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# Given that there are X boxes and the balls are arranged in such a way

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Manager
Joined: 26 Nov 2018
Posts: 96
Concentration: Technology, Entrepreneurship
GPA: 3.3
WE: Manufacturing and Production (Manufacturing)
Given that there are X boxes and the balls are arranged in such a way  [#permalink]

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05 Mar 2019, 01:04
00:00

Difficulty:

65% (hard)

Question Stats:

24% (01:36) correct 76% (02:19) wrong based on 25 sessions

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Given that there are X boxes and the balls are arranged in such a way that no ball is left. If the number of boxes is reduced by 3 and if 12 balls are arranged in them, then 5 balls are left behind, what is the original number of boxes X?

A. 30
B. 31
C. 32
D. 33
E. 34
Manager
Joined: 24 Jun 2013
Posts: 142
Location: India
Schools: ISB '20, GMBA '20
Given that there are X boxes and the balls are arranged in such a way  [#permalink]

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Updated on: 22 Mar 2019, 03:16
Rashed12 wrote:
Given that there are X boxes and the balls are arranged in such a way that no ball is left. If the number of boxes is reduced by 3 and if 12 balls are arranged in them, then 5 balls are left behind, what is the original number of boxes X?

A. 30
B. 31
C. 32
D. 33
E. 34

From the question steam we can write

X-3 = 12q + 5 ( 12 balls arranges with 5 as remainder (left behind))
simplifying

X=12q + 8, putting Q = 0,1,2,3....

we get ; X = 8, 20, 32, 44 ....

we see only 32 is present in ans options

Ans C 32

Originally posted by doomedcat on 19 Mar 2019, 09:15.
Last edited by doomedcat on 22 Mar 2019, 03:16, edited 1 time in total.
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Concentration: Sustainability, Marketing
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Re: Given that there are X boxes and the balls are arranged in such a way  [#permalink]

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19 Mar 2019, 11:43
1
Rashed12 wrote:
Given that there are X boxes and the balls are arranged in such a way that no ball is left. If the number of boxes is reduced by 3 and if 12 balls are arranged in them, then 5 balls are left behind, what is the original number of boxes X?

A. 30
B. 31
C. 32
D. 33
E. 34

given info
x-3= 12a+5
a=1,2,3,
we get
x=12a+8
x= 20,32,44
Rashed12
IMO C is right
Re: Given that there are X boxes and the balls are arranged in such a way   [#permalink] 19 Mar 2019, 11:43
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