GATE CSE 2014 Set 1 | Question: 37

Question

There are $5$ bags labeled $1$ to $5$. All the coins in a given bag have the same weight. Some bags have coins of weight $10$ gm, others have coins of weight $11$ gm. I pick $1, 2, 4, 8, 16$ coins respectively from bags $1$ to $5$ Their total weight comes out to $323$ gm. Then the product of the labels of the bags having $11$ gm coins is ___.

Answer 1

The total number of coins taken=31

The minimum possible weight is 310gm , but given total weight of the coins is 323gm.

We need 13gm, which is possible with only 1st bag, 3rd bag and 4th bag.

Ans: 1×3×4=12

Answer 2

There are 5 bags numbered 1 to 5.

We don't know how many bags contain 10 gm and
11 gm coins.

We only know that the total weights of coins is 323.

Now the idea here is to get 3 in the place of total
sum's unit digit.

Mark no 1 bag as having 11 gm coins.
Mark no 2 bag as having 10 gm coins.
Mark no 3 bag as having 11 gm coins.
Mark no 4 bag as having 11 gm coins.
Mark no 5 bag as having 10 gm coins.

Note: The above marking is done after getting false
results for some different permutations, the permutations
which were giving 3 in the unit place of the total sum.

Now, we have picked 1, 2, 4, 8, 16 coins respectively
from bags 1 to 5.

Hence total sum coming from each bag from 1 to 5 is 11,
20, 44, 88, 160 gm respectively.

For the above combination we are getting 3 as unit digit
in sum.

Lets find out the total sum, it's 11 + 20 + 44 + 88 + 160 = 323.

So it's coming right.

Now 11 gm coins containing bags are 1, 3 and 4.
Hence, the product is : 1 x 3 x 4 = 12.

Answer 3

Total weight given is 323. We can get 3 at the end only by multiple of 11. If we take 3 coins we get weight distribution as-

290+33= 323.

We can have bag 1 and bag 2 for having 3 coins of weight 11 but remaining 4,8,16 coins of weight 10 account to only 280.

So our only choice left is to have 13 coins of weight 11.

11*13=143

323-143=180. The remaining coins 16+2=18*10=180.

Hence bag 1,3,4 contains coins of weight 11. So 12 is the answer.

Answer 4

SIMPLEST EXPLANATION 

ASSUMPTION TABLE BELOW: That all Weights picked is of 11

BAG	No of coins picked	Weight	Weight for each Bag
1	1	11	1 * 11    =  11
2	2	11	2 * 11    =  22
3	4	11	4 * 11    =  44
4	8	11	8 * 11    =  88
5	16	11	16 * 11   =  176

 

SUM OF ALL ABOVE TOTAL WEIGHTS = 11+22+44+88+176

                                                                   =   341

 

NOW REQUIRED TOTAL WEIGHT AS PER QUESTION IS

                                                                   =   323

 

THUS,     341 – 323 =  18 

 

THAT IMPLIES TO SIMPLY REMOVE 18 WEIGHTS FROM TOTAL

 

TO DO THAT , REMOVE BY ASSUMING HAVING 10 WEIGHTS FROM BAG 5 AND 2,  (The only combination possible for 18)

RESULTING IN REDUCTION OF 16 AND 2 WEIGHTS: 18, (since changes from 11 to 10)

 

THUS , BAG :2 , 5      HAS    10 WEIGHTS  

   AND  BAG  :1 , 3, 4  HAS   11 WEIGHTS, 

 

FINALLY ANSWER : 1 * 3 * 4 = 12