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# A factory producing tennis balls stores them in either big

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SVP
Joined: 04 May 2006
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A factory producing tennis balls stores them in either big [#permalink]

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27 May 2008, 22:17
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Difficulty:

65% (hard)

Question Stats:

53% (01:08) correct 47% (01:04) wrong based on 331 sessions

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A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 1
B. 2
C. 3
D. 4
E. 5

M18-05
[Reveal] Spoiler: OA

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Director
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Re: A factory producing tennis balls stores them in either big [#permalink]

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27 May 2008, 22:27
sondenso wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

1
2
3
4
5

25*3 + 17 = 92 so C.3 should be the answer

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Manager
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Re: A factory producing tennis balls stores them in either big [#permalink]

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27 May 2008, 22:37
I think we can put that as 25X1+17X4=93 hence 2 is the answer ; I tried by checking for 94, 93 from the answer options and think is the quickest (took 1 min)

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Re: A factory producing tennis balls stores them in either big [#permalink]

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27 May 2008, 22:39
alpha_plus_gamma wrote:
sondenso wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

1
2
3
4
5

25*3 + 17 = 92 so C.3 should be the answer

I think the answer is B - 2. 25*1 + 17*4 = 93. I don't think there's an quick way example plug in numbers starting with multiples of 25.

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Re: A factory producing tennis balls stores them in either big [#permalink]

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27 May 2008, 22:41
lucyqin wrote:
alpha_plus_gamma wrote:
sondenso wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

1
2
3
4
5

25*3 + 17 = 92 so C.3 should be the answer

I think the answer is B - 2. 25*1 + 17*4 = 93. I don't think there's an quick way example plug in numbers starting with multiples of 25.

yes B should be right, my mistake!

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Re: A factory producing tennis balls stores them in either big [#permalink]

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27 May 2008, 22:42
why not 0

the question does not state that the boxes have to be full.

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SVP
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Re: A factory producing tennis balls stores them in either big [#permalink]

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28 May 2008, 00:16
Thanks all, Oa is B

alpha_plus_gamma wrote:
25*3 + 17 = 92 so C.3 should be the answer

In theory, I think maximum 3 times 25, and then force times of 17 as above. But this question does not follow the theory? What do you think? Thanks!
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Re: A factory producing tennis balls stores them in either big [#permalink]

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28 May 2008, 10:58
gmatnub wrote:
why not 0

the question does not state that the boxes have to be full.

I agree, this question is worded horribly. You could fill the 75 balls into 3 of the large boxes and then put the remaining 20 balls into another large box and still have room for 5 more balls. Answer should be zero. Now, if they asked what is the least number of boxes that could be used, that would make more sense.
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Re: A factory producing tennis balls stores them in either big [#permalink]

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28 May 2008, 12:27
2
KUDOS
B

We have to work with multiples of 17 and 25.

First, we must know the limits of this multiples, so:
95/25= 3....so the max is 3
95/17=5...so the max is 5

If we have 3 boxes of 25 (75 u1) and 1 box of 17 (75+17=92) we have 3 balls out. (95-92)

This is a trap, because as I said before we must work with

17 25
34 50
51 75
68 100
85
102 NOT

Here, you can see that 68+25=93, so we have 2 balls out, so B.

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Re: A factory producing tennis balls stores them in either big [#permalink]

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21 Feb 2013, 06:26
Do we have any algebraic soln to this ? It took me 2:29 mins to solve this by plugging in numbers and testing cases?
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Re: A factory producing tennis balls stores them in either big [#permalink]

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17 Oct 2013, 16:44
sondenso wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 1
B. 2
C. 3
D. 4
E. 5

Do we have a nice and elegant approach for solving this one? Tried first with 17*4 = 91. Then since I thought it was too easy gave it a second shot with 25*3 + 17 = 92. But I wasn't expecting 2 as the answer. Very tricky

Will provide Kudos for some nice and short approaches
Cheers
J

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Re: A factory producing tennis balls stores them in either big [#permalink]

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05 Jul 2014, 02:14
jlgdr wrote:
sondenso wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 1
B. 2
C. 3
D. 4
E. 5

Do we have a nice and elegant approach for solving this one? Tried first with 17*4 = 91. Then since I thought it was too easy gave it a second shot with 25*3 + 17 = 92. But I wasn't expecting 2 as the answer. Very tricky

Will provide Kudos for some nice and short approaches
Cheers
J

The only "fast" approach identified by me is the following:

1. Put possible combinations in two columns:

17 25
34 50
68 75
85

2. Start picking two units digits from each row to get the greatest possible unit digit in the possible final combinations (descending order) - 94 -> 93 -> 92 > 91 -> 90

in 94 it is 4 => 50 + 34 -> no
in 93 it is 3 => 25 + 68 = 93, got it!

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Re: A factory producing tennis balls stores them in either big [#permalink]

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01 Jan 2017, 14:46
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Re: A factory producing tennis balls stores them in either big [#permalink]

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02 Jan 2017, 04:53
sondenso wrote:
A factory producing tennis balls stores them in either big boxes, 25 balls per box, or small boxes, 17 balls per box. If 95 freshly manufactured balls are to be stored, what is the least number of balls that can be left unboxed?

A. 1
B. 2
C. 3
D. 4
E. 5

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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Re: A factory producing tennis balls stores them in either big   [#permalink] 02 Jan 2017, 04:53
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