# Free DI and LR Practice Test - CAT

### Question 1

In 2005, What is the difference between the non-local NRI population from America and the European category of Foreign Nationals?

#### SOLUTION

Solution :D

20012002200320042005City A937211252612712345987748973City B107658328705693621312548636City C128231167513157141061613267893City D7352913711346134511576957055City E876710789125231432316239626414907951181502096358771142

Total non-local floating population in 2005= 71142

Number of people from the NRI category= 55% of 71142 = 39128

Number of people from the American NRI category = 27.8% of 39128 = 10878

Number of people fromt eh Foreign Nationals category = 18.8% of 71142 = 13375

Number of European NRI's = 16% of 13375= 2140

Difference = 10878 - 2140 = 8738.

### Question 2

What is the percentage change in the percentage increase in the number of non-local North Indian people in City A and non-local Foreign Nationals of the Asian category in City D, from 2001 to 2002?

#### SOLUTION

Solution :B

It seems that the calculation is intensive, but you should realize that most of the numbers cancel out

number of non-local North Indian people in City A in 2001= 17% of 26.2% of 9372

number of non-local North Indian people in City A in 2002= 17% of 26.2% of 11252

hence, percentage change is [11252−93729372]×100%=20%

Non-local Foreign Nationals of the Asian category in City D in 2001= 46% of 18.8% of 7352

Non-local Foreign Nationals of the Asian category in City D in 2002= 46% of 18.8% of 9137

hence, percentage change is [9137−73527352]×100%=24%% change in % increase =420×100=20%

### Question 3

The average amount spent by an American Foreign National for staying in a hotel in city E is Rs 3800. The average amount spent by a North Indian for staying in a hotel in city D is Rs 2375. What is the difference in expenditure on hotel stay by these two non-local groups over the given period? (Assume that all the individuals in the above mentioned groups stay in hotels during this period)

350

291.5

300

250.25

#### SOLUTION

Solution :B

Number of non-local people from the American Foreign National category in City E in this period = 20% of 18.8% of 62641 = 2355 thousand

Total expenditure on hotels in this period in City E due to the American Foreign National category = (3800×2355 thousand) = Rs 895 crore

Number of non-local people in City D from the North Indian category in this period = 17% of 26.2% of 57055 = 2541 thousand

Total expenditure on hotels in this period in City D due to the North Indian category = (2375×2541 thousand) =Rs 603.5 crore

Difference in expenditure = 291.5 crore.

### Question 4

**What is the percentage increase in the number of Foreign Nationals from the category "others” over the given period?**

45%

65%

76%

52%

#### SOLUTION

Solution :A

Since the percentages remain the same, as in the second question of this caselet, we can take the total of 2001 and 2005 to consider the percentage increase percentage increase = [71142−4907949079] × 100% = 45%.

### Question 5

**What is the highest percentage growth in the number of non-local people from East India, between any two consecutive years?**

30%

27%

21%

32%

#### SOLUTION

Solution :B

By simple observation, it can be deduced that the highest percentage change occurs from 2003 to 2004.

This percentage change can be computed as 63587−5020950209 ≈ 27% (note that the sub groups do not matter, as they eventually get cancelled out).

### Question 6

Given that pqrs≠0, is pq2r3s4<0?

(1) pq2r3<0

(2) q2r3s4<0

#### SOLUTION

Solution :A

Option (a)

Statement (1) alone is sufficient, as "s” is raised to an even power and will not alter the state of the expression (positive or negative)

Statement (2) is not sufficient as we do not know anything about p, and p is raised to an odd power (1). Hence, the state of the expression (i.e. positive or negative) depends on "p"

### Question 7

Does the equation y = (x - a)(x - b) intercept the x-axis at the point (2,0)?

(1) ab = -8

(2) -2 - a = b

#### SOLUTION

Solution :B

At y = 0

0 = (x - a)(x - b). This product would only be zero when xis equal to a or b. thus, we need to find out if a or b = 2. Both statements are required to answer this

(1) INSUFFICIENT: We can't find the value of a or b from this equation.

(2) INSUFFICIENT: We can't find the value of a or b from this equation.

(1) AND (2) SUFFICIENT: we have 2 simultaneous eqns which can be solved.If b = 2, a = -4 and if b = -4, a = 2. Either way either a or b is equal to 2.

### Question 8

Who among them scored highest in Maths?

Amit

Dinesh

Bijay

Ajit

#### SOLUTION

Solution :A

From the given data.

As Ajit and Dinesh belong to same group, their last statements cannot be simultaneously true.

Hence, their 2nd statements must be true.

Similarly, Bijay and Amit's second statements are false.The final table

MathsScienceEnglish1stAmitDineshDeepak2ndDineshBijayAmit3rdDeepakAjitDinesh4thAjitDeepakBijay5thBijayAmitAjit

### Question 9

Who among them is 1st in English?

Ajit

Dinesh

Deepak

Amit

#### SOLUTION

Solution :C

From the given data.As Ajit and Dinesh belong to same group, their last statements cannot be simultaneously true.Hence, their 2 statements must be true.Similarly, Bijay and Amit's second statements are false.The final table

MathsScienceEnglish1stAmitDineshDeepak2ndDineshBijayAmit3rdDeepakAjitDinesh4thAjitDeepakBijay5thBijayAmitAjit

### Question 10

Who among them scored minimum in Science?

Deepak

Dinesh

Bijay

Amit

#### SOLUTION

Solution :D

From the given data.As Ajit and Dinesh belong to same group, their last statements cannot be simultaneously true.Hence, their 2 statements must be true.Similarly, Bijay and Amit's second statements are false.The final table

MathsScienceEnglish1stAmitDineshDeepak2ndDineshBijayAmit3rdDeepakAjitDinesh4thAjitDeepakBijay5thBijayAmitAjit

### Question 11

Who among them scored the 2nd minimum in Maths?

Dinesh

Ajit

Bijay

Deepak

#### SOLUTION

Solution :B

From the given data.As Ajit and Dinesh belong to same group, their last statements cannot be simultaneously true.Hence, their 2 statements must be true.Similarly, Bijay and Amit's second statements are false.The final table

### Question 12

How many Indian citizens in the age group of 55-60 years like walking?

10

12

13

14

#### SOLUTION

Solution :C

From statement V, number of women walking in US = number of women walking in India for both years

In the group 55-60 number of women walking in US = number of women walking in India = 10

In the group 60-65 number of women walking in US = number of women walking in India = 15

Let x, p be the number of Indian and US men walking in the age group 55-60

And let y, q be the number of US men walking in the age group 60-65

Thus, x+y=8 and p+q=8. Also, from statement IV, xp=yq

And x+p=6, y+q=10

Combining these three statements together, we get x=p=3 and y=q=5

From statement 3, Among the Indians the number of men in the age group 60-65 years who like cycling is the same as the number of men in the age group of 55-60 years who like jogging and also the same as the number of men in the age group 55-60 years who like walking = 3 and from statement 1, no woman in India does cycling and no woman in US does Yoga.

Continuing this way, we can fill the table as follows:

Also x+y=5

3+2x +a = 6 (given)

The only values which satisfy are for a=1, x=1. thus, the table can be filled as:

Now the questions can be answered10+3=13

### Question 13

How many men in US like Cycling?

32

34

38

#### SOLUTION

Solution :D

Total men liking cycling = 20 + 23 = 43

Total Indian men liking cycling = 5

Total US men liking cycling = 43 - 5 = 38

### Question 14

What is the total number of American women in the age group of 60-65 years?

17

20

22

21

#### SOLUTION

Solution :C

15+4+3= 22

### Question 15

If there are 32 Indian men in the age group 60-65 years, then how many Indian men are there in the age group 55-60 years?

23

25

15

21

#### SOLUTION

Solution :A

If there are 32 men in the age group of 60-65 years, then q = 23. Thus p = 15. Then, the number of Indian men in the age group of 55-60 years is 15 + 2 + 3 + 3 = 23.

### Question 16

How many more Indian men like Yoga than Cycling?

11

22

38

#### SOLUTION

Solution :C

p + q = 38. Thus the difference is 38 - 5 = 33.

### Question 17

Who must be in the same group as H?

K

V

P

N

#### SOLUTION

Solution :D

Group 1: P, R

Group 2: S, V

H and N must be same group.

K and M must be same group.

### Question 18

If N is in GROUP II, then in how many ways the GROUP I can be selected?

4

3

2

1

#### SOLUTION

Solution :D

If N is in group II, then

Group 1: P, R, K and M.

Group 2: S, V, H and N.

### Question 19

If M is in GROUP II, then in how many ways the GROUP I can be selected?

4

3

2

1

#### SOLUTION

Solution :D

If M is in GROUP II, then

Group 1: P, R, H and N.

Group 2: S, V, K and M.

### Question 20

If N is selected in GROUP I, who must be selected in GROUP II?

I) M II) P III)S IV) R

Only I

Only III

Both II and IV

Both I and III

#### SOLUTION

Solution :D

If N is selected in GROUPI, then

Group 1: P, R, H and N.

Group 2: S, V, K and M.

### Question 21

If V is in GROUP II, then who must be in GROUP I?

H

K

M

None of these

#### SOLUTION

Solution :D

If V is in GROUP II, then P and R must be in GROUP I.

### Question 22

If the processes cannot take place simultaneously, what is the minimum time (In hours) required to get one unit of the final product?

ProcessProcess(es) to be completed before the process in column 1P−QP,RR−SQTQ,SUY,T,VVSWV,XXSYP,R

#### SOLUTION

Solution :Final product is achieved if any of U or W is completed.

To complete U:

P + R + Q + S + T + Y + V + U = 6 + 4 + 7 + 2 + 4 + 14 + 3 + 10 = 50 hours

To complete W:

P + R + Q + S + V + X + W = 6 + 4 + 7 + 2 + 3 + 7 + 9 = 38 hours∴ The minimum time required to get one unit of final product is 38 hours.

### Question 23

If the processes can take place simultaneously, what is the minimum time (In hours) required to get one unit of the final product?

#### SOLUTION

Solution :Processes P and R will be completed in 6 hours.

Then, processes Y and Q can be started simultaneously. Q will be completed at the end of 13 hours and Y at the end of 20 hours.

After process Q, S will get over at the end of 15 hours.

After process S, processes T, V and X can be started. Processes T, V and X will get over at the end of 19, 18 and 22 hours respectively.

Now, process U can be started immediately after 20 hours and it will get over in 10 more hours i.e., at the end of 30 hours.

Immediately process X gets over, i.e., after 22 hours, W can be started which will be completed at the end of 31 hours.

Thus, minimum time taken to complete one unit of the product is 30 hours.

### Question 24

A process needs to be completed n times if n units are to be produced. Only different processes can take place simultaneously. What is the minimum time (In hours) required to get two units of the final product? (Given: The final product can only be completed if both the processes W and U are over.)

#### SOLUTION

Solution :As 2 units of the final product are required, every process has to be completed twice.

Processes P and R are independent processes. Process P will run for 6 hours for the first time and immediately for next 6 hours for the second time. Process R will run for 4 hours for the first time and immediately for next 4 hours for the second time.

Process Q and Y start as soon as both P and R get over. i.e., process Q starts immediately after 6 hours and run for 7 hours for one unit and again for next 7 hours for the second unit. Similarly, process Y starts immediately after 6 hours and run for 14 hours for one unit and again for next 14 hours for the second unit. So, process Y will get over at the end of 20 hours for the first time and 34 hours for the second time.

Thus, at the end of first 13 hours, process Q gets over for the first time and at the end of 20 hours it gets over for the second time. Process Y will get over at the end of 20 hours for the first time and 34 hours for the second time.

So process S can start immediately after 13 hours for the first time and after 20 hours for the second time. S runs for 2 hours and finishes at the end of 15 hours and 22 hours respectively.

Now, processes U and W start immediately after 20 and 22 hours respectively and get over at the end of 30 and 31 hours respectively for the first time.

For the second time, processes U and W start immediately after 34 and 31 hours respectively and get over at the end of 44 and 40 hours respectively.

Thus, at the end of 44 hours, 2 units of the final product will be achieved.

### Question 25

**Assume that DREAM PINK, CREAM, and ORANGE LAIT has the same Selling Price(SP). Which of the three is the most profitable to manufacture?**

#### SOLUTION

Solution :B

To Manufacture 1 litre of each paint minimum cost is:

Paint Money Dream Pink11+9=20Cream15×0.7+25×3=18ORANGE LAIT11+7.5=18.5

Thus, the minimum cost of cream will yield the maximum profit.

### Question 26

**ORANGE LAIT can be manufactured by mixing**

CREAM and RED in the ratio 14:10

YELLOW and PINK in the ratio 1:1

RED, YELLOW, and WHITE in the ratio 1:1:2

#### SOLUTION

Solution :D

ORANGE LAIT= orange + white (1:1) and orange = red + yellow(1:1)

Let orange taken be x then white taken is x and red and yellow required for x orange is x2 each

Hence red, yellow and white can be mixed in the ratio 1:1:2.

### Question 27

**The cheapest way to manufacture DREAM PINK paint would cost**

Rs.19.50 per litre

Rs.19.75 per litre

Rs.20.00 per litre

Rs.20.25 per litre

#### SOLUTION

Solution :B

The cheapest way to manufacture Dream Pink=orange +(red+white) in the ratio 2:1:1

The cost involved is = 222 + 204 + 154 = 19.75 per litre

### Question 28

**Out of the couples surveyed by ABC across all the regions, how many couples have exactly one child?**

7

8

9

Cannot be determined

#### SOLUTION

Solution :D

The solution cannot be determined from the given data

### Question 29

**Out of the couples surveyed by ABC, in how many regions is the number of couples having at least one child lesser than the number of couples having at least one child in P?**

4

3

2

0

#### SOLUTION

Solution :D

At least 1 ⇒ all - (0 children) = (less than 3 + more than 2) - (0 children) ,

P = 34

Q=46

R=50

S=39

T= 49

U= 47

This is the least in P

### Question 30

Find the total number of couples surveyed by ABC across all the regions.

#### SOLUTION

Solution :Total number = sum of (less than 3 + more than 2) in every city

P = 39

Q=55

R=53

S=52

T= 53

U= 58

Total = 310

### Question 31

**In which city is the number of couples having more than four children and less than seven children is the least?**

P

Q

T

S

#### SOLUTION

Solution :A

More than 4 and less than 7 = (less than 7 - more than 4) ,

P = 14

Q = 37

R = 24

S = 33

T = 33

U = 33

which is in the order P<R<S = T = U<Q

### Question 32

If the number of couples having at least eight children in S is zero, then find the number of couples in S having exactly seven children

#### SOLUTION

Solution :Exactly 7 = (more than 2 + less than 3) - (less than 7) = 21 + 31 - 47 = 5