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# A factory producing tennis balls stores them in either big

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SVP
Joined: 04 May 2006
Posts: 1895
Schools: CBS, Kellogg
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:

52% (02:09) correct 48% (01:06) wrong based on 318 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
Joined: 14 Aug 2007
Posts: 728
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
Manager
Joined: 24 Apr 2008
Posts: 161
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)
Manager
Joined: 21 Mar 2008
Posts: 81
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.
Director
Joined: 14 Aug 2007
Posts: 728
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!
Director
Joined: 23 Sep 2007
Posts: 783
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.
SVP
Joined: 04 May 2006
Posts: 1895
Schools: CBS, Kellogg
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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Manager
Joined: 11 Apr 2008
Posts: 128
Location: Chicago
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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Senior Manager
Joined: 22 Sep 2005
Posts: 276
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.
Director
Status: Gonna rock this time!!!
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Posts: 520
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
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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Joined: 06 Sep 2013
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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
Intern
Joined: 26 Sep 2012
Posts: 37
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!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15916
Re: A factory producing tennis balls stores them in either big [#permalink]

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01 Jan 2017, 14:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Posts: 39589
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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