Question

Given the following clues, can you work out the number of gold, silver and bronze medals that France, Italy and Japan got in this international sports competition?

Japan has 1 more gold medal, but 3 fewer silver medals, than Italy.

France has the most bronze medals (18), but fewest gold medals (7).

Each country has at least 6 medals of each type.

Italy has 27 medals in total.

Italy has 2 more bronze medals than gold medals.

The three countries have 38 bronze medals in total.

France has twice as many silver medals as Italy has gold medals.

Answer 1

Given : clues, about number of gold, silver and bronze medals that France, Italy and Japan got in this international sports competition

To find :  Each country medal tally

Solution:

Each country has at least 6 medals of each type.

France has 18 bronze medal

The three countries have 38 bronze medals in total.

=> Italy + Japan has 38 - 18 = 20 Bronze medals

Italy has 2 more bronze medals than gold medals. so Italy has minimum 8 bronze medals

Let say Italy Has    8 + B bronze medal   Then   Japan has 20 - (8 + B) =  12 - B  bronze medal

B lies between 0 & 6  

Italy has gold medal = 6 + B  

Italy total medal = 27

Italy Silver Medal  = 27 - (8 + B) - (6 + B)  = 13  - 2B

13  - 2B  > 6

=> B lies between 0  & 3

Japan Gold medal = 6 + B + 1 = 7 + B

Japan has Silver medals =  13 - 2B - 3  = 10  - 2B

10  - 2B  ≥ 6

=> B ≤  2  

Italy has gold medal = 6 + B  

France has  fewest gold medal  = 7

=> 6 + B > 7

=> B > 1

1  < B ≤  2  

Hence only possible value of B = 2

Italy gold medal = 6 + 2 = 8

Italy Bronze medal = 8 + 2 = 10

italy Silver medal = 13 - 2B  =  9

Japan gold medal = 7 + 2  = 9

Japan Silver Medal = 9 - 3 = 6   or 10 - 2B =  6

Japan Bronze model = 12 - B = 12  - 2 = 10

France Bronze medal = 18

France silver medal = 2 x 8  = 16

France gold medals  = 7

                         

                         GOLD        SILVER         BRONZE

JAPAN                   9                  6                   10

ITALY                     8                  9                   10

FRANCE                 7                 16                   18

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