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CAT Practice Test: August 11 - CAT MCQ


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CAT Practice Test: August 11 - Question 1

If a, b, c are in AP and x, y, z are in GP, then xb - c. yc - a. za - b equals

Detailed Solution for CAT Practice Test: August 11 - Question 1

Since a, b, c are in AP, therefore
b - a = c - b = d and c - a = 2d.
∴ xb - c × yc - a × za - b = x-d × y2d × z-d
= (xz)-d × y2d = y-2d × y2d = 1. (∵ y2 = xz)

CAT Practice Test: August 11 - Question 2

If a, b, c, d, e and f are AMs between 2 and 12, then a + b + c + d + e + f is equal to  

Detailed Solution for CAT Practice Test: August 11 - Question 2

As, 2, a, b, c, d, e, f, 12 are in AP
So, 2 + a + b + c + d + e + f + 12 = 8/2 (2 + 12)
2 + a + b + c + d + e + f + 12 = 4 × (2 + 12)
a + b + c + d + e + f = 4 × (2 + 12) - 2 - 12
a + b + c + d + e + f = 42

CAT Practice Test: August 11 - Question 3

If the fifth term of an AP is twice its third term, then the first term of the AP is

Detailed Solution for CAT Practice Test: August 11 - Question 3

t5 = 2t3
(a + 4d) = 2(a + 2d)
⇒ a = 0

CAT Practice Test: August 11 - Question 4

The sum of 3rd and 15th terms of an arithmetic progression is equal to the sum of 6th, 11th and 13th terms of the same progression. Which term of the given progression should necessarily be equal to zero?

Detailed Solution for CAT Practice Test: August 11 - Question 4

Let the AP be a, a + d, a + 2d, …
∵ Tn = a + (n - 1)d
T3 + T15 = T6 + T11 + T13
2a + 2d + 14d = 3a + 5d + 10d + 12d
0 = a + 11d
0 = T12
Thus, the 12th term of the AP is 0.

CAT Practice Test: August 11 - Question 5

Find the sum of all even numbers from 10 to 200 (inclusive), excluding those, which are multiples of 6.  

Detailed Solution for CAT Practice Test: August 11 - Question 5

10 + 12 + 14 + ------- + 200
a = 10, d = 2
Tn = 200 = 10 + (n - 1) × 2
⇒ n = 96


Sum of the numbers, which are multiple of 6:
12 + 18 + _ _ _ _ _ + 198
198 = 12 + (m - 1) 6
m = 32

Required Sum = 10,080 - 3,360 = 6,720

CAT Practice Test: August 11 - Question 6

The average speed of a cyclist who covers first, second and third km at speeds of 20 km/hr, 16 km/hr and 12 km/hr, respectively, is

Detailed Solution for CAT Practice Test: August 11 - Question 6

Direct formula:

Average speed = 3abc/(ab+ bc+ca) 
(where a, b, c are the different speeds for different km)

CAT Practice Test: August 11 - Question 7

The average marks of students A, B and C are 48. Another student (D) joins the group and the new average becomes 44 marks. If again, another student (E), who has three marks more than D, joins the group, the average of students B, C, D and E becomes 43 marks. How many marks did A get in the exam?

Detailed Solution for CAT Practice Test: August 11 - Question 7

A + B + C = 48 × 3 = 144 ............(i)
A + B + C + D = 44 × 4 = 176 ............(ii)
(ii) - (i) gives, D = 176 - 144 = 32
Marks of E = 32 + 3 = 35
B + C + D + E = 43 × 4 = 172
B + C + D = 172 - 35 = 137 .........(iii)
(ii) - (iii) gives,
A = 176 - 137
A = 39

CAT Practice Test: August 11 - Question 8

Average of three numbers is x. Instead of the first number if we take only half of that number, the average will be x - 1. If twice the first number is taken in place of the first number, what will be the average?

Detailed Solution for CAT Practice Test: August 11 - Question 8

If half of the first number is removed, the average decreases by 1, that means, the total decreases by 3.We assume that the number is z.

Therefore, if we take 2z instead of z, the total will increase by 6 and the average increases by 2.
So, it will be x + 2.

 

CAT Practice Test: August 11 - Question 9

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders, and Rs. 600 when there are 50 boarders. What will be the average expense per boarder when there are 100 boarders?

Detailed Solution for CAT Practice Test: August 11 - Question 9

Let x be the fixed cost and y be the variable cost.
17,500 = x + 25y ……..(i)
30,000 = x + 50y ……..(ii)
Solving the equations (i) and (ii), we get
x = 5,000, y = 500
Now, if the average expense of 100 boarders be `A`, then
100 × A = 5,000 + 500 × 100
∴ A = 550

CAT Practice Test: August 11 - Question 10

Directions: Find the missing number in the following series.

210, 21, 189, ?, 170.1, 17.01

Detailed Solution for CAT Practice Test: August 11 - Question 10

The given series follows a pattern as given below:
210 ÷ 10 = 21
21 × 9 = 189
189 ÷ 10 = 18.9
18.9 × 9 = 170.1
170.1 ÷ 10 = 17.01
So, the missing number is 18.9.

CAT Practice Test: August 11 - Question 11

Directions: Find the wrong term in the following number series.

22, 21, 41, 128, 513, 2564

Detailed Solution for CAT Practice Test: August 11 - Question 11

The given series follows the pattern as shown below:

22 × 1 - 1 = 21

21 × 2 + 1 = 43

43 × 3 - 1 = 128

128 × 4 + 1 = 513

513 × 5 - 1 = 2564

Therefore, 41 is the wrong term in the series.

CAT Practice Test: August 11 - Question 12

Directions: Find the wrong term in the following series.

8, 15, 41, 169, 841, 5041, 35281

Detailed Solution for CAT Practice Test: August 11 - Question 12

The given series follows a pattern as shown below.
8 x 2 - 1 = 16 - 1 = 15
15 x 3 - 2 = 45 - 2 = 43
43 x 4 - 3 = 172 - 3 = 169
169 x 5 - 4 = 845 - 4 = 841
841 x 6 - 5 = 5046 - 5 = 5041
5041 x 7 - 6 = 35287 - 6 = 35281
So, the wrong term in the given series is 41.

CAT Practice Test: August 11 - Question 13

What should come in place of the question mark in the following number series?

4, 8, 6, 18, 10, 50, ?, 98

Detailed Solution for CAT Practice Test: August 11 - Question 13

The given series is an alternate series. Odd series is double of consecutive prime numbers.
i.e.
2 × 2 = 4
3 × 2 = 6
5 × 2 = 10
7 × 2 = 14

Even series is as:

42/2 = 8

62/2 = 18

102/2 = 50

142/2 = 98

CAT Practice Test: August 11 - Question 14

Directions: Study the diagram given below carefully and answer the following question.
I – Males
II – Indians
III – Sportsperson
IV – Educated

Which of the following sections represents non-Indian females who are educated table tennis players?

Detailed Solution for CAT Practice Test: August 11 - Question 14

The people belonging to section D are non-Indian females who are educated table tennis players.

CAT Practice Test: August 11 - Question 15

Directions: Study the diagram given below and answer the following question.
Here, the letters represent people.

Who likes to watch Game of Thrones only?

Detailed Solution for CAT Practice Test: August 11 - Question 15


According to the diagram, X likes to watch Game of Thrones only.

CAT Practice Test: August 11 - Question 16

Directions: The question below contains four elements. These four elements may or may not have some linkage. The group of elements may fit into one of the diagrams given in the options. You have to indicate the diagram for the given group of elements.

Males, Athletes, Musicians, Lawyers

Detailed Solution for CAT Practice Test: August 11 - Question 16

Among the given four categories, one is gender and the other three are professions. Any gender can have this profession and one can have more than one profession as well, i.e. a male can be both an athlete and a lawyer or a male can be an athlete, a lawyer and a musician or a musician can also be a lawyer etc.
Thus, diagram in option (3) is correct.

CAT Practice Test: August 11 - Question 17

Directions: From the alternatives, choose the diagram that best represents the relationship among the given classes.
Dances, Kathak, Bharatnatyam, Pongal

Detailed Solution for CAT Practice Test: August 11 - Question 17

Kathak and Bharatnatyam are dance forms, whereas Pongal is a festival.

CAT Practice Test: August 11 - Question 18

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 18

Statements B, A, E and C can be arranged in a sequence to form a paragraph.
Statements A and B are both examples of relief operations by India, hence, both have to be relevant since only one statement is out of context.
The cause of scepticism in statement C is evident in statement E --- Indian institutions could it without the intervention of politicians.
How the Nepalese responded to India's relief operation is a related topic but unrelated to the context. Statement D is odd one out.

CAT Practice Test: August 11 - Question 19

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 19

Sentence D must follow A; manpower (asset) is related to various product lines (car or cosmetics). Sentence C must follow E; 'scientific manpower planning' caters to both performers and non-performers.
Getting something is what reward is; but sentence B says something contrary to the context.

CAT Practice Test: August 11 - Question 20

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 20

'It' in (B) refers to 'the students dress in a style' in (D). This gives a hint that the passage is about hipster clothing. This implies that (D) begins the para by providing context and is followed by (B). Next should be (A) and (C) as these talk about the situation of two clothing companies related to the hipster style. This leaves (E) as the odd one out.

CAT Practice Test: August 11 - Question 21

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 21

The correct sequence is C, E, A, D.
Odd one out: 'B'
All the sentences, except 'B', are focusing on the main cause of global warming and elaborating on fossil fuels. On the other hand, sentence 'B' states about the effect of global warming on the persons who cause it.

CAT Practice Test: August 11 - Question 22

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 22

(B) provides the context for the paragraph as it refers to picturing something. It is followed by (E) as 'these children' refers to 'baby in a sling and a recently weaned four-year old' mentioned in the preceding sentence. Next in order is sentence (C) as 'Instead, they are indulged' is a continuation to 'No one ever scolds' stated in (E).
Now, out of (A) and (D), it is only (A) that relates to the context as 'mother, grandmother and baby' are also talked about in one of the other sentences. (D) finds no link to any of the other sentences, hence the answer.

CAT Practice Test: August 11 - Question 23

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 23

The correct sequence is D, A, C, E.
Odd one out: 'B'
Sentence 'B' is explaining about the field of education - its components, whereas, other sentences are focusing on the importance of education.

CAT Practice Test: August 11 - Question 24

Directions: Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.

Detailed Solution for CAT Practice Test: August 11 - Question 24

 The correct sequence is B, C, E, D.
Odd one out: 'A'
Sentence 'A' is against the flow of the other sentences, as it states the claims of the companies. It shows that companies do not promote child-labour. Whereas, all other sentences - B, C, E, D - explain the facts about child labour. They mainly focus on the explanation of the term 'child labour'.

CAT Practice Test: August 11 - Question 25

Directions: In the following question a short passage is given with one of the lines in the passage missing and represented by a blank. Select the best out of the five answer choices given, to make the passage complete and coherent (coherent means logically complete and sound).

Once we take the numbers present at the protests out of the equation what distinguishes a fringe group from a civil society protest would usually be that civil society movements have a more rational and morally justified case to make. ___________ The dependence on rationality in trying to change urban public opinion is not what it was, anywhere in the world. The Indian politicians have, over a much longer period, treated some issues as being matters of faith, and hence not subject to the rules of rational discourse. With rational argument no longer the sole determinant of the direction public discourse will take, the debates in our cities are increasingly between those who would like to take a somewhat old world liberal view, and those who insist their beliefs do not require rational confirmation.

Detailed Solution for CAT Practice Test: August 11 - Question 25

The preceding sentence mentions that the civil society movements were based on rational and morally justified case whereas the succeeding sentences convey the opposite. Therefore, option 1 fits here the best.

CAT Practice Test: August 11 - Question 26

Directions: In the following passage, the opening statement has been deleted. From among the statements given below, choose the statement that should precede the passage.

To begin with, banks and NBFCs will no longer need to report each credit exposure to different systems in different formats. Instead, the Public Credit Registry (PCR) will function as a single-point data repository, and different players in the financial system (banks, NBFCs, credit bureaus, regulators, etc.) will draw data from it adhering to strictly-defined access rules. Secondly, the report proposes an enabling legal framework, which will regulate the collection and sharing of this data. Thirdly, information on each default will be shared on a realtime basis, alerting lenders and triggering corrective actions.

Detailed Solution for CAT Practice Test: August 11 - Question 26

The phrase 'secondly, the report proposes' indicates that certain proposals or recommendations have been presented. So, a beginning sentence should be about these proposals or recommendations. Only in fifth option we have such a mention. So, option E is the correct answer.

CAT Practice Test: August 11 - Question 27

Directions: In the following question a short passage is given with one of the lines in the passage missing and represented by a blank. Select the best out of the five answer choices given, to make the passage complete and coherent (coherent means logically complete and sound).

The Almighty once decided that he would bestow on the human being every possible virtue that the Almighty could conjure up. ____________ The Almighty called together a conclave of angels and asked for suggestions on what to do. Some angels suggested that the Almighty take away the virtues and stash them in the sky, for Man may never look there. The Almighty reminded them that Man had already traveled to the moon and therefore one day he might discover the virtues hidden in the sky. A few other angels recommended that the almighty bury the virtues under the ocean. The Almighty once again sought the indulgence of the angels and told them that Man would one day send a submarine and discover the virtues. Not having got satisfactory suggestions the Almighty decided that he would consign all the virtues in Man's heart for he would rarely look within.

Detailed Solution for CAT Practice Test: August 11 - Question 27

The preceding sentence mentions that the Almighty bestowed human being with every possible virtue. Whereas the succeeding sentences have a mention of the suggestions given by the angels to hide away the virtues and Almighty paying heed to these suggestions. So, among the given answer choices, it is option 5 that leads to this transition.

CAT Practice Test: August 11 - Question 28

Directions: The last sentence in the following passage has been deleted. Select the sentence, out of the available options, that best suits the end of the passage.

In the past, customers knew that the computers they bought were not going to run the company. Today - despite wishes to the contrary - they`re realizing that the software they buy is not going to create applications. In the end, customers want results - not just applications that run on computers. How are these results delivered? Through the provision of services.

Detailed Solution for CAT Practice Test: August 11 - Question 28

The last option is a logical continuation of the last sentence. This is the only one that connects the services with the computers. Hence, it is the correct answer.

CAT Practice Test: August 11 - Question 29

Directions: Read the paragraph and answer the question that follows.
Every one has heard people quarrelling. Sometimes it sounds funny and sometimes it sounds merely unpleasant; but however it sounds, I believe we can learn something very important from listening to the kind of things they say.
Now what interests me about all these remarks is that the man who makes them is not merely saying that the other man's behaviour does not happen to please him. He is appealing to some kind of standard of behaviour which he expects the other man to know about. And the other man very seldom replies: To hell with your standards. Nearly always he tries to make out that what he has been doing does not really go against the standard, or that if it does there is some special excuse. He pretends there is some special reason in this particular case why the person who took the seat first should not keep it, or that things were quite different when he was given the bit of orange. It looks, in fact, very much as if both parties had in mind some kind of Law or Rule of fair play or decent behaviour about which they really agreed. If they had not, they might, of course, fight like animals, but they could not quarrel in the human sense of the word. Quarreling means trying to show that the other man is in the wrong. And there would be no sense in trying to do what unless you and he had some sort of agreement as to what Right and Wrong are; just as there would be no sense in saying that a footballer had committed a foul unless there was some agreement about the rules of football.

Detailed Solution for CAT Practice Test: August 11 - Question 29

The passage brings forth the basis of quarrel. It is implied that the purpose of quarreling is to prove the other person wrong and one can be proven wrong only if there is some sort on agreement on what is right and what is wrong. This is the law of human nature. This is explicitly stated in option B. 
Option A only touches upon an aspect of the given context. 
Option C is incorrect as there is no third party intervention or arbitration, mentioned anywhere in the passage.
Option D is extraneous as this is not the focus of the author. 
Option E is incorrect as the passage is not focusing on the way of quarrel; however, it focuses on the reason that governs the quarrel. 
Hence, option B is the correct answer.

CAT Practice Test: August 11 - Question 30

Directions: Read the given context and answer the question that follows.
Cyril Connolly once wrote: 'The more books we read, the clearer it becomes that the true function of a writer is to produce a masterpiece and that no other task is of any consequence.' This is tosh, of course, for if every book were a masterpiece, no book would be a masterpiece and we could not know a masterpiece when we read it. They also serve who only sit and write trash. To know the good, we have to know the bad and ________________ .

Which sentence best suits the end of the passage?

Detailed Solution for CAT Practice Test: August 11 - Question 30

The sentence mentions that it is important to know the bad in order to understand the importance of the good. So, the context of the filler must also revolve around the same. Due to this reason, A and B are eliminated as they fail to mention this context.
Option D is related but is unable to complete the sentence. Option E highlights the current prevalence of the bad, which finds no context in the passage. So, the correct answer is 'C'.

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