# Free DI and LR Practice Test - CAT

### Question 1

**If the Organizers want to ensure that all participants travelling from S to T take the same time (travelling time and task time combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of task time (in hours) at junctions A, B, C, and D respectively to achieve this goal is:**

2,5,3,2

0,5,3,1

1,5,3,2

Both (b) and (c)

#### SOLUTION

Solution :D

As B - C is unusable, S - B - C - T is not possible.

The other possible ways are : S - A - T, S - B - A - T , S - D - T, and S - D - C - T

From these if we apply all the options:

Both option (b) and (c) are true, as in both the cases total time is same for each of the four routes.

### Question 2

**If the organizers wants to ensure that no participant should travel on the street from D to T, while equal number of participants should travel through junctions A and C, then a feasible set of task time (in hours) at junctions A, B, C, and D respectively to achieve this goal is:**

0,5,2,2

1,4,4,3

1,5,4,2

0,5,2,3

#### SOLUTION

Solution :A

No traffic flows from D - T. Now apply each of the options. New time will be as follows.

As it is given that traffic flow at junction A is same as that at junction C.

∴ Number of routes involving A that can be used must be same as that involving C.

Further, only the routes with minimum time can be used.

That happened in only (a), as no of the routes that can be used, the number of routes involving A is two (S-A-T and S-B-A-T) and that involving C is also two (S-B-C-T and S-D-C-T)

### Question 3

**If the Organizers wants to ensure that all routes from S to T get the same number of participants, then a feasible set of task time (in hours) at junctions A, B, C, and D respectively to achieve this goal is:**

0,5,2,2

0,5,4,1

1,5,3,3

1,5,3,2

#### SOLUTION

Solution :D

To ensure that all the routes from S to T get the same number of participants, Going by the answer options

As the time must be same for all the routes, it must be option (d).

### Question 4

**If the Organizers wants to ensure that the number of participants at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of task time(in hours) at junctions A, B, C, and D respectively to achieve this goal is:**

0,5,4,1

0,5,2,2

1,5,3,3

1,5,3,2

#### SOLUTION

Solution :A

From the given options

It is very likely that option (d) is selected. But if all the five routes has the same time taken, then there will be an equal number of participant in all the five routes i.e. 20% in each route.

But then the percentage of participant in

S-A = 20%

S-B = 40% (As there are two routes involving S-B)

S-D = 40% (For the same reason as above)But here the given condition that number of participant in S-A is equal to that in S-B, which in turn is equal to S-D is not satisfied.

As S-A = S-B = S-D.

Of the routes, that can be used the number of routes involving S-A must be the same as S-B, which in turn is same as that as S-D. It happened in only option (a).

### Question 5

**The Organizers wants to devise a task time policy such that the total time to the participants to reach treasure is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The time taken by the participants travelling from point S to point T under this policy will be:**

7 hours

9 hours

10 hours

8 hours

#### SOLUTION

Solution :C

There must be one other route other than those involving B with the least cost as most only 70% participants can only use this route.

We must take S-D-C-T as the other route.

S-B-C-T, if task time at B = 3, total time= 10.

S-D-C-T, if task time at D and C is 0, total time is 10.

∴ 10 hours is the least time.

### Question 6

Who plays HOCKEY?

A

B

D

E

#### SOLUTION

Solution :A

The given information can be tabulated below.

PERSONSPORTNATIVEPLAYSBChennaiMumbaiCSwimsX PuneFootballX PunePuneHockeyHyderabadDX ChessX BangaloreBangalore

From the above table we can deduce that

1 ) D is a native of Pune

2) B plays Chess and D pays Cricket

3) C plays in Hyderabad

4) Since E is a native of Bangalore, the only row available for this is row 3 and thus, we can also deduce that E plays Football in Pune

5) therefore, C is a native of Mumbai. The table can now be completely filled

PERSONSPORTNATIVEPLAYSBChessChennaiMumbaiCSwimsMumbaiHyderabadEFootballBangalorePuneAHockeyHyderabadChennaiDCricketPuneBangalore

A plays HOCKEY. Option (a)

### Question 7

In which city is Swimming played?

Chennai

Bangalore

Mumbai

Hyderabad

#### SOLUTION

Solution :C

The given information can be tabulated below.

PERSONSPORTNATIVEPLAYSBChennaiMumbaiCSwimsX PuneFootballX PunePuneHockeyHyderabadDX ChessX BangaloreBangalore

From the above table we can deduce that

1 ) D is a native of Pune

2) B plays Chess and D pays Cricket

3) C plays in Hyderabad

4) Since E is a native of Bangalore, the only row available for this is row 3 and thus, we can also deduce that E plays Football in Pune

5) therefore, C is a native of Mumbai. The table can now be completely filled

PERSONSPORTNATIVEPLAYSBChessChennaiMumbaiCSwimsMumbaiHyderabadEFootballBangalorePuneAHockeyHyderabadChennaiDCricketPuneBangaloreSwimming is played in Mumbai.

### Question 8

If A is not playing CRICKET, then who is the native of Pune?

A

C

D

either A or C

#### SOLUTION

Solution :C

The given information can be tabulated below.

PERSONSPORTNATIVEPLAYSBChennaiMumbaiCSwimsX PuneFootballX PunePuneHockeyHyderabadDX ChessX BangaloreBangalore

From the above table we can deduce that

1 ) D is a native of Pune

2) B plays Chess and D pays Cricket

3) C plays in Hyderabad

4) Since E is a native of Bangalore, the only row available for this is row 3 and thus, we can also deduce that E plays Football in Pune

5) therefore, C is a native of Mumbai. The table can now be completely filled

PERSONSPORTNATIVEPLAYSBChessChennaiMumbaiCSwimsMumbaiHyderabadEFootballBangalorePuneAHockeyHyderabadChennaiDCricketPuneBangalore

D is a native of Pune. Option (c)

### Question 9

You need to select 7 members for a Cabinet. For political issues, the party has decided to select them from the following pool of members.

Five from North - A, B, C, D, E

Five from South - L, M, N, O, P

Conditions:

i) There must be at least three members each from north and south

ii) If A is selected, E cannot be selected.

iii) If L is selected, neither O nor P can be selected.

iv) If M is selected, P cannot be selected.

Who should always be selected?

#### SOLUTION

Solution :C

The correct option is c - Only B, C, D and N.

South:

Out of L, M, N, O, P, you can at max select 3 only.

If L is selected then O and P cannot be selected.

Therefore, 3 selected are L, M and N satisfying the conditions.

If L is not selected and M is selected, then

3 selected are M, N and O

If M is not selected then 3 selected are N, O and P.

In all cases N is selected.

North:

A, B, C, D and E

We need to select 4 from this zone.

As only one of A or E is selected, B, C and D are always there.

### Question 10

10 students enter into a class after A and 15 students before B. Also, 5 students enter between A and B. How many students are there in total if A entered before B?

10

5

15

20

#### SOLUTION

Solution :D

A enters before B. 15 students before B including the 5 between and A. Therefore total 9+A+5+B+4=20

### Question 11

In the Database H, a max of how many persons can be there such that for each of them, the data on exactly five of the six features is available?

#### SOLUTION

Solution :C

For Database H, total number of entries =1,00,000

We will represent the number of people (in percentage terms) whose data is available by lines as shown in the figure.

As the maximum of 5 out of 6 is asked, we will first consider the 5 details with maximum number of people.

Starting with Name, draw a line to corresponding to 100% people

Now, when we represent students whose address is available,70 % of them, we should ensure that these 70%people are also a part of the 100% whose name details are available. This way, we are maximizing the number of people for whom both the name & address is available

If you want to visualize this using the circles we are used to

Similarly, for the remaining 3 details, we try to have the maximum area of overlap.

For the next 3 details, the figure would be:

Thus the number of people for whom all five of Name Address Email Mobile and Age data is available Is 30%

However, there are 10% people with Fax No. also who have not been considered. We will place those people strategically, them so that the overlapped region for 5 lines, becomes maximum as follows.

Now count the regions where 5 lines are overlapping. It is 40% of the total

Answer is 40% of 100000= 40000. Option (c)

### Question 12

In Database E, the number of persons, each of whose name, fax number as well as telephone number are available, is at least

#### SOLUTION

Solution :C

The second question asks for exactly the opposite of the first question. We need minimum overlap of the three regions (name, fax and telephone number)

1) Database E= Total Entries= Using line technique, we will try drawing lines in such a way that the overlap is minimized as follows

NameFax NumberTelephone Number1005080

Thus, the region of minimum overlap of 3 lines is 30% of 15000 = 4500. Option (c)

To visualize this using venn diagrams, see below

Line technique is an alternative and better representation of sets where there is no upper limit to the details which need to be compared.

### Question 13

**If exports to Korea from China forms 80% of the exports to Asia and imports from Korea forms 73% of import from Asia then trade balance of China as defined earlier with Korea is**

#### SOLUTION

Solution :C

Strategy- Change the scale to minimize calculation

From both Import and Export figures, strike out the last 4 digits = 1750 & 1400 approximately

The answer options are far apart, therefore we can easily approximate.

ChinaImports(1750)Exports(1400)Asia(40%)1750×40%=7001400×40%=560Korea(73%, 80%)700×73%=511560×80%=448

Trade Deficit= Import- Export = 511 - 448≈63. Hence answer is option (c)

### Question 14

**If the foreign exchange reserves in the beginning of 1998-99 were Rs.11341 bn and Rs.2961 bn were withdrawn by Chinese residing abroad, then what will be the reserve at the end of year after adjusting trade deficit of the year?**

#### SOLUTION

Solution :C

Strategy- Change the scale to minimize calculation (strike out the last 2 from billion figures and last 5 from million figures)

Trade Deficit for China= 175 - 140≈35 billion

Initial foreign exchange reserve = 11341

After withdrawal = 113 - 29 = 84

After adjusting trade deficit, 84 - 35 ≈ 49

### Question 15

**The total import to China in 1998-1999 from Europe and Africa was nearly balanced by the total export from China to**

#### SOLUTION

Solution :D

Total import to China in 1998-1999 from Europe and Africa =39

which is 48% of the exports

Hence, Exports from Asia, Africa and others will balanced the total imports

### Question 16

**If the import is growing at an annual rate of 15 % and export is growing at an annual rate of 5 % then percentage increase in trade deficit from 1998-1999 to 2000-01 will be nearest to ?**

#### SOLUTION

Solution :A

Initial trade deficit≈ 3449510

Import increases at a rate of 15% every year for 4 years. This means that it's final value will be

17609863×1.054= 21404898

Similarly Export increases at a rate of 5% every year for 4 years. This means that it's final value will be

14160353×1.154=24766545

New trade deficit ≈ 3361647

Percentage increase is from 3449510 to 3361647 ≈ 290% increase.

### Question 17

If there are no surprise wins (a lower ranked team beating a higher ranked team) in the first round, and only match Nos. 6, 7, 8 of the second round result in upsets, then who would meet Italy in quarter finals, in case Italy reaches quarter finals?

Spain

Germany

Nigeria

Czech R

#### SOLUTION

Solution :D

Italy / rank 2's opponent in Round 3 is what we need.

Ideal Scenario in round 3 Italy (2) opponent is 7 (as 2+7=9).

We could mark Rank 8(Spain) to be Italy's opponent in the quarters but we know Match No.7 in round 2 was an upset so Spain (7) will be replaced by the team which played and beat 7 in round 2.

Round 2, Team 7 would ideally play Team 10 (7+10=17 "Round 2 Magic Number”) so Team 10 beats 7 and replaces its position in round 3!

Answer is Team 10- Czech R (d)

### Question 18

If Netherlands and Portugal lose in the second round, while Spain and Germany make it to the semi-finals, then who would play Brazil in the quarterfinals, in the event Brazil reaches quarterfinals?

Sweden

Spain

Germany

Nigeria

#### SOLUTION

Solution :D

Brazil / rank 1's opponent in Round 3 is what we need.

Ideal Scenario in round 3 Brazil (1) opponent is 8 (as 1+8=9).

We could mark Rank 8(Portugal) to be Brazil's opponent in the quarters but we know Portugal lost in round 2.

In Round 2, Portugal (8) would ideally play team 11 (8+11=17: "Round 2 Magic Number”) so Team 11 beats Portugal and plays Brazil in round 3!

Answer is Team 11- Nigeria (d)

### Question 19

If, in the first round, all even numbered matches (and none of the odd numbered ones) results in surprise wins, and there are no surprise wins in the second round, then who would be the lowest ranked team facing Brazil in semi-finals?

Switzerland

Egypt

Germany

England

#### SOLUTION

Solution :A

Brazil (1) plays rank 4 in semi-finals (Round 4 - magic number is 5)

But, we know all even numbered matches of round 1 and all even ranked teams lose in round 1, hence lets trace rank 4's path to know which is the LOWEST ranked team that can replace it.

Round 1: 4 + 29 ("Magic number for round 1 is 33=4+29”) => 29 qualifies and takes 4's place

Round 2: 4 + 13 ("Magic number for round 2 is 17=4+13”)

But, now the round 2 match is not 4 v/s 13 but 29 v/s 13 => 13 is a better rank team and no upsets occur in round 2 so 13 qualifies and takes 4's place in the next round.

Round 3: 4 + 5 ("Magic number for round 3 is 9=4+15”)

But now here 4 is replaced by 13 so its 13 v/s 5. The winner of this match meets 1 in the next round(Semi-finals). We have the liberty to choose any of these two teams but the choice has to be of the LOWER team hence, choose rank 13 =Switzerland as the ANSWER (a)

### Question 20

If the top eight ranked teams make it to the quarter finals, then who, amongst the teams listed below, would definitely not play against Brazil in the final, in case Brazil reaches final?

Argentina

Netherlands

France

Italy

#### SOLUTION

Solution :C

The answer options are 2-3-4-6 ranked teams which have no chance of playing Brazil (1) in the Final.

Rank 1 (Brazil) will have to meet rank 4 in the semi-final after which they can never play in the final. The right answer is option (c)

In the ideal scenario, 1 will play 2 in final so option (d) Italy is incorrect

Rank 2 will play rank 3 in the semifinals so it's possible for rank 3 to beat rank 2 and meet Brazil in the finals; so option (a) is incorrect. Rank 2 can also meet with rank 6 in the semi-finals if rank 6 beats rank 3 in the quarter-finals and hence even rank 6 has a possibility of reaching the final by replacing 2 and without having the chance to have an encounter with brazil (rank 1); so option (b) is incorrect

### Question 21

If Ghosh Babu stopped playing the game when his gain would be maximized, the gain in Rs. would have been

#### SOLUTION

Solution :GameOpeningPlayer′spick Dealer′s pick Closing balancebalanceDebitCreditDebitCredit(−)(+)(−)(+)1008160−82−801001012312066012412081604

### Question 22

The initial money Ghosh Babu had (before the beginning of the game sessions) was Rs. X. At no point did he have to borrow any money. The minimum possible value of X is

#### SOLUTION

Solution :GameOpeningPlayer′spick Dealer′s pick Closing balancebalanceDebitCreditDebitCredit(−)(+)(−)(+)1008160−82−801001012312066012412081604

Since the maximum negative that Ghosh Babu goes into is -8, he should begin with at least Rs. 8, so that he does not have to borrow any money at any point.

### Question 23

If the final amount of money that Ghosh Babu had with him was Rs. 100, the initial amount he had with him is

#### SOLUTION

Solution :GameOpeningPlayer′spick Dealer′s pick Closing balancebalanceDebitCreditDebitCredit(−)(+)(−)(+)1008160−82−801001012312066012412081604

From the above table it is evident that in four games, Ghosh Babu makes a profit of Rs. 4. Hence, if the final amount left with Ghosh Babu is Rs. 100, the initial amount that he had would be Rs. 96.

### Question 24

How many Priests left the precinct at 18:00 hrs?

1

2

1 or 2

Cannot be determined

#### SOLUTION

Solution :D

Cannot be determined

If at 14:00 hrs 1 staff member and no priest entered, then no priest left (after 4 hrs) at 18:00 hrs.

1 devotee who entered at 16:00 hrs might have left at 17:00 hrs (after 1 hr) or at 18:00 hrs (after 2 hrs).

Then, 1 priest left at 18:00 hrs (after 4 hrs) or no staff member left at 18:00 hrs (after 4 hrs). Hence, the result cannot be determined.

### Question 25

If no staff member entered the precinct at 14:00 hrs, then at 17:00 hrs:

#### SOLUTION

Solution :D

None of these.

As no staff member entered at 14:00 hrs, no staff member could have left at 17:00 hrs (after 2 hrs). Hence (b) is not true.

As no devotee entered at 15:00 hrs, no devotee could have left at 17:00 hrs (after 2 hrs). Hence (c)is not true.

If at 15:00 hrs, 1 staff member and 1 priest entered, then 1 staff member left at 17:00 hrs (after 2 hrs).

If at 15:00 hrs, 2 staff members entered, then 2 staff members left at 17:00 hrs (after 2 hrs). Hence (a) may or may not be true.

Hence, none of these options.

### Question 26

The number of Staff members entering the precinct at 12:00 hrs and 13:00 hours respectively couldn't have been:

0, 2

1,1

0,0

2,0

#### SOLUTION

Solution :C

0,0

If no staff member would have entered at 12:00 hrs and 13:00 hrs, no staff member would have left at 15:00 hrs (after 2 or 3 hrs). But it is not possible as 6 people left at 15:00 hrs and not more than 2 priests and 2 devotees could leave at the same time.

### Question 27

If during the entire day from 8:00 hrs, no devotee left the precinct only at 9:00 hrs, then how many times did exactly 2 devotees leave the precinct together?

nil

once

twice

thrice

#### SOLUTION

Solution :C

option c. twice

As no devotee left at 9:00 hrs, 1 visitor who entered at 8:00 hrs left at 10:00 hrs. 2 devotees entered at 9:00 hrs and left at 11:00 hrs or 1 left at 10:00 hrs and 1 at 11:00 hrs. Keeping in mind that at no other time did no staff member leave the unit, the table can be completed as follows:

Hence, (c ) is the answer.

### Question 28

If 2 staff members entered the precinct at 12:00 hrs and 13:00 hrs each, then at 15:00 hrs (refer to data from previous questions):

#### SOLUTION

Solution :C

option c. 2 priests left after 3 hrs.

From the previous question, we know that 1 devotee left at 15:00 hrs (after 1 hr) and another 1 at 15:00 hrs (after 2 hrs). Thus options (a) and (d) are incorrect.

If 2 staff members left (after 3 hrs) at 15:00 hrs, then 2 staff members who entered at 13:00 hrs must have left (after 3 hrs) at 16:00 hrs and hence at 16:00 hrs no priest left (after 3 or 4 hrs). This is not possible as there are 3 priests who entered at 12:00 hrs and at least one of them left at 16:00 hrs (after 4 hrs) as not more than 2 could leave at the same time. Hence (b) is not true.

Thus, the only option possible is (c ).

### Question 29

Is |n| < 1 ?

(1) nx−n<0

(2) x−1=−2

#### SOLUTION

Solution :C

The question is "Does n lie between -1 & 1?”

(1) INSUFFICIENT: If we add n to both sides of the inequality, we can rewrite it as the following:nx<n

we cannot decide the answer based on this

if n = 12 and x = 2 then −1<n<1

however, if n = -3 and x = 3 , n is less than -1

thus, the answer cannot be determined based on statement (1) alone

(2) INSUFFICIENT: x−1=−2 can be rewritten as x=−2−1=−12. However, this statement contains no information about n. hence, answer cannot be determined based on this statement alone as well.

(1) AND (2) SUFFICIENT: If we combine the two statements by plugging the value for x into the first statement, we get n−1/2<n.

The only values for n that satisfy this inequality are those greater than 1.

The correct answer is (C).

### Question 30

Person A and Person B are both at Point A (above). Starting at the same time, Person A drives to point B while Person B drives to point C. Who arrives at his destination first?

(1) Person A's average speed is 23 that of Person B's.

(2) Person B's average speed is 20 kilometers per hour greater than Person A's.

#### SOLUTION

Solution :A

Since AB = BC, triangle ABC is a 45-45-90 triangle. Such triangles have fixed side ratios as follows:

AB: BC: AC → 1:1:√2

Thus, we can call Person A's distance (AB) x, while Person B's distance (AC) is.

Person B has a greater distance to travel

Let's first analyze Statement (1) alone: Person A's average speed is that of Person B's.

This indicates that Person B is traveling 1.5 times faster than Person A. If Person A's rate is r, than Person B's rate is 1.5r. However, recall that Person B also has a greater distance to travel.

To determine who will arrive first, we use the distance formula: Rate x Time = Distance. Whoever has a shorter TIME will arrive first.

Person A's timePerson A's time=Distancerate=xrDistancerate=1.4x1.5r=93(xr)

Since person B is traveling for less time, he will arrive first Statement(1) alone is sufficient.

Let's now analyze Statement (2) alone: Person B's average speed is 20 kilometers per hour greater than Person A's.

This gives us no information about the ratio of Person B's average speed to Person A's average speed. Thus, although we know that Person B's distance is approximately 1.4 times Person A's distance, we do not know the ratio of their speeds, so we cannot determine who will arrive first.

For example, if Person B travels at 25 kmph, Person A travels at 5 kmph. In this case Person B arrives first. However, if Person B travels at 100 kmph, Person A travels at 80 kmph. In this case Person A arrives first.

Therefore, Statement (2) alone is not sufficient.

Since statement (1) alone is sufficient, but statement (2) alone is not sufficient, the correct answer is A.

### Question 31

Last year, the five employees of Company X 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 :B

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 Company X 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) = 20

Required Average = 16 + 4 = 20

### Question 32

What is the average (arithmetic mean) height of the n people of a certain group?

(1) Height of the tallest person in the group is 6 feet 2.5 inches and the average height of the rest of the people in the group is 5 feet 10 inches

(2) The sum of the heights of the n people is 178 feet 9 inches

#### SOLUTION

Solution :C

From statement 1: 74.5+(n−1)70n

From statement 2: 74.5+(n−1)70=2145

Using both the statements, average height of the n people can be determined.