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ВОРОТА | GATE-CS-2014- (Set-1) | Вопрос 65

GATE

Есть 5 сумок с маркировкой от 1 до 5. Все монеты в данной сумке имеют одинаковый вес. В некоторых сумках есть монеты весом 10 грамм, в других — монеты весом 11 грамм. Я выбираю 1, 2, 4, 8, 16 монет соответственно из пакетов 1-5. Их общий вес составляет 323 грамма. Тогда произведение этикеток мешков с монетами 11 г составляет ___.
(А) 15
(Б) 12
(С) 8
(D) 1

Ответ: (Б)
Объяснение:

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.

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ВОРОТА | GATE-CS-2014- (Set-1) | Вопрос 65

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