How solve this DS?
Source: beatthegmat
A shop stores the bottles of soda in racks of 12 bottles and every rack is complete. On Sunday 60 more bottles of soda arrive and the shop has to store all the bottles in racks of 14 bottles so every rack is complete. How many bottles had the shop before Sunday?
a) The inicial amount was less than 110
b) The amount after Sunday was less than 120
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- cesar.rodriguez.blanco
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- sunny.jain
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Re: DS: A shop stores the bottles of soda
IMO : B
option 2 is sufficient.
Lets see how:
lets initial number of racks were x.
total number of bottle must be multiple of 12, because bottle were arranged in racks and rack racks has 12 bottle.
60 more bottle arrived.
so there must be 2*x bottle were used to adjust the initial racks(to make number from 12 to 14), and rest 60-2*x were used to settle in some new racks.
so 60-2*x must be divisible by 14.
number of factor of 14 in 60 : 14,28,42,56
14 means : 60-14 = 46 : 23 Racks or 23*12 bottles.
28 means : 60-28 = 32 : 16 racks or 16*12 bottles.
42 means : 18 : 9 racks or 9*12 = 108 bottles.
56 means : 2 racks or 24 bottles.
So Before these new bottles come, number of previous bottle has to be among
276, 196, 108, or 24.
Statement one:
1)Initial amount of bottle less than 110.
two option come in this category : 108 or 24 : Insufficient.
2) the amount after the bottle arrived was less than 120.
means previous it was 120-60 = 60
less than 60
means 24 only.
so B gives us the answer.
option 2 is sufficient.
Lets see how:
lets initial number of racks were x.
total number of bottle must be multiple of 12, because bottle were arranged in racks and rack racks has 12 bottle.
60 more bottle arrived.
so there must be 2*x bottle were used to adjust the initial racks(to make number from 12 to 14), and rest 60-2*x were used to settle in some new racks.
so 60-2*x must be divisible by 14.
number of factor of 14 in 60 : 14,28,42,56
14 means : 60-14 = 46 : 23 Racks or 23*12 bottles.
28 means : 60-28 = 32 : 16 racks or 16*12 bottles.
42 means : 18 : 9 racks or 9*12 = 108 bottles.
56 means : 2 racks or 24 bottles.
So Before these new bottles come, number of previous bottle has to be among
276, 196, 108, or 24.
Statement one:
1)Initial amount of bottle less than 110.
two option come in this category : 108 or 24 : Insufficient.
2) the amount after the bottle arrived was less than 120.
means previous it was 120-60 = 60
less than 60
means 24 only.
so B gives us the answer.
- edharmesh
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Re: DS: A shop stores the bottles of soda
I reached the same solution but slightly differently.
Out of the 60 bottles added, 14*4=56 went in to adding 4 new racks, remaining 4 went in to adjust the existing racks of 12.
Let's say there were n rack previously. So 12n+4 is a multiple of 14.
Out of first 12 multiples of 12, only 24 and 108 meet this condition.
A does not eliminate one or the other of 24 and 108.
B eliminates 108. So there were 2 racks earlier.
Out of the 60 bottles added, 14*4=56 went in to adding 4 new racks, remaining 4 went in to adjust the existing racks of 12.
Let's say there were n rack previously. So 12n+4 is a multiple of 14.
Out of first 12 multiples of 12, only 24 and 108 meet this condition.
A does not eliminate one or the other of 24 and 108.
B eliminates 108. So there were 2 racks earlier.
- RonPurewal
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Re: DS: A shop stores the bottles of soda
edharmesh Wrote:I reached the same solution but slightly differently.
Out of the 60 bottles added, 14*4=56 went in to adding 4 new racks, remaining 4 went in to adjust the existing racks of 12.
Let's say there were n rack previously. So 12n+4 is a multiple of 14.
Out of first 12 multiples of 12, only 24 and 108 meet this condition.
A does not eliminate one or the other of 24 and 108.
B eliminates 108. So there were 2 racks earlier.
nicely done.
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