# Free DI and LR Practice Test - CAT

### Question 1

The highest amount given by SAI is

#### SOLUTION

Solution :B

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 APPROACHAny 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 12 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 tableSTATESPORTAMOUNTVOLLEYBALL400BENGAL500????550TOTAL AMOUNT SAI distributes1500

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:STATESPORTAMOUNTVOLLEYBALL400BENGALATHLETICS500MAHARASHTRA350TOTAL AMOUNT SAI distributes1500

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 APPROACHRepresentation 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.

STATE/SPORTATHLETICSBASKETBALLCRICKETFOOTBALLHOCKEYVOLLEYMoneyANDHRA(AP)XXXXXPAIRNot highestBENGAL(B)CELL 7CELL 8CELL 9CELL 10CELL 11XKERALA(K)CELL 13CELL 14CELL 15XCELL 17XMAHARASTRA(M)CELL 19XCELL 21CELL 22CELL 23XPUNJAB(P)CELL 25CELL 26CELL 27CELL 28CELL 29X50/100TAMILNADU(TN)CELL 31CELL 32CELL 33CELL 34CELL 35XMONEY/AMOUNT

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 APPROACHThe 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.

STATESPORTAMOUNT

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.STATESPORTAMOUNTPUNJABHOCKEY50MAHARASHTRACRICKET100KERALAATHLETICS250TAMILNADUBASKETBALL200ANDHRAVOLLEYBALL400BENGALFOOTBALL500TOTAL AMOUNT SAI distributes1500

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!

### Question 2

Which of the following is the Athletics team?

#### SOLUTION

Solution :C

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 APPROACHAny 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 12 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 tableSTATESPORTAMOUNTVOLLEYBALL400BENGAL500????550TOTAL AMOUNT SAI distributes1500

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:STATESPORTAMOUNTVOLLEYBALL400BENGALATHLETICS500MAHARASHTRA350TOTAL AMOUNT SAI distributes1500

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 APPROACHRepresentation 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.

STATE/SPORTATHLETICSBASKETBALLCRICKETFOOTBALLHOCKEYVOLLEYMoneyANDHRA(AP)XXXXXPAIRNot highestBENGAL(B)CELL 7CELL 8CELL 9CELL 10CELL 11XKERALA(K)CELL 13CELL 14CELL 15XCELL 17XMAHARASTRA(M)CELL 19XCELL 21CELL 22CELL 23XPUNJAB(P)CELL 25CELL 26CELL 27CELL 28CELL 29X50/100TAMILNADU(TN)CELL 31CELL 32CELL 33CELL 34CELL 35XMONEY/AMOUNT

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 APPROACHThe 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.

STATESPORTAMOUNT

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.STATESPORTAMOUNTPUNJABHOCKEY50MAHARASHTRACRICKET100KERALAATHLETICS250TAMILNADUBASKETBALL200ANDHRAVOLLEYBALL400BENGALFOOTBALL500TOTAL AMOUNT SAI distributes1500

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!

### Question 3

The amount given by SAI to the Volleyball team is

#### SOLUTION

Solution :D

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 APPROACHAny 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 12 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 tableSTATESPORTAMOUNTVOLLEYBALL400BENGAL500????550TOTAL AMOUNT SAI distributes1500

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:STATESPORTAMOUNTVOLLEYBALL400BENGALATHLETICS500MAHARASHTRA350TOTAL AMOUNT SAI distributes1500

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 APPROACHRepresentation 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.

STATE/SPORTATHLETICSBASKETBALLCRICKETFOOTBALLHOCKEYVOLLEYMoneyANDHRA(AP)XXXXXPAIRNot highestBENGAL(B)CELL 7CELL 8CELL 9CELL 10CELL 11XKERALA(K)CELL 13CELL 14CELL 15XCELL 17XMAHARASTRA(M)CELL 19XCELL 21CELL 22CELL 23XPUNJAB(P)CELL 25CELL 26CELL 27CELL 28CELL 29X50/100TAMILNADU(TN)CELL 31CELL 32CELL 33CELL 34CELL 35XMONEY/AMOUNT

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 APPROACHThe 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.

STATESPORTAMOUNT

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.STATESPORTAMOUNTPUNJABHOCKEY50MAHARASHTRACRICKET100KERALAATHLETICS250TAMILNADUBASKETBALL200ANDHRAVOLLEYBALL400BENGALFOOTBALL500TOTAL AMOUNT SAI distributes1500

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!

### Question 4

The team which Andhra Pradesh represents is

#### SOLUTION

Solution :A

APPROACH ONE -

REVERSE APPROACHdata 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 tableSTATESPORTAMOUNTVOLLEYBALL400BENGAL500????550TOTAL AMOUNT SAI distributes1500

Data point VIII); hence Maharashtra=350m. let's see the match table:STATESPORTAMOUNTVOLLEYBALL400BENGALATHLETICS500MAHARASHTRA350TOTAL AMOUNT SAI distributes1500

Ans for question 15 is (c)

APPROACH TWO:

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

APPROACH THREE:

MATCH TABLE APPROACH

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.

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!

### Question 5

How much did Deepak get in English Paper II?

94

96.5

97

98

#### SOLUTION

Solution :C

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)

### Question 6

Students who obtained Group Scores of at least 95 in every group are eligible to apply for a prize. Among those who are eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:

Swati

Rohan

Anita

Deepak

#### SOLUTION

Solution :D

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

### Question 7

Each of the ten students was allowed to improve his/her score in exactly one paper of choice with the objective of maximizing his/her final score. Everyone scored 100 in the paper in which he or she chose to improve. After that, the topper among the ten students was:

Anil

Prakash

Anita

Deepak

#### SOLUTION

Solution :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)

### Question 8

**The aggregate stock of T and F produced by G was the maximum in?**

#### SOLUTION

Solution :C

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

### Question 9

**G had the maximum stock of F in the month of**

#### SOLUTION

Solution :C

F has the maximum stock in August

### Question 10

**The number of T brand stock produced by G was maximum in**

#### SOLUTION

Solution :A

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

### Question 11

**In which month was the rejected stock of F, higher than that of T?**

#### SOLUTION

Solution :D

Rejected Stock of T for the months May, June, July, and August are 52.5, 41, 22 and 50 respectively

Similarly for F, it is 45, 17, 60 and 125

Therefore Stock of F is greater that that of T for the months July and August.

### Question 12

**Which of the following indicates the highest absolute difference between the stocks passed the test and produced newly, for any product, during a month?**

#### SOLUTION

Solution :D

Go from answer options. Answer is option (d)

### Question 13

**If no one switched from Gurumath to Edustar at the beginning of August and atleast one person switched to Gurumath at the beginning of August, what is the minimum number of people who should have switched out of Matonline at the beginning of August?**

7

9

10

3

#### SOLUTION

Solution :C

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.

### Question 14

**If no one shifted to Gurumath and if noone switched from Gurumath to Edustar at the beginning of August, which of the following is correct?**

I. The percentage of students shifting out of a tutoring service as a percentage of the students at the beginning of the previous month was highest at the beginning of August for Matonline.

II. The number of students who shifted out of Edustar is the same as those who shifted out of Gurumath at the beginning of August

Only II is true

Both I and II are true

#### SOLUTION

Solution :B

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

### Question 15

If at the beginning of September no one shifted between Matonline and Gurumath, what is the minimum number of students who shifted from Gurumath to Edustar at the beginning of September?

#### SOLUTION

Solution :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

### Question 16

**Which of the following is correct if no one shifted between Matonline and Gurumath at the beginning of September?**

I) One student shifted out of Gurumath at the beginning of September

II) 2 students shifted to Matonline

II is true only if I as true

II is not true if I is true

II is true only if I is not true

Both statements are not true

#### SOLUTION

Solution :A

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.

### Question 17

**How many "Rank 1" votes did West Indies get?**

83

82

81

80

#### SOLUTION

Solution :B

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”.

### Question 18

Of all the votes that had West Indies as "Rank 1” and England as "Rank 2”, how many had Australia as "Rank 3”

#### SOLUTION

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

### Question 19

What was Australia's "vote point" at the end of the second round of counting?

#### SOLUTION

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

### Question 20

**Of all the votes that had West Indies as "Rank 1” and Australia as "Rank 2”, how many could have had England as "Rank 3”?**

15

17

18

#### SOLUTION

Solution :D

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.

### Question 21

Of all the votes that had England as "Rank 1”, how many had Australia as "Rank 2”?

#### SOLUTION

Solution :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.

### Question 22

**Who won the elections and by what margin of "vote point”?**

#### SOLUTION

Solution :D

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.

### Question 23

**Which of the following will not affect the final result?**

#### SOLUTION

Solution :D

In options (a), (b) and (c), India’s final vote-count will increase by 2 to 176, thus making India the winner with 176 votes. In option (d), the votes with England as “First”, West Indies as “Second” and Australia as “Third Rank” decreases from 12 to 10. Then as a result. The number of votes with, England as “First Rank” and Australia as “Second Rank” will increase from 32 to 34. Thus, the overall vote point of C will remain unchanged at 176. Hence (d)

### Question 24

Is x a natural number?

(1) |x + 3| = 4x - 3

(2) |x + 1| = 2x - 1

#### SOLUTION

Solution :C

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 equationAnd

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

-x - 3 = 4x - 3

0 = 5x

0 = xBut 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 ⇒-x - 1 = 2x - 1 ⇒ 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)

### Question 25

Given that P is a natural number. Is P>1010?

1) P>234

2) P=235

#### SOLUTION

Solution :D

From statement 1−P>234

234=(210)3×24=16×(210)3

Now 210=1024, and 1024 is greater than 103.

Therefore

234>16×(103)3=1.6(1010)

Since 234>1.6(1010)>1010, from statement 1 alone; the answer can be determined

From statement 2−P=235

### Question 26

**The ratio of the budgeted amount for Applied Research by the Defence to the budgeted amount for Development by sectors other than Defence is**

#### SOLUTION

Solution :A

The required ratio=5.6%×53%×66.733.4%×47%×66.7=53×5.633.4×47= 0.18

### Question 27

**What is the ratio of the budgeted amount for Development by Defence to the total budgeted amount for sectors other than Defence?**

#### SOLUTION

Solution :A

The ratio of budgeted amount for Development by Defence and total budget of non-defence 90.8%×53%×66.747%×66.7, which is just greater than 4847 and hence the answer will be just greater than 1

### Question 28

**If the Federal Research and Development Budget in 2002 increases by 10% over that of 2001, by what percentage will the budget for Basic Research by Defence increase?**

#### SOLUTION

Solution :D

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

### Question 29

**In the Federal Research and Development Budget for 2001, what is the ratio of the budgeted amount for Basic Research and that for Applied Research?**

#### SOLUTION

Solution :A

The required ratio will be 2.1%×53×31.2%×475.6%×53×31.2%×47

The denominator will be greater and by a very small amount. Eliminate option (c) & (d), the only answer possible is 1 : 1.11

### Question 30

**The percentage of doctors that fall into the 35 to 40 years age group (both inclusive) is at least**

#### SOLUTION

Solution :C

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 = (430)×100=13.33%

### Question 31

**Given the information above, the percentage of doctors older than 35 can be at most**

#### SOLUTION

Solution :C

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

The required percentage = 76.67%

### Question 32

**The percentage of respondents aged less than 40 years is at least**

10%

16.67%

20.0%

30%

#### SOLUTION

Solution :D

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 (930)×=30%