This caselet is of a tabular arrangement type.But since there are three parameters( states, games, amount) and 6 in each category making a three dimensional table to find all the match pairs is cumbersome. So Let's try a reverse approach using answer options.

APPROACH ONE - REVERSE APPROACH

Any DI question set consists of the storyline and your data points but then the third and the most important part the QUESTIONS and options. We should ideally go through the questions & options once we are done with understanding the storyline and data points of any DI case-let.

Question 1 talks about highest amounts and that can be any things less than 600mn so all answer options are alive.

For question 2 data point VIII clearly states that Athletics is 150 more than Maharashtra so option a) is INCORRECT. According to data point VII we know Maharashtra received twice the amount Punjab did so it's not possible for Punjab to take up Athletics as its amount allocation is even lower than Maharashtra so option b) is INCORRECT

Looking at question 3 we know through data point VII which talks about volleyball, we know volleyball get twice the amount that TN gets or inversely speaking TN gets of $\frac{1}{2}$ volleyball. But if we take option a) to be true then TN gets 25mn (and that's not a multiple of 50) if we assume option b) to be true then TN=75mn; in the same lines options c) will also not work.We only have option d) in front of us!

As volleyball is 400mn, Bengal has to be 100mn more (data point VI).So now Bengal is at 500mn. The highest amount has to be either 500mn OR 550mn. Let's hope its 550mn and make our match table

$\begin{array}{ccc}\text{STATE}& \text{SPORT}& \text{AMOUNT}\\ & \text{VOLLEYBALL}& 400\\ \text{BENGAL}& & 500\\ ??& ??& 550\\ & & \\ & & \\ & & \\ \text{TOTAL AMOUNT SAI distributes}& & 1500\end{array}$

400 + 500 + 550 is allocated to the top three teams that's already 1450mn. We can't distribute 50mn to 3 states-sports. Hence 550mn is not the highest amount it can only be 500mn.Question 1 - ANS b)

Some more pondering and assuming will bring us closer to the remaining answers. Athletics has to be Kerala or Bengal. Let's assume it to be Bengal which has 500mn allocated to it; so if athletics is 500mn the Maharashtra has to be 150mn lesser then athletics (Data point VIII); hence Maharashtra=350m. let's see the match table:

$\begin{array}{ccc}\text{STATE}& \text{SPORT}& \text{AMOUNT}\\ & \text{VOLLEYBALL}& 400\\ \text{BENGAL}& \text{ATHLETICS}& 500\\ \text{MAHARASHTRA}& & 350\\ & & \\ & & \\ & & \\ \text{TOTAL AMOUNT SAI distributes}& & 1500\end{array}$

Three state-sport pairs have taken 1250mn(400 + 500 + 350), we have 250mn to distribute to 3 states-sport pairs. But no amount can be split and given to the remaining three so athletics can't be Bengal so the only option left is Kerala = athletics.

Ans for question 15 is (c)

APPROACH TWO: GRID APPROACH

Representation is the key and the easiest way to go about doing this is through columns and rows.

Using this representation all state-sport pairs can be matched by filling in the 36 cells and mark all the combinations that are not possible.

$\begin{array}{cccccccc}\text{STATE/SPORT}& \text{ATHLETICS}& \text{BASKETBALL}& \text{CRICKET}& \text{FOOTBALL}& \text{HOCKEY}& \text{VOLLEY}& \text{Money}\\ \text{ANDHRA(AP)}& X& X& X& X& X& \text{PAIR}& \text{Not highest}\\ \text{BENGAL(B)}& \text{CELL 7}& \text{CELL 8}& \text{CELL 9}& \text{CELL 10}& \text{CELL 11}& X& \\ \text{KERALA(K)}& \text{CELL 13}& \text{CELL 14}& \text{CELL 15}& X& \text{CELL 17}& X& \\ \text{MAHARASTRA(M)}& \text{CELL 19}& X& \text{CELL 21}& \text{CELL 22}& \text{CELL 23}& X& \\ \text{PUNJAB(P)}& \text{CELL 25}& \text{CELL 26}& \text{CELL 27}& \text{CELL 28}& \text{CELL 29}& X& 50/100\\ \text{TAMILNADU(TN)}& \text{CELL 31}& \text{CELL 32}& \text{CELL 33}& \text{CELL 34}& \text{CELL 35}& X& \\ \text{MONEY/AMOUNT}& & & & & & & \end{array}$

The above table is after going through one iteration of the data points but almost 20 cells still remain. This conventional method if continued will definitely get you the answer but takes a lot of time and hence is not to be used in CAT.

APPROACH THREE: MATCH TABLE APPROACH

The three variables are STATE - SPORT - AMOUNT and each of them has one single possible match pair. This ideally should bring out a match table representation.

$\begin{array}{ccc}\text{STATE}& \text{SPORT}& \text{AMOUNT}\\ & & \\ & & \end{array}$
We know for a fact that Punjab can only get either 50mn or 100mn as data point IV states that Punjab will get less than 150mn. The moment we get 6 pairs the job's done but it all begins by starting with Punjab=50mn and then going through all the data points to get all the 6 pairs. If grid method is a negation approach this is the exact opposite.

$\begin{array}{ccc}\text{STATE}& \text{SPORT}& \text{AMOUNT}\\ \text{PUNJAB}& \text{HOCKEY}& 50\\ \text{MAHARASHTRA}& \text{CRICKET}& 100\\ \text{KERALA}& \text{ATHLETICS}& 250\\ \text{TAMILNADU}& \text{BASKETBALL}& 200\\ \text{ANDHRA}& \text{VOLLEYBALL}& 400\\ \text{BENGAL}& \text{FOOTBALL}& 500\\ \text{TOTAL AMOUNT SAI distributes}& & 1500\end{array}$
With this table the SAI puzzle is solved again! We don't need to make a hundred equations, we don't need to fill up 36 to 42 cells in a grid; we just need 6 match pairs.

But in short,

Grid Approach: 15-20 minutes at least

Match table Approach: 10-15 minutes

Reverse Approach: 5 minutes and if you really try hard you can take 10 minutes!

If used to its optimum there's nothing that can make a CAT topper out of you then the reverse approach! It's not ethical but starting from your answers will be an approach that we'll help you deploy and help you master throughout this course. With the added power of mixing the reverse technique with our other techniques, DI might soon end up being your scoring section!