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?

A. 9200

B. 10234

C. 8644

D. 8738

SOLUTION

Solution : D

$\begin{matrix} 2001 & 2002 & 2003 & 2004 & 2005 C i t y A & 9372 & 11252 & 6127 & 12345 & 9877 & 48973 C i t y B & 10765 & 8328 & 7056 & 9362 & 13125 & 48636 C i t y C & 12823 & 11675 & 13157 & 14106 & 16132 & 67893 C i t y D & 7352 & 9137 & 11346 & 13451 & 15769 & 57055 C i t y E & 8767 & 10789 & 12523 & 14323 & 16239 & 62641 49079 & 51181 & 50209 & 63587 & 71142 \end{matrix}$
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?

A. 11%

B. 20%

C. 16%

D. 31%

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 $[\frac{11252 - 9372}{9372}] \times 100 % = 20 %$
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 $[\frac{9137 - 7352}{7352}] \times 100 % = 24 %$
% change in % increase $= \frac{4}{20} \times 100 = 20 %$

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 $\times$ 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 $\times$ 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 = $[\frac{71142 - 49079}{49079}]$ $\times$ 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 $\frac{63587 - 50209}{50209}$ $\approx$ 27% (note that the sub groups do not matter, as they eventually get cancelled out).

Question 6

Given that pqrs $\neq$ 0, is $p q^{2} r^{3} s^{4} < 0 ?$
(1) $p q^{2} r^{3} < 0$
(2) $q^{2} r^{3} s^{4} < 0$

A. IF statement (1) alone is sufficient, but statement (2) is not or If Statement (2) alone is sufficient but statement (1) is not

B. If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient

C. If Each statement ALONE is sufficient

D. Statement s (1) and (2) TOGETHER are not sufficient

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

A. IF statement (1) alone is sufficient, but statement (2) is not or If Statement (2) alone is sufficient but statement (1) is not

B. If Both statements TOGETHER are sufficient, but neither statement ALONE is sufficient

C. If Each statement ALONE is sufficient

D. Statements (1) and (2) TOGETHER are not sufficient

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 $2^{n d}$ statements must be true.
Similarly, Bijay and Amit's second statements are false.

The final table

$\begin{matrix} Maths & Science & English 1^{s t} & Amit & Dinesh & Deepak 2^{n d} & Dinesh & Bijay & Amit 3^{r d} & Deepak & Ajit & Dinesh 4^{t h} & Ajit & Deepak & Bijay 5^{t h} & Bijay & Amit & Ajit \end{matrix}$

Question 9

Who among them is $1^{s t}$ 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

$\begin{matrix} Maths & Science & English 1^{s t} & Amit & Dinesh & Deepak 2^{n d} & Dinesh & Bijay & Amit 3^{r d} & Deepak & Ajit & Dinesh 4^{t h} & Ajit & Deepak & Bijay 5^{t h} & Bijay & Amit & Ajit \end{matrix}$

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

$\begin{matrix} Maths & Science & English 1^{s t} & Amit & Dinesh & Deepak 2^{n d} & Dinesh & Bijay & Amit 3^{r d} & Deepak & Ajit & Dinesh 4^{t h} & Ajit & Deepak & Bijay 5^{t h} & Bijay & Amit & Ajit \end{matrix}$

Question 11

Who among them scored the $2^{n d}$ 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

$\begin{matrix} Maths & Science & English 1^{s t} & Amit & Dinesh & Deepak 2^{n d} & Dinesh & Bijay & Amit 3^{r d} & Deepak & Ajit & Dinesh 4^{t h} & Ajit & Deepak & Bijay 5^{t h} & Bijay & Amit & Ajit \end{matrix}$

Question 12

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

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, $\frac{x}{p} = \frac{y}{q}$
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 answered
10+3=13

Question 13

How many men in US like Cycling?

C. 36

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?

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?

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?

C. 33

SOLUTION

Solution : C

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

Question 17

Who must be in the same group as H?

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?

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?

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?

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?

$\begin{matrix} P r o c e s s & P r o c e s s (e s) t o b e c o m p l e t e d b e f o r e t h e p r o c e s s i n c o l u m n 1 P & - Q & P, R R & - S & Q T & Q, S U & Y, T, V V & S W & V, X X & S Y & P, R \end{matrix}$
___

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?

A. DREAM PINK.

B. CREAM.

C. ORANGE LAIT.

D. Data Insufficient

SOLUTION

Solution : B

To Manufacture 1 litre of each paint minimum cost is:

$\begin{matrix} P a i n t & M o n e y D r e a m P i n k & 11 + 9 = 20 C r e a m & 15 \times 0.7 + 25 \times 3 = 18 O R A N G E L A I T & 11 + 7.5 = 18.5 \end{matrix}$

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

B. CREAM and RED in the ratio 3:1

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 $\frac{x}{2}$ 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 = $\frac{22}{2}$ + $\frac{20}{4}$ + $\frac{15}{4}$ = 19.75 per litre

Question 28

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

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?

SOLUTION

Solution : D

At least 1 $\Rightarrow$ 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?

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

Free DI and LR Practice Test - CAT

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Question 2

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Question 3

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Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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Question 10

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Question 11

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Question 12

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Question 13

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Question 14

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Question 15

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Question 16

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Question 17

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Question 18

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Question 19

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Question 20

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Question 21

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Question 22

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Question 23

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Question 24

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Question 25

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Question 26

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Question 27

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Question 28

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Question 29

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Question 30

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Question 31

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Question 32

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