Free DI and LR Practice Test - CAT

Question 1

If 1 $m^{3}$ = 750 kg for saw timber, find in which year was the difference in prices of saw timber and logs the least?

A. 1989

B. 1990

C. 1991

D. 1992

SOLUTION

Solution : B

1 tonne $= \frac{4}{3} = 1.33 m^{3}$
$\begin{matrix} YEAR & Saw Timber (Price in Rs/Tonnes) & Saw Timber (Price in Rs/Cubic meters) & Logs price in(Rs/cubic meters) & Difference in price 1989 & 12 & 9 & 18 & 9 1990 & 10 & 7.50 & 15 & 7.50 1991 & 13 & 9.75 & 18 & 8.25 1992 & 15 & 11.25 & 19 & 7.75 \end{matrix}$
It is hence, clear that the difference is least in the year 1990.
Shortcut!
The beauty of the question is that the conversion need not even be done! Just observe the graph and you see the lines of Saw Timber & logs the closest to each other in 1990!

Question 2

If one cubic meter = 700 kg for plywood and 800 kg for saw timber, find in which year was the difference in the prices of plywood and saw timber (per cubic meter) the maximum?

1989

1990

1991

1992

SOLUTION

Solution : D

1 tonne of plywood = $(\frac{10}{7})$ m $^{3}$ = 1.43m $^{3}$ and 1 tonne of saw timber = $(\frac{5}{4})$ m $^{3}$ = 1.25m $^{3}$
The difference is maximum for the year 1992.

Question 3

If the volumes of sales of plywood, saw timber and logs were 40%, 30% and 30% respectively, then what was the average realization in 1993 per cubic meter of sales? (One cubic meter of saw dust and plywood both = 800 kg)

18.6

12.5

13.5

SOLUTION

Solution : B

Ratio of volumes of plywood, saw timber and logs = 4 : 3 : 3.So, the average realization per meter $^{3}$ of sales =
$\frac{[(4 \times 5.6) + (3 \times 14.28) + (3 \times 20)]}{(4 + 3 + 3)}$ = Rs 12.5

Question 4

In the previous question, if in 1994 prices increased by 5%, 1% and 10% while the volume of sales break-up was 40%, 30% and 30% for plywood, saw timber and logs respectively, then want was the average realization?

18.95

16.45

13.15

10.25

SOLUTION

Solution : C

The change for price increase = $\frac{[(4 \times 5.26 \times 1.05) + (3 \times 14.28 \times 1.01) + (3 \times 20 \times 1.1)]}{(4 + 2 + 3)}$ = Rs 13.15

Question 5

What was the total output of coconuts?

24,000

36,000

18,000

48,000

SOLUTION

Solution : B

Let the amount invested by Gopal and Ram be 2x and 3x respectively. Gopal further invested Rs 2 lakh. Given (2x + 2) = 3x or x = 2 lakh. Hence, initial amount paid by Gopal and Ram to Krishna is 4 lakh and 6 lakh respectively. Hence, total money invested by them together = (6 + 6) = 12 lakh.

The total revenue generated = 12 × 25% = 3 lakh. The ratio of revenue from coconut and lemon trees are in the ratio 3 : 2. Hence, revenue from coconut = Rs 1,80,000 and revenue from lemons = Rs 1,20,000. So, total output of coconut = $(\frac{1, 80, 000}{5})$ = 36,000.

Question 6

What was the amount received by Gopal in 1997?

Rs 1.5 lakh

Rs 3 lakh

Rs 6 lakh

None of these

SOLUTION

Solution : A

Since, revenue of Rs 3,00,000 is equally divided by Gopal and Ram. Hence, amount received by Gopal in 1997 = 0.5× 3,00,000 = Rs 1,50,000.

Question 7

What was the value of output per tree for coconuts?

Rs 36

Rs 360

Rs 3,600

Rs 240

SOLUTION

Solution : B

Let the amount invested by Gopal and Ram be 2x and 3x respectively. Gopal further invested Rs 2 lakh. Given (2x + 2) = 3x or x = 2 lakh. Hence, initial amount paid by Gopal and Ram to Krishna is 4 lakh and 6 lakh respectively. Hence, total money invested by them together = (6 + 6) = 12 lakh.

The total revenue generated = 12 × 25% = 3 lakh. The ratio of revenue from coconut and lemon trees are in the ratio 3 : 2. Hence, revenue from coconut = Rs 1,80,000 and revenue from lemons = Rs 1,20,000.
So, output per tree for coconuts = $(\frac{1, 80, 000}{500})$ = 360.

Question 8

If 1300 Scooters were sold in Mumbai, what was the total number of vehicles sold in Bengaluru?

1750

2500

1250

None of these

SOLUTION

Solution : A

Number of Scooters sold in Mumbai = $\frac{26}{100}$ $\times$ b = 1300 $\Rightarrow$ b = 5000
Number of trucks sold in Mumbai = $\frac{13}{100}$ $\times$ 5000 = 650, which is 26% of total number trucks sold in all given cities.
Number of trucks sold in Mumbai = $\frac{26}{100}$ $\times$ s = 650 $\Rightarrow$ s = 2500.
Number of trucks sold in Bengaluru = $\frac{7}{100}$ $\times$ 2500 = 175, which is 10% of total number of vehicle sold in Bengaluru.
The total number of vehicles sold in Bengaluru = 1750.

Question 9

If 4800 vehicles were sold in Delhi, what was the total number of vehicles sold in Chennai?

4800

2400

5100

None of these

SOLUTION

Solution : A

Number of Auto Rickshaws sold in Delhi = $\frac{24}{100}$ $\times$ 4800 = 1152, Which is 24% of total number of Auto Rickshaws sold in the given cities.
So, total number of Auto Rickshaws = 4800.
Number of Auto Rickshaws sold in Chennai = $\frac{10}{100}$ $\times$ 4800 = 480, which is 10% of total number of vehicles sold in Chennai.
The total number of vehicles sold in Chennai = 4800

Question 10

The number of vehicles sold in Mumbai is same as the number of vehicles sold in which of the following category?

Cars

Bikes

Scooters

None of these

SOLUTION

Solution : D

If we compare the row of Mumbai from first table to the column of Mumbai from second table, we can easily determine

Question 11

What is the ratio of number of Bikes sold in Hyderabad to that of Buses in Kolkata?

27 : 8

8 : 27

4:27

cannot be determine

SOLUTION

Solution : B

Let total number of vehicle sold in Mumbai = 100. Total number of buses and Bikes sold in the given cities are 75 and 40 respectively.
Total number of Bikes sold in Hyderabad = $\frac{10}{100}$ $\times$ 40 = 4
Total number of Buses sold in Kolkata = $\frac{18}{100}$ $\times$ 75 = $\frac{27}{2}$
Ratio = 8 : 27

Question 12

If Akash stopped playing the game when his gain would be maximized, the gain in Rs. Would have been:

SOLUTION

Solution : A

We can summarize the four rounds of play in the table given below :

$\begin{matrix} R o u n d & B a s e C a r d & \frac{E a r n i n g s -}{D e a l e r / P l a y e r} & T o p C a r d & \frac{E a r n i n g s -}{D e a l e r / P l a y e r} I & 8 - C l u b s & 8 - P l a y e r & Q u e e n - C l u b s & 16 - D e a l e r I I & 10 - H e a r t s & 10 - P l a y e r & 2 - S p a d e s & 10 - P l a y e r I I I & 6 - D i a m o n d & 6 - P l a y e r & A c e - H e a r t s & 6 - D e a l e r I V & 8 - S p a d e s & 8 - P l a y e r & J a c k - S p a d e s & 16 - D e a l e r \end{matrix}$
Akash's gain would be maximized at the end of Round II which is = -8 (Round I earnings) + 20 (Round II earnings) = Rs. 12.

Question 13

If the final amount of money that Akash had with him was Rs. 100, what was the initial amount he held with him?

120

SOLUTION

Solution : D

At the end of Round IV, Akash's earnings = -8 (Round I) + 20 (Round II) + 0 (Round III) -8 (Round IV) = Rs. 4
If total = Rs. 100, then the initial amount with Akash = Rs. 100 - Rs. 4 = Rs. 96.

Question 14

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

100

SOLUTION

Solution : B

In Round I, Akash has to pay Rs. 16 to the dealer but he makes only Rs. 8 in that Round. So to take care of this deficit, he should have a minimum of Rs. 8 as the initial amount. Rest all is taken care of. Therefore, answer is option (b).

Question 15

Four friends A, B, C and D are out shopping. A has less money than three times the amount that B has. C has more money that B. D has an amount equal to the difference of amounts with B and C. A has three times the money with D. They each have to buy at least one shirt, or one shawl, or one sweater, or one jacket that are priced Rs. 200, Rs. 400, Rs. 600, and Rs. 1000 apiece, respectively. C borrows Rs. 300 from A and buys a jacket. B buys a sweater after borrowing Rs. 100 from A and is left with no money. A buys three shirts. What is the costliest item that D could buy with his own money?

A shirt

A shawl

A sweater

A jacket

SOLUTION

Solution : B

From the information given in the question, we can deduce the following:
Amount with A $<$ 3* (Amount with B) ... (1)
Amount with C $>$ Amount with B ... (2)
Amount with D = (Amount with C) - (Amount with B) ... (3)
Amount with A = 3 * (Amount with D) ... (4)
Now, C + Rs. 300 (borrowed from A) $\geq$ Rs. 1000 (Since he bought a jacket) ... (5)
Also, B + Rs. 100 (borrowed from A) $\geq$ Rs. 600 (Since he bought a sweater) ... (6)
We can deduce from (6) that B had at least Rs. 500.
Thus, following (1), (5) and (6),
1000 $\leq$ Amount with A $\leq$ 1500.
Thus, Amount with D $\leq \frac{1500}{4}$ .
Therefore, the costliest item that D can buy is a Shawl thus making answer option (B) the correct answer choice.

Question 16

In a "keep-fit” gymnasium class, there are fifteen females enrolled in a weight-loss program. They all have been grouped in any one of the five weight-groups $W_{1}, W_{2}, W_{3}, W_{4}$ or $W_{5}$ One instructor is assigned to one weight-group only. A, B, C, and D belong to the same weight-group. A and E are in one weight-group, F and G are also in one weight-group. E, H, G, I, and J belong to different weight-groups. K cannot be with J, and L cannot be with H. M cannot be with H, K, or J. D is in $W_{1}$ and K is in $W_{4}$ with I. N and O cannot be with F, but are in a weight-group with total membership of four. No weight-group can have more than five or less that one member. P, Q, R, S, and T are instructors of weight-groups with membership sizes 5, 4, 3, 2 and 1, respectively. Who is the instructor of H? /p>

SOLUTION

Solution : B

Based on the information available in the passage, we can come up with the following table:
$\begin{matrix} G r o u p s & W_{1} & W_{2} & W_{3} & W_{4} & W_{5} M e m b e r s & A, B, C, D, E & H & G, F, M & I, K, N, O & J, L I n s t r u c t o r s & P & T & R & Q & S \end{matrix}$

Therefore, we can deduce that the instructor of H is T, thus making answer option (b) the correct answer choice.

Question 17

A king has unflinching loyalty from eight of his ministers $M_{1}$ to $M_{8}$ , but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three person selected.
$M_{1}$ likes fishing and smoking, but hates gambling,
$M_{2}$ likes smoking and drinking, but hates fishing,
$M_{3}$ likes gambling, but hates smoking,
$M_{4}$ likes mountaineering, but hates drinking,
$M_{5}$ likes drinking, but hates smoking and mountaineering,
$M_{6}$ likes fishing, but hates smoking and mountaineering,
$M_{7}$ likes gambling and mountaineering, but hates fishing, and
$M_{8}$ likes smoking and gambling, but hates mountaineering.
Who are the four people selected by the king?

$M_{1}, M_{2}, M_{5}, M_{6}$

$M_{3}, M_{4}, M_{5}, M_{6}$

$M_{4}, M_{5}, M_{6}, M_{8}$

$M_{1}, M_{2}, M_{4}, M_{7}$

SOLUTION

Solution : D

Answer option (a) is rejected because $M_{1}$ hates Gambling which is not hated by any of the other three. Answer option (b) is rejected because $M_{3}$ likes Gambling which is not liked by any of the other three. Answer option (c) is rejected because $M_{4}$ likes Mountaineering which is not liked by any of the other three. Option (d) is the correct answer choice because it fulfills both the conditions

Question 18

What is the mascot of China?

Fox

Lion

C. Wolverine

D. Wolf

SOLUTION

Solution : A

From the condition (1) and (4), we can easily determine below table.

$\begin{matrix} C o u n t r y N a m e & M e d a l W o n & M a s c o t S w i t z e r l a n d & S l i v e r & W o l f G e r m a n y N o r w a y & B r o n z e & T i g e r C h i n a C a n a d a & N o m e d a l \end{matrix}$

From the condition (2) we can determine Germany won gold medal and from condition (5) we can determine
Germany's mascot lion. And from condition (5), we can determine china's mascot is fox. Finally, we can make
below table.
$\begin{matrix} C o u n t r y N a m e & M e d a l W o n & M a s c o t S w i t z e r l a n d & S l i v e r & W o l f G e r m a n y & G o l d & L i o n N o r w a y & B r o n z e & T i g e r C h i n a & N o m e d a l & F o x C a n a d a & N o m e d a l & W o l v e r i n e \end{matrix}$

Question 19

Who won gold medal?

China

Germany

Canada

Switzerland

SOLUTION

Solution : B

Option B is the correct answer.

Question 20

Wolverine is mascot of which country?

China

Germany

Canada

Switzerland

SOLUTION

Solution : C

Option C is the correct answer.

Question 21

How many correct predictions were made by D?___

SOLUTION

Solution :
From the given condition "if any person had predicted that a single horse would win each of the eight games, he would not have gained or lost any amount". It means, every horse won 2 races.

From the given condition "B received the maximum amount of 16000". Let B predicted x races and y races incorrect.

3000 x-1000 y=16000 ...................(1) And x+y=8......................... (2)

From equation (1) and (2), we can determine x=6 and y=2

From the second condition "Had C made one more correct prediction and B made one more incorrect prediction.
The amounts gained by them at the end of the races would have interchanged". We can conclude C predicted 5
races correct and 3 races incorrect. And E neither gained nor lost any amount. So, E predicted 2 races correct and 6
races incorrect.

$\begin{matrix} P e r s o n s & W i n & L o s e & S c o r e B & 6 & 2 & 16, 000 C & 5 & 3 & 12, 000 E & 2 & 6 & 0 \end{matrix}$

Now, from the given table, we can easily conclude below table :-
$\begin{matrix} R_{1} & R_{2} & R_{3} & R_{4} & R_{5} & R_{6} & R_{7} & R_{8} C h e e t a h & B i n g o & A z u r e & B i n g o \end{matrix}$

Because B's 6 predictions are correct. Out of 8 predictions, 4 times B predicted "Dylan". And we know Dylan won only two times. It means B's predictions for Race $R_{2}, R_{4}, R_{5}$ and $R_{8}$ were correct.

$\begin{matrix} R_{1} & R_{2} & R_{3} & R_{4} & R_{5} & R_{6} & R_{7} & R_{8} A z u r e & C h e e t a h & D y l a n & B i n g o & A z u r e & C h e e t a h & D y l a n & B i n g o x & (B, C) & (A, B, C, D) & (A, B, D, E) & (A, B, C) & (A, C, D) & (B, C, D) & (B, E) \end{matrix}$

Now, we can conclude below table. Because, E's 2 predictions were correct and Cheetah won 2 times. So, cheetah
has to win Race $R_{5}$ . C's 5 predictions were incorrect. So, C cannot be winner of race $R_{1}$

Question 22

The amount gained by A at the end of the eight races is___

SOLUTION

Solution :

Question 23

In how many the races was the winner not a participator predicted by any of the following person?___

SOLUTION

Solution :

Question 24

Which branch has the lowest average income?

A. Ahmedabad

B. Bangalore

C. Calcutta

D. Delhi

SOLUTION

Solution : C

The data points which are closest to the "x” axis should be considered. It can be clearly observed that this is satisfied by the Calcutta Branch.

Question 25

Which branch has the lowest average Profit?

A. Ahmedabad

B. Bangalore

C. Calcutta

D. Delhi

SOLUTION

Solution : D

The lowest profit will be the data points closest to the x=y line. Thus, the answer is option (d)- Delhi Branch

Question 26

The highest amount of Profit accrues to a cost centre of which branch?

A. Ahmedabad

B. Bangalore

C. Calcutta

D. Delhi

SOLUTION

Solution : A

The highest profit will be can be represented by the point furthest from the x axis and closest to the y axis. Answer is option (a)-Ahmedabad Branch

Question 27

How much did C get in PI?

96.5

SOLUTION

Solution : D

The overall score for C is given as 95
The easier way to calculate this, will be to consider the deviation of the average of each group's score from 95
Eg) the average of the Section I = 98. Deviation from the total average 95=3
Similarly for Essay Writing =0
For Section II = -0.5
For Vernacular Group = 0
Let the Personal Skills group =x
Thus, 3+0-0.5+0+x=0 $\Rightarrow$ x= 2.5. this implies that the Average of the Personal Skills Group = 95+2.5= 97.5
Now C's score in GD=96 & the average of the group is 97.5. Thus C's PI score = 99

Question 28

Aspirants who scored a group average of atleast 95 are eligible for the Round II Interview. How many such aspirants are there?

SOLUTION

Solution : B

Among the ten aspirants, only C satisfies the required criteria.

Question 29

A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves?

(1) There are 25 books on the upper shelf. (2) There are 24 books on the lower shelf.

A. if the question can be answered by one of the statements alone but not by the other

B. if the question can be answered by using either statement alone

C. if the question can be answered by using both the statements together but cannot be answered using either statement alone

D. if the question cannot be answered even by using both the statements A and B.

SOLUTION

Solution : C

Statement (1) Insufficient: The information given says nothing about the number of books on the lower shelf. If there are fewer than 25 books on the lower shelf, then the median number of pages will be the number of pages in one of the books on the upper shelf or the average number of pages in two books on the upper shelf. Hence, the median will be at most 400. If there are more than 25 books on the lower shelf, then the median number of pages will be the number of pages in one of the books on the lower shelf or the average number of pages in two books on the lower shelf. Hence, the median will be at least 475; NOT sufficient.

Statement (2) Insufficient: An analysis very similar to that used in (1) shows the information given is not sufficient to determine the median; NOT sufficient. Given both (1) and (2), it follows that there is a total of 49 books. Therefore, the median will be the 25th book when the books are ordered by number of pages. Since the 25th book in this ordering is the book on the upper shelf with the greatest number of pages, the median is 400. Therefore, (1) and (2) together are sufficient. The correct answer is C; both statements together are sufficient

Question 30

Each packet of SOAP costs Rs 10. Inside each packet is a gift coupon labeled with one of the letters S, O, A, and P. If a customer submits four such coupons that make up the word SOAP, the customer gets a free SOAP packet. Ms. X kept buying packet after packet of SOAP till she could get one set of coupons that formed the word SOAP. How many coupons with label P did she get in the above process?
1. The last label obtained by her was S and the total amount spent was Rs 210.
2. The total number of vowels obtained was 18

A. if the question can be answered by one of the statements alone but not by the other.

B. if the question can be answered by using either statement alone

C. if the question can be answered by using both the statements together but cannot be answered using either statement alone

D. if the question cannot be answered even by using both the statements A and B

SOLUTION

Solution : C

Both statements are needed to answer the question,
$(\frac{210}{10})$ =21 is the total no. of soaps bought. Last one was S . Therefore, O, A and P constitute 20. Total no.of P can be calculated if statement B is given.

Question 31

Many of the students at the International School speak French or German or both. Among the students who speak French, four times as many speak German as don't. In addition, ${(\frac{1}{6})}^{t h}$ of the students who don't speak German do speak only French. What fraction of the students speak German?
(A) Exactly 60 students speak French and German.

(B) Exactly 75 students speak neither French nor German.

A. if the question can be answered by one of the statements alone but not by the other.

B. if the question can be answered by using either statement alone.

C. if the question can be answered by using both the statements together but cannot be answered using either statement alone

D. if the question cannot be answered even by using both the statements A and B

SOLUTION

Solution : D

Let the total number of students be indicated as T
From the question stem, Among the students who speak French, four times as many speak German as don't. Thus, if the number of students who speak only French are indicated as "x", then the number of students who speak both French and German are indicated as "4x"
Let the number of students who do not speak French but speak German = "y" and let the number of students who don't speak both =z
It is also given that $(\frac{1}{6})$ of the students who don't speak German do speak French
Thus, $(\frac{1}{6}) x (X + Z) = X$
From this, z = 5x
Using the both statements, we cannot answer the question.

Question 32

There are a certain facts about the software engineers working with an IT firm. Total number of software engineers is 70 out of which 30 are females. 30 people are married. 24 software engineers are above 25 years of age. Out of all married software engineers, 19 are above 25 years, of which 7 are males. 12 males are above 25 years and overall 15 males are married. The number of unmarried females which are above 25 is___.

SOLUTION

Solution :
15 males are married, so 15 females are married
now 7 males above 25 are married. so(19-7)=12 females above 25 are married
given that 12 males are above 25 years so 24-12=12 females are above 25 years
so all females above 25 years are married
This means 0 unmarried female above 25

Free DI and LR Practice Test - CAT

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Question 2

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Question 4

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Question 8

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Question 11

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Question 14

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Question 15

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Question 16

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Question 19

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Question 26

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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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