Free DI and LR Practice Test - CAT 

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!

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!

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!

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!

When finding the average of each group, consider difference from the total average, rather than the actual number, so that we need to add and subtract smaller numbers.  E.g. Deepak's average score for PCB is 98, overall average is 96, so this is +2 (98-96).

Similarly Maths is -1, social science -0.5 (95.5-96), vernacular -1 (95-96), let English be x. This should add up to 0.

+2 - 1 - 0.5 - 1 + x = 0, so x is +0.5. So English average is 96 + 0.5 = 96.5. So, paper 2 score is 97, option (c)

Only Deepak is eligible for the prize, so will receive the prize. Option (d)

Lesser the number of subjects in the group an increase in that subject's score will shoot up the scores of that group and also of the students total!

You can easily eliminate Anil and Prakash from the options as their total score is 2 points less than that of Anita and Deepak.

So the answer is option (d)

In august, G produces a maximum stock of (277 + 316)

F has the maximum stock in August

Number of T brand stock produced by G was maximum in June. 

Go from answer options. Answer is option (d)

3 students moved out of Edustar in the beginning of August, and the total people tutoring at Edustar in August has increased to 36. So, atleast 9 students have shifted to Edustar atthe beginning of august. The one addition to Gurumath could have been from Edustar or Matonline.

CASE 1- If it had been from Matonline, then 9 students have switched to Edustar at the beginning of August. As none shifted to Edustar from Gurumath,the entire 9 should have shifted out of Matonline and one person who shifted to Gurumath should have also been from Matonline, so minimum=10

CASE 2- If the one addition to Gurumath had been from Edustar, then 4 students would have shifted out of Edustar and hence, 10 students should have shifted to Edustar at the beginning of  august. As none shifted from Gurumath to Edustar, a minimum of 10 people should have shifted out of Matonline.

If no one shifted to Gurumath at the beginning of august, then 3 have shifted out of Gurumath and these 3 should have gone to matonlne as none shifted from Gurumath to Edustar. So, a total of 9 students have shifted out of Matonline, 3 out of Gurumath and 3 out of Edustar at the beginning of august. As a percentage, Edustar at 10% is the highest. Hence only statement II is true

If 11 students shifted to Edustar at the beginning of September, and the total students tutoring at Edustar has increased only by 7, then 4 students shifted out of Edustar at the beginning of September. Of these, atleast one should have shifted to Gurumath as its total number has increased to 39 from 38. the remaining 3 could have shifted to Matonline. So a minimum of no students needed to have shifted from Gurumath to Edustar

We know that 4 students have shifted out of Edustar. If one student shifts out of Gurumath (Assuming statement I as true) and the strength of Gurumath has increased to 39, then 2 students have shifted to Gurumath. As no one shifted between Gurumath and Matonline, the remaining 2 students move out of Edustar should have shifted to Matonline. So statement II is provided statement I is true.

Let the number of "First Rank” votes of Australia and West Indies be equal to c and d respectively.

The "First Rank” votes of India, England. Australia and West Indies should add up to 350.

Therefore, 101 + 84 + c + d = 350 , c + d = 165 , c = 165 - d

Now, 84 $>$ c $>$ 165 - c

Therefore c = 83 and d = 82. Hence, (b)

After the second round of counting,

India's vote - count = India's "First Rank” votes + West Indies's "First Rank” votes that have India as "Second Rank” = 101 + 17 = 118

Let the number of West Indies's "First Rank” votes that have England and Australia as the "Second Rank” be x and y respectively.

Therefore, 17 + x + y = 82 y = 65 - x.

England's vote-count = England's "First Rank” votes + West Indies's "First Rank” votes that have England as the "Second Rank” = 84 + x.

Australia's vote-count = Australia's "First Rank” votes + West Indies's "First Rank” votes that have Australia as the "Second Rank” = 83 + y = 83 + 65 - x = 148 - x.

As India led while England was eliminated.

118 $>$ 148 - x $>$ 84 + x , x = 31.

Therefore, 31 of West Indies's "First Rank” votes have England as the "Second Rank”.

Of these 16 have India as "Third Rank” (given). Hence, 31 - 16 = 15 will have Australia as "Third Rank”. 

"Vote Point” of Australia at the end of second round = 148 - x =148 - 31 = 117.

West Indies's "First Rank” votes that have Australia as the "Second Rank” = y = 65 -31 = 34. Therefore, West Indies's "First Rank” votes that have Australia, as the "Second Rank” and England as "Third Rank” 34.

Of the 84 votes where "Rank 1” was England, the number of votes with India as "Rank 2” = 18 (given)

The number of votes with West Indies as "Rank 2” = 22 +12 = 34 (given)

The number of votes with Australia as "Rank 2” = 84 - (18 + 22 +12) = 32. 

After the third round of counting,

India's vote point = India's vote point after the second round + Number of votes with England as "First Rank” and India as "Second Rank” + Number of votes with England as "First”, West Indies as "Second” and India as "Third Rank”. + Number of votes with West Indies as "First”, England as "Second” and India as "Third Rank”.

= 118 + 18 + 22 + 16 = 174 votes.

Therefore, Australia's vote - count = 350 - 174 = 176 votes

Therefore, Australia won by a margin of 176 - 174 =2 votes. 

From Statement 1

x + 3 = 4x - 3
6 = 3x
x=2
When x + 3 is positive,x= 2, a positive value. X=2 satisfies the original equation

And

-1(x + 3) = 4x - 3
-x - 3 = 4x - 3
0 = 5x
0 = x

But x=0 does not satisfy the original equation

Therefore, there is no solution when x + 3 is negative and we know that 2 is the only solution possible and we can say that x is definitely positive.

Statement 2

|x + 1| = 2x - 1
x + 1 = 2x - 1
x = 2.

Here again, x = 2 satisfies the original equation.

And

|x + 1| = 2x - 1 $\Rightarrow$-x - 1 = 2x - 1 $\Rightarrow$ x = 0
x = 0 does not satisfy the original equation.

We can determine using each statement alone, that the answer can be obtained as x=2 . Answer is option (C)

The required ratio$=\frac{5.6\%\times 53\%\times 66.7}{33.4\%\times 47\%\times 66.7}=\frac{53\times 5.6}{33.4\times 47}$= 0.18
 

The ratio of budgeted amount for Development by Defence and total budget of non-defence $\frac{90.8\%\times 53\%\times 66.7}{47\%\times 66.7}$, which is just greater than $\frac{48}{47}$ and hence the answer will be just greater than 1

In 2002, we do not know how the budget will be distributed across the sectors and aspects of research.

The minimum percentage of doctors that fall into the 35 to 40 years age group (both inclusive) is:

1 male with 0 post graduate degrees &38 years age,1 female with 1 post graduate degree &35 years age,1 female with 2 post graduate degrees & 37 years age and 1 female with 3 post graduate degrees &40 years age must be at least lie in this range.

Hence the required percentage = $\left(\frac{4}{30}\right)\times$100=13.33%

Doctors at most above 35 = 30 - at least≤ 35 = 30 - (1+1+2+1+1+1)= 23

The required percentage = 76.67%

number of such doctors = (1+1+1+1+1+1+2+1) = 9

(male- 0 post graduate degree + female-0 post graduate degree +male-1 post graduate degree + female- 1 post graduate degree + female- 2post graduate degree+male with 2 post graduate degree+ 2 males with 3 post graduate degree+1 female with 3 post graduate degrees...........)

Required percentage $\left(\frac{9}{30}\right)\times$=30%