A factory producing tennis balls stores them in either big b

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sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Sat Feb 06, 2016 6:53 am

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

OA is B

I just want to know if my reasoning is correct or not

Case 1: 25*3 = 75
94 – 75 = 19 balls left
These 19 ball can be put in a small box of 17, so 2 balls are left

Case 2: 17*4 = 68
95 – 68 = 26 balls left
These 26 balls can now be put in a big box of 25, so 1 ball is left

Now the question asks what is the least no. of balls that can be left unboxed. So, it is 1 ball as in case 2.
Please let me know if my reasoning is correct

Thanks & Regards
Sachin

Last edited by sachin_yadav on Sat Feb 06, 2016 12:19 pm, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sat Feb 06, 2016 6:53 am

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sat Feb 06, 2016 9:32 am

What you did looks good to me.

I went through and tested the other cases, 0 x 25 and 2 x 25, just to be sure.

Maybe you did too.

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by [email protected] » Sat Feb 06, 2016 9:43 am

Hi sachin_yadav,

Your approach to this question is perfect. This question essentially comes down to brute force - since the numbers involved are rather specific and the total number of balls is relatively small, you really just have to do enough work to test the following options:

No 25-ball boxes
1 25-ball box
2 25-ball boxes
3 25-ball boxes

One of those options will produce the result that the question is asking for.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

A factory producing tennis balls stores them in either big b

by ceilidh.erickson » Thu Feb 11, 2016 5:03 pm

Your solution is the best - in fact, the only - solution to employ in a case like this. Whenever you are given a word problem with INTEGER CONSTRAINTS (in this case, we can't have half a ball) and it's asking you about possible combinations, your only option is to test out the numbers.

My recommendation is to use a chart to keep things organized:

The methodology is the same, though.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

sachin_yadav: Master | Next Rank: 500 Posts; Posts: 212; Joined: Mon Dec 06, 2010 12:52 amFollowed by: 1 member; Location: India; Thanked: 5 times

by sachin_yadav » Mon Feb 15, 2016 1:12 am

Thank you all. Appreciate your replies.

Regards
Sachin

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