CAT 2025 DILR Slot 2 Question 12

Question

What was the SI of C in 2024?

Accepted Answer

Let us assume the values of A, B, C, D, E and F to be a, b, c, d, e and f in 2016.For A:Value in 2020 = increased by 25% from 2016 = left(1 + dfrac{25}{100}right)a = dfrac{5}{4}aValue in 2024 = increased by 50% from 2020 = left(1 + dfrac{50}{100}right)times dfrac{5a}{4} = dfrac{15}{8}aFor B:Value in 2020 = decreased by 25% from 2016 = left(1 - dfrac{25}{100}right)b = dfrac{3}{4}bValue in 2024 = decreased by 25% from 2020 = left(1 - dfrac{25}{100}right)times dfrac{3b}{4} = dfrac{9}{16}bFor C:Value in 2020 = decreased by 20% from 2016 = left(1 - dfrac{20}{100}right)c = dfrac{4}{5}cValue in 2024 = increased by 40% from 2020 = left(1 + dfrac{40}{100}right)times dfrac{4c}{5} = dfrac{28}{25}cFor D:Value in 2020 = increased by 100% from 2016 = left(1 + dfrac{100}{100}right)d = 2dValue in 2024 = increased by 20% from 2020 = left(1 + dfrac{20}{100}right)times 2d = dfrac{12}{5}dFor E:Value in 2020 = increased by 25% from 2016 = left(1 + dfrac{25}{100}right)e = dfrac{5}{4}eValue in 2024 = increased by 20% from 2020 = left(1 + dfrac{20}{100}right)times dfrac{5e}{4} = dfrac{3}{2}eFor F:Value in 2020 = increased by 100% from 2016 = left(1 + dfrac{100}{100}right)f = 2fValue in 2024 = decreased by 25% from 2020 = left(1 - dfrac{25}{100}right)times 2f = dfrac{3}{2}fWe are given that the value of E is 90 in 2024. We can calculate the value of e as,dfrac{3e}{2} = 90e = 60The value of E in 2016 is 60, and its value in 2020 can be calculated as,dfrac{5e}{4} = dfrac{5}{4}times 60 = 75We are given that B, C, E, and A had ranks 1, 2, 3, and 4, respectively, in 2016, and F has the lowest rank(6) in all the years.Putting the values in the table, we get, We know that F is ranked 6 and B is ranked 1 in 2016, and we are also given that the range of SI in 2016 and 2024 is 60. This means that the value of b-f = 60, and we can conclude that b is definitely greater than 60, as we know that f is an integer greater than 0.We know that all the SI values in all the years are integers, and for SI of B to be an integer in 2024, the value of b must be a multiple of 16. The multiples of 16 that are greater than 60 and less than 100 are 64, 80 and 96.CASE 1: b = 64If b = 64, then the value of f becomes 4, as we know b - f = 60.If f = 4, then the value of F in 2024 is 3f/2 = 12/2 = 6.We already know the value of E in 2024 is 90.In that case, the range of SI in 2024 is at least 90 - 6 = 84, but we are given that the range is 60 in 2024, which is not possible in this case.So, we can eliminate this case.CASE 2: b = 96If b = 96, then the value of f becomes 36, as we know b - f = 60.If f = 36, then the value of F in 2024 is 3f/2 = 108/2 = 54.The value of B in 2024 = 9b/16 = (9 * 96)/16 = 54We calculated the value of B and F to be 54 in 2024, which is not possible, as we are given that F had a lower SI than any other country in 2024, and we obtained its value to be the same as B.So, we can eliminate this case.CASE 3: b = 80If b = 80, then the value of f becomes 20, as we know b - f = 60.If f = 20, then the value of F in 2024 is 3f/2 = 60/2 = 30.The value of B in 2024 = 9b/16 = (9 * 80)/16 = 45We can see that no condition is violated in this case, as F is less than B in 2024, and the range in 2024 from the obtained values as of now is 90 - 30 = 60.So, we can conclude that the value of b = 80 and f = 20.Substituting the values in the table, we get, We know that C is ranked 2nd in 2016, and we know the values of 1st and 3rd to be 80 and 60. We also know that SI of C has to be integers in 2016, 2020 and 2024. So, for the value of SI of C to be an integer in 2024, the value of c has to be a multiple of 25.So, we know that c lies between 80 and 60, and is also a multiple of 25. The only multiple of 25 that lies between 60 and 80 is 75. So, the value of c has to be 75, and the value of C in 2024 can be calculated as,C in 2024 = 28c/25 = (28 * 75)/25 = 84.Hence, the correct answer is 84.

Login

Passage

Question 12

No video explanation yet — we're uploading soon!

Master CAT Preparation with Previous Year Papers

Why Practice CAT Previous Year Questions?

Additional Preparation Resources