GATE2012 CY: GA-9

Question

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

• A. $2$
• B. $3$
• C. $4$
• D. $8$

Comments

Simplest way to understand this question- https://www.youtube.com/watch?v=fLBwNfNx4FY

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minimum number of weighing required

what does it mean

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https://math.stackexchange.com/questions/1536963/n-marbles-puzzle-find-the-heaviest-among-them

 

what about this generalization?

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If two-pan weighing balance ⚖️

Ans -- 2

If one-pan weighing balance

Ans -- 4

Is it correct?

Answer 1

Answer is $a)$ i.e 2

 Divide in to $3-3-2$ and then take $3-3$ pair and then if they are equal then weigh the remaining $1-1$.

 

if out of $3-3$ one is heavier then take the heavier group and divide it $1-1-1$ take any two of these group and weigh again to get the heavier.

Comments

talha hashim 

What about the case 3 - 2 ???

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For such questions how do we decide no.of groups and no. Of bags in each group?

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pick the heavier one by observing the balance.

@krish__ aren’t we weighing it too? So this makes count to 3.

Answer 2

remember in this types of question we always consider the worst case  in minimum terms

as we have 8 bags total so just divide it into equal parts

       (1st partition ) 4 bags and 4 bags then weigh balance (take out 4 bags whose have maximum weight)

then for that 4 bags again divide into 

   (2nd partition ) 2 bags and 2 bags then weigh balance (take out 2 bags whose have maximum weight)

then for that 2 bags again divide into 

 (3rd  partition ) 1 bag and 1 bag then weigh balance(so in the last anyone out of these two will heavier bag  )

Answer 3

1. Take 3 bags and compare it with another 3 bags, if they are equal, then take remaining two bags and compare. Total wieghtings = 2.

2. If in step one, if 3 bags are not equal to another three bags. Then take the heavier 3 bag group and pick any 2 bags and compare , if they are same, then 3rd bag is heavy bag.If not, the we will get heavy bag anyway.

So, in either case only 2 wieghtings is required. Hence , Answer is A.

Comments

Take 3 bags and compare it with another 3 bags, if they are equal, then take remaining two bags and compare. Total wieghtings = 2.

Comparing 3 bags with another 3 takes 2 weighing itself. how you counting it 2 overall?

Answer 4

We have 4 options 2, 3, 4, 8 and we have to find the minimum weighings required, so the approach should to be to use minimum weights first and check if it's possible.

Taking 2 :

Lets say weight in each bag = 5 and in slightly higher one = 6

So bags becomes 5 5 5 5 5 5 5 6

Putting in 2 machines equally :

1st machine : 20, 2nd Machine : 21

We will apply the same procedure on the 4 bags that combined weighs 21

Eventually we will seperate that weight of 6 using just 2 machines.