GATE CS 2014 Set 1 — Question 47
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Digital Logic → Analytical Aptitude → Number Base Conversions
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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 ___.
Correct answer
12 to 12
Solution
Let the weight of coins in bag be .
Let be the number of coins picked from bag . We are given .
The total weight is .
Let , where if the bag has 11 gm coins, and if it has 10 gm coins.
Then,Sum of coins .We need to express 13 as a sum of the values . Since these are powers of 2, the representation is unique (binary representation of 13).This corresponds to , , and .
So, , and .
The bags with 11 gm coins are Bag 1, Bag 3, and Bag 4.
The product of their labels is .
Let be the number of coins picked from bag . We are given .
The total weight is .
Let , where if the bag has 11 gm coins, and if it has 10 gm coins.
Then,Sum of coins .We need to express 13 as a sum of the values . Since these are powers of 2, the representation is unique (binary representation of 13).This corresponds to , , and .
So, , and .
The bags with 11 gm coins are Bag 1, Bag 3, and Bag 4.
The product of their labels is .
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