What is the smallest possible sum of nonnegative integers a, b, anD

Question

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

BrentGMATPrepNow · Accepted Answer

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 = 4

173 - 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 = 4

If  a = 4  and  b = 4 , then 36a + 6b + c = 144 + 24 + c = 173
So,  c = 5

So, the minimum value of a + b + c is  4  +  4  +  5  = 13
Answer:  C

Cheers,
Brent

mesutthefail · Answer

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.

C

BillyZ · Answer

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.

matthewsmith_89 · Answer

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

Anupama_1090 · Answer

My approach :
6(6a+b)+c = 173 => the nearest multiple of 6 for the number 173 is 168 
therefore the expression can be expressed as 6 +5 => a=4, b=4 and c=5. these are the least values of a,b and c that satisfy the equation.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the smallest possible sum of nonnegative integers a, b, anD

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the smallest possible sum of nonnegative integers a, b, anD

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards