Correct answer
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Method
The approach to this question is to first target the low hanging fruit. In other words, let's find the ones that are easy to calculate or require less calculation.
Let's start with country E, as this is the most straightforward. The medals are in the order of prime numbers.
The first three prime numbers are 2, 3 and 5. So the medals for E are,
Gold = 2, Silver = 3 and Bronze = 5
Total medals = 2 + 3 + 5 = 10
(Remember 1 is not a prime number because it only has one factor. Prime numbers have exactly two factors.)
There are 26 events that mean there are 26 gold, 26 silver and 26 bronze medals to be won. The total number of medals to be won in the whole event are
= 26 + 26 + 26
Total of all medals = 78
Next, let's focus on C as we have a lot more information about C than others.
C has won a total of 17 medals out of which 4 are bronze. This means that the remaining 13 are gold and silver.
As per the question, if C won x gold medals then their silver medals are (x+1).
We also know that, gold + silver = 13
We can put this information in an equation.
So, x + (x + 1) = 13
2x + 1 = 13
2x = 13 - 1
2x = 12
x = 12/2 = 6
This means that there are 6 gold and 7 silver.
Next, let's look at D. Because we know that the teams are arranged in the order of medals won and we know that the total of C is 17 and E is 10. The total medals of D must be some number between 10 and 17. It can be 11, 12, 13, 14, 15 or 16. Which we need to figure out.
As per the question, if the number of gold medals won by D is x.
Then, silver = 2 times gold and bronze = 2 times silver.
Silver = 2x and Bronze = 4x.
The total medals won by D are then,
x + 2x + 4x = 7x
7x must be equal to 11, 12, 13, 14, 15 or 16. So now let's understand how do we narrow it down to one of those numbers.
If 7x = 11, then x = 11/7.
We cannot divide 11 into 7 equal parts so this cannot be the answer. In a similar, way the only number in the list that is divisible by 7 is 14.
If 7x = 14, then x = 14/7.
Then x = 2.
Gold = 2, Silver = 4 and Bronze = 8
The total of gold medals across all 26 events is 26. Out of which B has 7, C has 6, D has 2 and E has 2. So gold for A can be calculated with the data we have.
A = 26 - (7 + 6 + 2 + 2)
A = 26 - 17
A = 9
The total of bronze medals across all 26 events is 26. Out of which A has 2, C has 4, D has 8 and E has 5. So bronze for B can be calculated with the data we have.
B = 26 - (2 + 4 + 8 + 5)
B = 26 - 19
B = 7
The question does not give us any other clues about A and B. So we need to think out of the box.
We know that the total medals are 78.
We also know now that total of C is 17, D is 14 and E is 10
Total of C,D and E are = 17 + 14 + 10 = 41
This means that the remaining medals, that A and B have are
78 - 41 = 37
Remember that the countries are arranged in the order of position. That means that B must have more medals than C.
If we assume that B has 18, then the number of medals left for A must be more than 18 for A to be in the first position.
Let's put that in an equation and see what we get.
A = total left - B
A = 37 - 18
A = 19. This looks good so far but let's perform one more test.
If we assume that B has 19. Then
A = 37 - 19 = 18
This cannot be true because being in the first position must have more than B.
So the only possibility is that A has 19 and B has 18.
Now calculate the silver medals for A.
Silver = total - (gold + bronze)
Silver = 19 - (9 + 2)
Silver = 19 - 11 = 8
Now calculate the silver medals for B.
Silver = total - (gold + bronze)
Silver = 18 - (7 + 7)
Silver = 18 - 14 = 4
Finally we have,
A = 9G + 8S + 2B = 19
B = 7G + 4S + 7B = 18
C = 6G + 7S + 4B = 17
D = 2G + 4S + 8B = 14
E = 2G + 3S + 5B = 10
