Solution

This is a growth–decline comparison and ranking set across three years: 2016, 2020, and 2024, involving six entities A, B, C, D, E, and F. Let the values of A, B, C, D, E, and F in 2016 be a, b, c, d, e, f respectively. Also, we can mark the ranks 1, 2, 3, 4 as given. Rank for F is 6 (lowest) in all years, which gives the 5^th rank to D in 2016. Using this info, we can find values in 2020 and 2024 as follows:

We have Value of E in 2024 = 90. We can find value of E in 2016, that is e:

= 90 ⟹ e=90 * = 60.

Value of E in 2020 = = * 60 = 75.

We know that F is ranked 6 and B is ranked 1 in 2016, and the range of SI in 2016 and 2024 is 60. This means that the value of b-f = 60, from which, we can conclude that b is definitely greater than 60, and f is an integer greater than 0.

We know that all the SI values in all the years are integers, 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. So the three cases must be checked:

Case 1: b=64

64-f = 60, gives f=4. The value of F in 2024 will be = = * 4 = 6. We know the value of E in 2024=90. In this case, the range of SI of 2024 = 90-6 = 84, but we are also given that the range in 2016 and 2024 must be 60. So, this case must be eliminated.

Case 2: b=96

96-f = 60, gives f=36. The value of F in 2024 will be = = * 36 = 54. The value of B in 2024 = = * 96 = 54.

Since, it is given that F has lower SI than any other country, it cannot be equal to B as in this case. So, this case must be eliminated.

Case 3: b=80

80-f = 60, gives f=20. The value of F in 2024 will be = = * 20 = 30. The value of B in 2024 = = * 80 = 45.

No conditions are violated in this case, so these values will b fixed. [When in exam, if all cases except the last are eliminated, we need not check the last case, as it must be satisfying. But don’t check only when you are sure all eliminated cases are 100% true for elimination.]

Value of B in 2020 = = * 80 = 60.

Value of F in 2020 = 2b = 2*20 = 40.

Now, we can fill all the values for B, E and F.

For value of c, we can see its rank in 2016 is 2, between b and e, that is between 80 and 60, and value of c must be a multiple of 25 to get integer value. Therefore, only number multiple of 25 and between 60 and 80 is 75. Therefore, c = 75. Then,

Value of C in 2020 = = = = * 75 = 60. This is same as B in 2020, but they can be equal as no info for them to be unequal is given.

Value of C in 2024 = = * 75 = 84.

Q1. SI of E in 2016 = 60, answer. [*could be answered after5 mins of reading question]

CAT