nonnegative integers a, b, and c such that 36a + 6b + c = 173? A. 5 B. 7 C. 13 D. 16 E. 18
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Re: What is the smallest possible sum of nonnegative integers a, b, anD
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21 Mar 2017, 08:11
Bunuel wrote: What is the smallest possible sum of nonnegative integers a, b, and c such that 36a + 6b + c = 173?
A. 5 B. 7 C. 13 D. 16 E. 18 First off, we can minimize the sum of a, b and c by maximizing the value of a. (36)(5) = 180, so 5 is too big (36)(4) = 144 So, a = 4173  144 = 29. So, we now have 6b + c = 29 We can minimize the sum of b and c by maximizing the value of b. (6)(5) = 30, so 5 is too big (6)(4) = 24 So, b = 4If a = 4 and b = 4, then 36a + 6b + c = 144 + 24 + c = 173 So, c = 5So, the minimum value of a + b + c is 4 + 4 + 5 = 13 Answer: Cheers, Brent
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Re: What is the smallest possible sum of nonnegative integers a, b, anD
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21 Mar 2017, 08:31
To make a,b and c as small as possible, we should maximize the value with greatest multiplied( 36a), and do the same operation on the remaining parts afterwards.
36= 36x5=180 so , 36x4 = 144, a =4
This leaves 6b+c = 29, ====> 6x5=30 ; 6x4= 24, b =4
c=5, therefore 4+4+5= 13.
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Re: What is the smallest possible sum of nonnegative integers a, b, anD
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21 Mar 2017, 22:54
Bunuel wrote: What is the smallest possible sum of nonnegative integers a, b, and c such that 36a + 6b + c = 173?
A. 5 B. 7 C. 13 D. 16 E. 18 OFFICIAL SOLUTION In order to minimize the total value of a, b, and c, we should make a as large as possible  since we'll simply reach 173 much faster moving in chunks of 36 than we would by moving in chunks of 6 or 1. Since 173÷36=4 remainder 29, we will choose a=4 and move on to consideration of b and c. In the same manner, we will now maximize b, since moving in chunks of 6 is much more efficient than moving in chunks of 1. Since 29÷6=4 remainder 5, we will choose b=4. At this point we will be left to choose c=5 to cover the remaining value. Thus the minimum possible value of a+b+c is 4+4+5=13, and answer C is correct.
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Re: What is the smallest possible sum of nonnegative integers a, b, anD
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22 Mar 2017, 13:56
My approach: Write a list of all of the multiples of:
36  36, 72, 108, 144 6  6, 12, 18, 24, 30, 36, 42, 48 1  1, 2, 3, 4, 5
Look at the numbers for a while.
You would observe that 144 + 24 + 5 = 173
Therefore a is 4, b is 4 and c is 5
Add up all numbers together 4 + 4 + 5 = 13
Which is answer C



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Re: What is the smallest possible sum of nonnegative integers a, b, anD
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11 Jul 2018, 11:00
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Re: What is the smallest possible sum of nonnegative integers a, b, anD
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