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M18-05

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Math Expert
Joined: 02 Sep 2009
Posts: 58396

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16 Sep 2014, 01:03
2
00:00

Difficulty:

65% (hard)

Question Stats:

60% (01:36) correct 40% (01:36) wrong based on 215 sessions

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A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, with 17 balls per box. If 94 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 0
B. 1
C. 2
D. 3
E. 4

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16 Sep 2014, 01:03
Official Solution:

A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, with 17 balls per box. If 94 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 0
B. 1
C. 2
D. 3
E. 4

There is no way to store 94 balls without leftovers: $$94 - 0*25 = 94$$, $$94 - 1*25 = 69$$, $$94 - 2*25 = 44$$, $$94 - 3*25 = 19$$ are not divisible by 17.

93 balls can be stored successfully: $$93 - 1*25 = 68$$ is divisible by 17. Thus, $$93 = 1*25 + 4*17$$ and we need 1 big box and 4 small boxes.

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10 Dec 2015, 04:47
@Bunuel...I stopped in the 1st step and marked answer C. But failed to proceed further whether I can still reduce the quantity. Can you please let me know if there is any particular method to solve problems like these?
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26 Jan 2016, 23:50
2
There should be a statement in the question saying all the boxes have to be filled to capacity.. otherwise we can just fill 4 boxes of 25 and last box is not completely filled.
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05 Feb 2016, 19:31
To solve this I found the easiest method was to test maximum number of 25 boxes and 17 boxes which gives you C. Since you have to find the least you can cross off D and E and test combinations to try if you can do better in which case you will find the answer B eventually. This is cumbersome but doable in less than 2 mins.
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10 Feb 2017, 18:45
3
Honestly, just listing multiples of 25 (0, 25, 50, 75) and 17 (0, 17, 34, 51, 68, 85) and eyeballing which led to the best combo worked well. "25+68 looks good. What's the total? 93. Can we do better...nope,", took 45 secs.
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07 Jun 2017, 06:28
4
For these kind of Questions, one of the better ways to Organize the data is somewhat like this:

A) Form an Equation: Here, 25x + 17y = 94 (ideally it's less than equal to 94) for your own understanding. Thus, 17y = 94 - 25x ....
B) Then take the bigger no (Here, 25) and write the possible values of 25x upto or less than the required no: Here these will be 0, 25, 50, 75
C) Then subtract these from the required number (i.e. 94): Here these nos will be 94, 69, 44, 19
D) Now take the smaller no (Here, 17) and check the possible values of 17y nearest to the results of step C: Here these will be (85, 68, 34, 17)
E) Subtract the results of Step D from those of Step C to find the Leftover: Here the leftovers are (9, 1, 10, 2)

While it might look complicated, but if you put it in a Table format (attached file) this is Easy,

Thus, least leftover = 1 (Ans: B)
>> !!!

You do not have the required permissions to view the files attached to this post.

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07 Jun 2017, 07:05
Accidentally hit A but the answer is B

For this I looked at the units digit. I made an assumption that at most, there would be only 1 large box. So then I thought how can I get 5 to add up to 14? (25 + x = 94). The units digit would be 9, but 17 will only have a units digit of 9 if multiplied by 7 which would obviously be too high.

The next closest would be 8, which would just be 17*4 = 68. 68 + 25 = 93. So 1 is the least amount of tennis balls left over.

This may seem convoluted, but if you can train your brain to see these patterns it shouldn't take too much time at all. This took me about 45 seconds and another 20 seconds or so to confirm.

Hope this method helps someone.

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08 Jun 2017, 03:52
The rephrased question

17x+25y=94

To find the minimum value, maximise either x or y

Case 1
If y is max, y=3 (Since y=4>94)
17x= 94-75
17x=19
So two box left unpacked ( Remainder: 2)

Case 2:
If x is max; x= 5
25y= 94-85
25y=9

As the remainder is big, reducing x further will yield a better value for y
If x =4
25y=94-68
25y=26
1 box left unpacked.

Option B
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14 Jun 2017, 02:46
A good tricky question .... Well explained above !
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17 Jun 2017, 00:02
Bunuel wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, with 17 balls per box. If 94 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 0
B. 1
C. 2
D. 3
E. 4

=============================================

what I can figure out that only option is trial the 17x and 25y by putting x=1,2,3,4 etc and y=1,2,3 etc but this is tedious and time consuming.
Is there any other method which would be efficient in GMAT and we can relate these type of problems in near future by that method..
Math Expert
Joined: 02 Sep 2009
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17 Jun 2017, 04:34
kawaljeet wrote:
Bunuel wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, with 17 balls per box. If 94 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 0
B. 1
C. 2
D. 3
E. 4

=============================================

what I can figure out that only option is trial the 17x and 25y by putting x=1,2,3,4 etc and y=1,2,3 etc but this is tedious and time consuming.
Is there any other method which would be efficient in GMAT and we can relate these type of problems in near future by that method..

If you check the stats above, you'll see that the average time for correct answer is just below 2 minutes. So, it's possible to solve this question in without spending extra time. There are solutions above which show how can you do that. In addition, please check discussion here: https://gmatclub.com/forum/a-factory-pr ... 64566.html That topic also presents several different solutions which might help.
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18 Oct 2018, 12:47
Should really say the boxes have to be filled to capacity. Nothing stops you from assuming that and choosing A
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12 Mar 2019, 18:04
Bunuel wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, with 17 balls per box. If 94 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 0
B. 1
C. 2
D. 3
E. 4

The question says ''either'' big box ''or'' small box - which means only one type of box is used and not both

slightly tricky

so is it correct to select option-B?
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02 Jun 2019, 06:25
I think this is a poor-quality question. Personally, I feel like the question leaves room for the option of all balls being stored.

There should be something to indicate that boxes have to be filled entirely.
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