# Free DI and LR Practice Test - CAT

### Question 1

**The average number of customers in a group is **.

2

5

4

6

#### SOLUTION

Solution :C

Total no. of customers who come in groups = (80 + 50 + 28 + 30 + 100 + 72) = 360

Total no. of bills issued for groups of customers = (230 - 210) + (130 - 120) + (57 - 50) + (70 - 60) + (200 - 180) + (154 - 130) = 81

Therefore, Avg. no.customer in a group =(36091)=4(approx)

### Question 2

**The average bill amount spend by customer in a group is approximately ______ times that spent by a customer when single?**

#### SOLUTION

Solution :A

Average bill amount spent by customer in a group =

Total bill amount spent by customers in a group =

=RS.[(80∗5.20) + (50∗4.30) + (28∗4) + (30∗3.9) + (100∗5.5) + (72∗6)][80+50+28+30+100+72]

= Rs 5.12

Total bill amount spent by single customers =

=RS.[6∗210)+(4.8∗120)+(4∗50)+(4.2∗60)+(5.8∗180)+(6.1∗130)][210+120+50+60+180+130]

= Rs.5.50

Ratio =5.125.50=0.9 (approx)

### Question 3

**During which 2-hour interval during the day is the collection amount maximum?**

#### SOLUTION

Solution :A

Total collection in 8 am - 10 am interval = Rs [(210×6)+(80×5.2)] = Rs 1676 Similarly calculate for all intervals and check. It is highest for 8 am - 10 am interval.

### Question 4

**If restaurant makes a profit of 5 % on the selling price of each item and is open 25 days in the month of August, what is the approximate profit amount in August?**

#### SOLUTION

Solution :D

Total collection for a day

Rs. [(1676 + 791 + 312 + 369 + 1594 + 1225)] = Rs. 5967

Profit for a day = Rs. (5967×5100) = Rs. 298.35

Profit for a month = Rs. [298.35 × 25]

= Rs 7458.75

= Rs. 7500 (approx)

### Question 5

**In the year 1971, country X spent 9% of its GDP on defence and in the year 1991, it spent 15% of its GDP on defense. Then what is the difference in the amounts spent on defence in these two years?**

#### SOLUTION

Solution :C

GDP in the year 1971=900002=45000 cr

9% is spent for defence = 4050 cr

GDP in the year 1991=19600003.8=515789 cr

15% is spent for defence= 77368 cr

Difference= 73318 cr

### Question 6

**Among the following which 10 year period shows the highest growth in GDP over the previous 10 year period ?**

#### SOLUTION

Solution :D

The answer can be obtained either by elimination of answer options or by following a trend in the graphs. The maximum increase is seen from 1981-1991

### Question 7

**What is the total GDP ( in Rs. crore) for the years 1951, 1961, 1971, 1981?**

#### SOLUTION

Solution :B

GDP in the year

1951 = 10666.66

1961= 16000

1971= 45000

1981= 126666

Sum = 198332.

### Question 8

**If the health expenditure in 2005 is 198000 cr, then the annual increase in the period 2001 to 2005 is nearest to ?**

#### SOLUTION

Solution :C

CAGR = (Final valueinitial value)1/n−1, here n = 4

Here (Final valueinitial value)= 2.544

Going from answer options

Assuming a middle answer option= 25%

Then (1.25)4 should give us something close to 2.5 if it is the correct answer option(1.25)4=(1.254×1.254)=(15.6×15.6)≈2.4. Thus this is the correct answer

### Question 9

If the Doctor stays in Kolkata, how many children does the teacher have?

1

2

0 or 1

#### SOLUTION

Solution :B

CASE 1

No of childrenOfficeProfessionLocation0AlphaPilotChennai1GammaTeacher/Doctor/EngineerKolkata1BetaDoctor/EngineerDelhi2DeltaTeacher/EngineerMumbai

CASE 2

No of childrenOfficeProfessionLocation0AlphaPilotChennai1GammaDoctorKolkata1DeltaEngineerDelhi2BetaTeacherMumbai

this is case (2) as shown above

### Question 10

If the teacher works with Delta Ltd., who works with Beta Ltd.?

Doctor

Engineer

Pilot or Doctor

#### SOLUTION

Solution :D

From case 1, we can only conclude as follows

No of childrenOfficeProfessionLocation0AlphaPilotChennai1GammaDoctor/EngineerKolkata1BetaDoctor/EngineerDelhi2DeltaTeacherMumbai

Thus the answer is option (d)

### Question 11

If the Engineer has two children, where does the Teacher stay?

Kolkata

Mumbai

Delhi

#### SOLUTION

Solution :A

From case 1 above

No of childrenOfficeProfessionLocation0AlphaPilotChennai1GammaTeacherKolkata1BetaDoctorDelhi2DeltaEngineerMumbai

### Question 12

If the person working with Delta Ltd. has 2 children and is a Teacher and the Doctor stays in Kolkata, who stays in Delhi?

Pilot

Teacher

Engineer

#### SOLUTION

Solution :C

From case 1 above

No of childrenOfficeProfessionLocation0AlphaPilotChennai1GammaDoctorKolkata1BetaEngineerDelhi2DeltaTeacherMumbai

### Question 13

**In 2000, if CAD/CAM forms 70% of the revenue from other product groups, what percentage of the total revenue is earned from CAD/CAM in 2000?**

#### SOLUTION

Solution :D

The question asks what percentage of the total revenue whereas the distribution of revenue across product groups is only given for Export Revenue. Thus, we do not know how much does CAD/CAM contribute to the Domestic Revenue.

### Question 14

**If the revenue from exports across different product groups were to be represented by a pie-chart, what angle would the sector depicting export earnings from Internet form at the centre of the piechart in year 2000?**

#### SOLUTION

Solution :B

All you need to find here is that, if the total is 100, then Internet is 29.5. Hence, if total is 360, then Internet will be 29.5 × 3.6 = 108 - 1.8 = 106.2.

### Question 15

**If Operating Profit is defined as Revenue - Expenses and OPM (Operating Profit Margin) as the Operating Profit as a percentage of Revenue, then which of the following statements is true?**

#### SOLUTION

Solution :B

Conventional ApproachHere we have to compare the ratios 5184/13386, 2318/6049, i.e. we have to compare 51.84% of 6049 and 23.18% of 13386.

50% of 6049 is 3024.5; 1% of 6049 is 60.49; 0.8% of 6049 is 48.392; 0.05% of 6049 is 3.0245. Thus, 51.85% of 6049 is 3024.5 + 60.49 + 48.392 + 3.02 = 3136.4.

Similarly, 20% of 13386 is 2677.2; 3% of 13386 is 401.58; 0.1% of 13386 is 13.386, and 0.08% is 10.708 and thus 23.18% of 13386 is 2677.2 + 401.58 + 13.38 + 10.70 = 3102.86.

Thus, the first ratio is greater and thus OPM of 2000 is greater than that for 1999.

ShortcutCut down the number of digits. (OPM)99 =13−813=513 and (OPM)2000 =6−33=36 or 12. Thus you can directly see that 12 is greater than 513.

### Question 16

**If the export revenue from Mainframe increased by 121% in 2000 over that in 1999, what percentage of the export revenue in 1999 was accounted by Mainframe?**

#### SOLUTION

Solution :C

The required percentage is (14%×132152.21×5981)×100%≈14%.

### Question 17

If the Histology HOD is a man, which of the following is definitely not true?

The Nephrology HOD is sitting in between the two women

The Nephrology HOD is sitting in between two men

The Cardiology HOD is a man

The Nephrology HOD is a woman

#### SOLUTION

Solution :A

Solution: condition 1 and 3 => the Cardiology HOD is a man. The Pediatrics HOD is also a man and as per the question the Histology HOD is also a man => Nephrology and Urology HOD are women.

### Question 18

If the Cardiology HOD always has a woman to his right, in how many different arrangements can the Nephrology HOD be a woman?

2

3

4

None of these

#### SOLUTION

Solution :D

From the above three figures, we can conclude that 6 arrangements are possible.

### Question 19

If the Urology HOD is sitting just to the right of the Pediatrics HOD, which of the following statement(s) is/are definitely True?

(I) The Nephrology HOD and the CardiologyHOD sit next to each other.

(II) The Histology HOD has to be a woman.

(III) The Urology HOD has to be a man.

(I) only

(I) and (II)

(I) and (III)

(II) and (III)

#### SOLUTION

Solution :A

From the above diagram, we can easily conclude that only statement I is true.

### Question 20

How many competitors does F have?

#### SOLUTION

Solution :CompaniesABCDEFGHNo.of competitors13647336

Since E has 7 competitors ,every other company is its competitor. A has only one competitor,thus only E is its competitor. H and C have 6 competitors each , so , all the companies except A will be their competitors. B AND G have only 3 competitors each , so, they won't have any competitor except E,C and H. To complete this, for the number of competitors for D to be 4, D and F should be each other's competitor.

COMPANIESCOMPETITORSAEBE,H,C,CE,B,D,F,G,HDE,H,C,FEA,B,C,D,F,G,HFE,H,C,DGE,H,C,HE,C,B,D,F,G

Hence, F has 4 competitors.

### Question 21

**The number of companies selling Frisbees in one zone is at most**

4

8

6

5

#### SOLUTION

Solution :D

Maximum cannot be 8 as then A will have more than 1 competitor.

If it is 7 , then A will be excluded from that zone and all the others will sell in that zone, then B will have more than 3 competitors. so, not possible.

If it is 6 , then we exclude B and A from that zone. then, D will have 5 competitors,not possible as given that D has 4 competitors.

If it is 5 , then we exclude A,B,G and this is a possible case.

### Question 22

**Each zone is given as many points as the number of companies who sold Frisbees in it. If there is exactly one zone where no company sold Frisbees, then the aggregate number of points given to all the zones is**

15

16

14

17

#### SOLUTION

Solution :A

Given that there is one zone where no company sold

Frisbees. Let Z4 be such a zone.

Assume that A sells Frisbees in zone Z1, so the other

company that sells Frisbees in Z1 has to be E.

Since G has three competitors, therefore the number of

companies selling Frisbees in the zone where G sells is 4.

Lets assume G sells in Z2, therefore the complete list of

companies selling Frisbees in Z2 is E, G, C and H.

The same holds true for B, which has three competitors.

Lets assume B sells in Z3, therefore the complete list of

companies selling Frisbees is E, B, C and H.

Now, since the number of competitors of D and F are 4

each the complete list of companies selling Frisbees in Z5 will

be E, D, F, C and H.

The following table can be made now.ZONECOMPANIESZ1A,EZ2E,G,C,HZ3E,B,C,HZ40Z5E,D,F,C,H

Aggregate number of points given to all the zones

= 2 + 4 + 4 + 5 = 15

### Question 23

**The number of zones in which the company A sold Frisbees is at most**

1

5

2

3

#### SOLUTION

Solution :C

Given that there is one zone where no company sold

Frisbees. Let Z4 be such a zone.

Assume that A sells Frisbees in zone Z1, so the other

company that sells Frisbees in Z1 has to be E.

Since G has three competitors, therefore the number of

companies selling Frisbees in the zone where G sells is 4.

Lets assume G sells in Z2, therefore the complete list of

companies selling Frisbees in Z2 is E, G, C and H.

The same holds true for B, which has three competitors.

Lets assume B sells in Z3, therefore the complete list of

companies selling Frisbees is E, B, C and H.

Now, since the number of competitors of D and F are 4

each the complete list of companies selling Frisbees in Z5 will

be E, D, F, C and H.

The following table can be made now.ZONECOMPANIESZ1A,EZ2E,G,C,HZ3E,B,C,HZ40Z5E,D,F,C,H

A has exactly one competitor. If you look at the table , A can have 0 competitors by being present in Z4 and 1 competitor by being present in Z1. Thus, the answer is option option (c)

### Question 24

How many rupees did Suvarna start with?

#### SOLUTION

Solution :Let the amounts held by Suvarna, Tara, Uma and Vibha at any stage be denoted by S, T, U and V respectively.

At the end of game 4, all of them have Rs 32 with them.

Since Vibha lost game 4, she would have doubled the other three players' amount.

Thus, at the end of the game 3 (or at the beginning of game 4), Suvarna, Tara and Uma would each have had Rs. 322= Rs. 16.

Also, Vibha would have had 32 + 16 + 16 + 16 = Rs. 80

Similarly, the amount with each person at the end of each game can be calculated as shown in the table below.

Game(End)STUV432323232316161680288724014683620Start66341810

It is evident from the table that Suvarna started with Rs. 66

### Question 25

What was the amount with Uma at the end of the second game?

#### SOLUTION

Solution :Let the amounts held by Suvarna, Tara, Uma and Vibha at any stage be denoted by S, T, U and V respectively.

At the end of game 4, all of them have Rs 32 with them.

Since Vibha lost game 4, she would have doubled the other three players' amount.

Thus, at the end of the game 3 (or at the beginning of game 4), Suvarna, Tara and Uma would each have had Rs. 322= Rs. 16.

Also, Vibha would have had 32 + 16 + 16 + 16 = Rs. 80

Similarly, the amount with each person at the end of each game can be calculated as shown in the table below.

Game(End)STUV432323232316161680288724014683620Start66341810

Uma had Rs. 72 at the end of the second game.

### Question 26

How much money did Tara lose or won?

#### SOLUTION

Solution :Let the amounts held by Suvarna, Tara, Uma and Vibha at any stage be denoted by S, T, U and V respectively.

At the end of game 4, all of them have Rs 32 with them.

Since Vibha lost game 4, she would have doubled the other three players' amount.

Thus, at the end of the game 3 (or at the beginning of game 4), Suvarna, Tara and Uma would each have had Rs. 322= Rs. 16.

Also, Vibha would have had 32 + 16 + 16 + 16 = Rs. 80

Similarly, the amount with each person at the end of each game can be calculated as shown in the table below.

Game(End)STUV432323232316161680288724014683620Start66341810

Starting amount = 34

Final amount = 32

Lose = 34-32 = Rs. 2

### Question 27

Three Students - Jose, Bharath and Simon - have to select three sports each out of the six sports- Hockey, Baseball, Tennis, Basketball, Cricket and Football.

(i)If Football is selected, then Hockey cannot be selected.

(ii)If Simon selects Tennis, then Jose does not select Football.

(iii)If Bharath selects Baseball, then Simon cannot select Tennis and if Jose selects Hockey, then Simon selects Cricket and Football.

If Simon selects Football and Bharath selects Baseball, then Simon cannot select.

Hockey and Tennis.

Baseball and Tennis.

Tennis and Basketball.

Hockey and Cricket.

#### SOLUTION

Solution :A

From statement (i) and (iii), it is clear that if Simon selects Football and Bharath selects Baseball, then Simon cannot select hockey and tennis.

### Question 28

**M, N, O, P, Q, R, S, T and U are the nine dance trainees in a company, who go to the chambers of their two head dance teachers A and B, for their yearly appraisal. Each head teacher has time for only three trainees. P has a priority and must be given preference by A or B. R and N do not wish to go to the same head teacher. S goes to A only and T goes to B only. O comes back saying that neither of the two head teachers has time to see him. M does not go with R and U does not go with Q. N and U do not go together. If Q, R and S go together and are seen by one of the head teachers, then which head teacher sees whom,?**

B - P, U, T or P, N, T

B - P, M, T or P, N, T

A - M, U, T or N, U, T

A - P, U, T or M, U, T

#### SOLUTION

Solution :A

It is given that P may go to A or B and must be seen, whereas S goes to only A, and T goes to only B. It is clear from the data that O has gone back and neither (M and R), nor (U and Q) go together. If Q, R, S go to one head teacher and meet him, the other head teacher sees any two of M, N, U and T along with P, who must be seen. M does not go with R and U doesn't go with Q, so PNT or PUT are seen. Only B can see them as S goes to A. So B - PNT or PUT is correct.

### Question 29

Guests at a conference ate a total of fifteen chicken samosas. Each guest who was neither a student nor a vegetarian ate exactly one chicken samosa. No chicken samosa was eaten by any guest who was a student, a vegetarian, or both. If half of the guests were vegetarians, how many guests attended the conference?

(1) The vegetarians attended the conference at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

(2) 30% of the guests were vegetarian non-students.

If Statement (1) alone is sufficient, but statement (2) alone is not sufficient. Or If Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

If BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

If Each statement ALONE is sufficient

If Statements (1) and (2) TOGETHER are NOT sufficient.

#### SOLUTION

Solution :A

Use a 2 set matrix to solve this problem.

First set is vegetarians vs. non-vegetarians; second set is students vs. non-students.

VEGETARIANNON-VEGETARIANTOTALSTUDENT NON-STUDENT 15 TOTALXX?

We are told that each non-vegetarian non-student ate exactly one of the 15 chicken samosas, and that nobody else ate any of the 15 chicken samosas. This means that there were exactly 15 people in the non-vegetarian non-student category. We are also told that the total number of vegetarians was equal to the total number of non-vegetarians; we represent this by putting the same variable in both boxes of the chart.The question is asking us how many people attended the conference;

Statement(2) INSUFFICIENT: This statement gives us information only about the cell labeled "vegetarian non-student"; further it only tells us the number of these guests as a

percentageof the total guests. The 30% figure does not allow us to calculate the actual number of any of the categories.Statement (1) SUFFICIENT: This statement provides two pieces of information. First, the vegetarians attended in the ratio, of 2:3 students to non-students.

We're also told that this 2:3 rate is half the rate for non-vegetarians; i.e. the rate for non-vegetarians is 4:3 We can represent the actual numbers of non-vegetarians as 4

aand 3aand add this to the chart below. Since we know that there were 15 non-vegetarian nonstudents,we know the missing common multiple, a is 153=5. Therefore, there were (4)(5) = 20 non-vegetarian students and 20 + 15 = 35 total non vegetarians (see the chart below). Since the same number of vegetarians and non-vegetarians attended the conference, there were also 35 vegetarians, for a total of 70 guests.

VEGETARIANNON-VEGETARIANTOTALSTUDENT 4a or 20 NON-STUDENT 3a or 15 TOTALx or 35x or 35? or 70

### Question 30

To pass to the next level (Batch A) in a school's sports team, students in the intermediate batch (Batch B) at Premier High School have to pass both a written and a practical test. Everyone has to take the tests, and no one failed both tests. If 30% of the students of Batch B who passed the written test did not pass the practical, how many Batch B students at Premier High School go to Batch A? (1) There are 188 Batch B students at Premier High School. (2) 20% of the Batch B students who passed the practical test failed the written test.

#### SOLUTION

Solution :B

For an overlapping set question, we can use a double-set matrix to organize theinformation and solve. The two sets in this question are the practical test (pass/fail)and the written test (pass/fail).

PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x.3xxWRITTEN - FAIL0TOTALS.3x

(1) INSUFFICIENT 1) INSUFFICIENT: If we add the total number of students to the information from thequestion, we do not have enough to solve for .7x.

PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x.3xxWRITTEN - FAIL0TOTALS.3x188

(2) INSUFFICIENT: If we add the fact that 20% of the

Batch B who passed thepractical testfailed the written test to the original matrix from the question, we cancome up with the relationship .7x= .8y. However, that is not enough to solve for .7x.PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x=.8y.3xxWRITTEN - FAIL.2y0.2yTOTALSy.3x

(1) AND (2) SUFFICIENT: If we combine the two statements we get a matrix that can be used to form two relationships between x and y;

PRACTICAL - PASSPRACTICAL - FAILTOTALSWRITTEN - PASS.7x=.8y.3xxWRITTEN - FAIL.2y0.2yTOTALSy.3x188

This would allow us to solve for x and in turn find the value of .7x, the number Batch B students who went to Batch A.

### Question 31

In Green Glen Layout last July, what was the average (arithmetic mean) home sale price?

(1) In Green Glen Layout last July, there were 100 homes sold for a total of $51 million.

(2) In Green Glen Layout last July, condominiums accounted for 60% of the home sales, and the average condominium price was $450,000.

#### SOLUTION

Solution :D

A suitable rephrase of this question is "What was thesum of the homes sale prices, and how many homes were sold?”

Statement (1):Insufficient

Seems SUFFICIENT as this statement tells us the sum of the home sale prices and the number of homes sold. Thus, the average home price is $51,000,000/100 =$510,000.

But we are not sure how many homes were there overall (may be more than 100). So INSUFFICIENT.

Statement (2) INSUFFICIENT:

This statement tells us the average condominium price, but not all of the homes sold in Green Glen Layout last July were condominiums. From this statement, we don't know anything about the other 40% of homes sold in Green Glen Layout, so we cannot calculate the average home sale price

Average=sum of condominium sale prices + sum of non - condominium sale pricesnumber of condominiums sold + number of non - condominiums sold

We have some information about the ratio of number of condominiums to non condominiums sold, 60%:40%, or 6:4, or 3:2, which could be used to pick working numbers for the total number of homes sold. However, the average still cannot be calculated because we don't have any information about the non-condominium prices.

### Question 32

Last year, the five employees of Alpha Ltd. took an average of 16 vacation days each. What was the average number of vacation days taken by the same employees this year?

(1) Three employees had a 50% increase in their number of vacation days, and two employees had a 50% decrease.

(2) Three employees had 10 more vacation days each, and two employees had 5 fewer vacation days each.

#### SOLUTION

Solution :A

The average number of vacation days taken this year can be calculated by dividing the total number of vacation days by the number of employees. Since we know the total number of employees, we can rephrase the question as: How many total vacation days did the employees of Alpha Ltd. take this year?

(1) INSUFFICIENT: Since we don't know the specific details of how many vacation days each employee took the year before, we cannot determine the actual numbers that a 50% increase or a 50% decrease represent. For example, a 50% increase for someone who took 40 vacation days last year is going to affect the overall average more than the same percentage increase for someone who took only 4 days of vacation last year.

(2) SUFFICIENT: If three employees took 10 more vacation days each, and two employees took 5 fewer vacation days each, then we can calculate how the number of vacation days taken this year differs from the number taken last year:

(10 more days/employee)(3 employees) - (5 fewer days/employee)(2 employees) = 30days - 10 days = 20 days

20 additional vacation days were taken this year.

In order to determine the total number of vacation days taken this year (i.e., in order to answer the rephrased question), we need to determine the number of vacation days taken last year. The 5 employees took an average of 16 vacation days each last year, so the total number of vacation days taken last year can be determine by taking the product of the two:

(5 employees)(16 days/employee) = 80 days

80 vacation days were taken last year. Hence, the total number of vacation days taken this year was 100 days.

Note: It is not necessary to make the above calculations -- it is simply enough to know that you have enough information in order to do so (i.e., the information given is sufficient)! The correct answer is (a).