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CAT Mock Test- 1 (October 13) - CAT MCQ


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30 Questions MCQ Test - CAT Mock Test- 1 (October 13)

CAT Mock Test- 1 (October 13) for CAT 2024 is part of CAT preparation. The CAT Mock Test- 1 (October 13) questions and answers have been prepared according to the CAT exam syllabus.The CAT Mock Test- 1 (October 13) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Mock Test- 1 (October 13) below.
Solutions of CAT Mock Test- 1 (October 13) questions in English are available as part of our course for CAT & CAT Mock Test- 1 (October 13) solutions in Hindi for CAT course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt CAT Mock Test- 1 (October 13) | 66 questions in 120 minutes | Mock test for CAT preparation | Free important questions MCQ to study for CAT Exam | Download free PDF with solutions
CAT Mock Test- 1 (October 13) - Question 1
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Which of the following could be the next line of discussion?

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 1

In the passage, the author pitches two competing moral theories against one another. One approach, known as rationalism, links moral sensibility to reason, and towards the end, a second approach links morality to emotion. Also, the author points out that the people promulgating the second approach typically focus on empathy. Hence, the next line of discussion should ideally be centred on the idea of empathy/empathetic concern and how it fares as a basis for explaining moral sensibility.  

Comparing the options, option C captures this theme correctly. Option C is the answer.

The author establishes that psychopaths experience empathy in the first paragraph. (" Like psychopaths, we can dial our empathy up and down; "). Hence, option A does not add much value to the overall discussion.

The author does not expand upon the role of fear in the passage and does not provide hints that suggest fear might have a dual role, as stated in option B. Hence, option B can be eliminated.

Option D is too narrow. The second camp typically focuses on empathy. Moreover, the author does not explicitly highlight the importance of personal distress anywhere in the passage. Hence, option D can be eliminated as well.

CAT Mock Test- 1 (October 13) - Question 2
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Why does the author cite the examples of several sportspersons in the first paragraph? 

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 2

In the opening line of the paragraph, the author states that the history of sport is full of suffering. And then to validate this statement, the author quotes several examples, including that of Micheal Jordan and Mohammed Ali. The author, hence, provides examples to validate his claim that sports are full of suffering. Only option C captures this and hence is the right answer.

Options A and B can be easily eliminated because it has not been implied in the first paragraph that these sports persons were victorious or successful in their endeavour.

Option D is out of scope. The author does not talk about the fear of defeat in the first paragraph.

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CAT Mock Test- 1 (October 13) - Question 3
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The author mentions Japanese-born New York Yankees pitcher Hiroki Kuroda to

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 3

In the penultimate paragraph, the author discusses the 'taibatsu' concept, which found popular acceptance in Japan as a form of training in the late 1920s. The taibatsu training is an extreme example of pain being tied with athletic discipline and being made an overt part of athletic training. The example of taibatsu is given to highlight the thinking that pain is an integral part of sports and sports training - it is in fact reflective of the athlete's discipline. Kuroda's example is given to show that this thinking continues to exist to this day.

Option D conveys the author's view correctly, as elucidated above. Option D is the answer.

Option A is far-fetched. The author does not present sufficient examples for us to conclude that the concept has produced several successful athletes.

Option B is not incorrect but is not the reason why the author mentions the Japanese pitcher.

Option C gives the reason behind why taibatsu is mentioned. But not why Kuroda is mentioned. Hence, D is the right answer.

CAT Mock Test- 1 (October 13) - Question 4
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The central idea of the passage is that
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 4

The author starts off by saying that pain and suffering are common in sports. He goes on to add that learning to tolerate pain is crucial to excelling in sports. Those who can tolerate pain better, gain a tactical advantage. Pain is almost seen as a positive - and is thus tied to the idea of sports discipline. The author concludes by saying that we have a complicated relationship with pain - on one hand, we try to minimize it and on the other, we idolize those who learn to tolerate it. Hence, the central idea of the passage is that tolerating pain is an integral part of sports and those who learn to do this gain a tactical advantage and rise above others.

Comparing the options, option A comes closest to the view given above. Option A is the answer.

The passage revolves around the role of pain in sports. While the author does extend this to broader life in the last paragraph, the focus remains on sports throughout the passage. Thus, options B and C, which miss the context of sports, can be eliminated.

Option D contains two distortions - enjoy pain and emerge as victors. The author states that putting one's competitors through greater pain is enjoyable to sportspersons. However, it does not state that learning to enjoy pain offers one any specific advantage. Secondly, the author does not state that those who tolerate pain better emerge as victors. The ability to tolerate pain is an advantage but not the sole advantage needed to succeed. Hence, D is incorrect.

CAT Mock Test- 1 (October 13) - Question 5
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The author is likely to agree with all of the following statements, EXCEPT
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 5

In the entire passage, the author attempts to bring out the fallacies of fantasy politics and make a case for real politics. Also, in the antepenultimate paragraph, the author states, "In the mid-term, the failure of populist fantasies like Brexit will no doubt reinforce their followers' cynicism and alienation." Hence, in the long-term, there is no other bona fide alternative except real politics. The author would agree with statement A.

Option B is a distortion. "..so long as large numbers of our fellow citizens are disinterested in outcomes and prefer wallowing in fantasy, populist politicians will make hay." The author argues that the citizens are disinterested, not unaware. Hence, the author is likely to disagree with the statement in option B.

"Real politics is a difficult and time-consuming activity that usually requires dissatisfactory compromise with reality and what other people want. It is much easier to make-believe our way to our favoured outcomes". Option C can be inferred.

"In the mid-term, the failure of populist fantasies like Brexit will no doubt reinforce their followers' cynicism and alienation." The author would agree with the statement in option D as well.

Option B is the answer.

CAT Mock Test- 1 (October 13) - Question 6
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Which of the following is a valid inference from the passage?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 6

Option A cannot be inferred. The author is wary of the popularity of fantasy politics and its impractical promises. But the author does not refer to these populist theories as evil anywhere in the passage. 

Option B has not implied in the passage. Though the failure results in followers relapsing into a state of scepticism and alienation, it cannot be inferred whether the leaders were expecting such outcomes. 

The author begins the discussion by stating the following: "Fantasy politics starts from the expectation that wishes should come true, that the best outcome imaginable is not just possible but overwhelmingly likely. The great appeal of fantasy politics is that it puts you in complete control. Using the power of your imagination, you get to control not only what you will do but also how everyone else will react..." Note the author's tone in the passage - he does not appear to be a big fan of fantasy politics. In this introductory part, the author highlights the underlying elements that contribute to the appeal of fantasy politics. There is a subtle tinge of sarcasm wherein the author emphasises the way individuals feel when they engage in fantasy politics - it makes you feel in control; are you truly in control? Not so much! Subsequently, the author delves into the reason behind the appeal of fantasy politics and highlights how quotidian/everyday situations are elevated to the level of decisive moral battles. Thus, given the points underlined in the passage, the false sense of control imparted by indulgence in fantasy politics adds to its appeal. Option C aligns with this idea.

Option D is incorrect. The author does not make such an assertion. 

Hence, Option C is the correct choice.

CAT Mock Test- 1 (October 13) - Question 7
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Why does the author cite the Centers for Disease Control and Prevention's COVID-19 pandemic response in the final paragraph?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 7

Through the passage, the author first introduces us to the three forms of racism. She then puts forward ideas to tackle third-degree racism. Finally, in the last paragraph, the author highlights what is at stake - not fighting third-degree racism could cost us many lives. Of the options, only option A highlights the purpose of the example - showing the impact of third-degree racism with the help of an example. 

The example of pandemic response is used to make a larger point of how we need to tackle third-degree racism. As options B and C focus on the example instead of the larger point, they are incorrect. Moreover, option B is an extreme statement.

Option D is in line with the passage - and it is a valid conclusion that can derived from the last paragraph. However, it does not answer "why" the example is given. The purpose behind the example is captured by option A and hence is the right answer.

*Answer can only contain numeric values
CAT Mock Test- 1 (October 13) - Question 8
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DIRECTIONS for the question: The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

  1. These views are largely impervious to argument or appearance and have some resonance with our deeply polarized society today.
  2. When believers and nonbelievers discuss or witness a seemingly miraculous event, they find little common ground, as if one is speaking French and the other Swahili.
  3. And yet, surprisingly, some recent proposals in physics reveal that believers and nonbelievers may have more in common than they think.
  4. Such radically different attitudes represent radically different views of the world.

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 8

Sentence 2 is the opening sentence, as it sets the context, describing the situation that ensues when believers and non-believers discuss a seemingly miraculous event. 4 has to follow 2 because the 'radically different attitudes' that 4 refers to the difference in attitudes of believers and non-believers, discussed in 2. 1 follows 4, as it expands on the idea described in 4, i.e., the different views of the world. Finally, 3 concludes the paragraph, presenting an alternate possibility (despite the differing views, there might be some common ground). Hence, 2413 is the answer. 

CAT Mock Test- 1 (October 13) - Question 9
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The passage given below is followed by four alternative summaries. Choose the option that best captures the essence of the passage.

Julius Ceaser is considered one of the most important works of William Shakespeare. However, even after centuries, connoisseurs of literature are divided as to who was the hero of the play. Many claim that even though the title of the play is Julius Ceaser, the actual hero of the play is Brutus. Brutus not only occupies more screentime than Caesar, but he also drives the theme of the play. Much like Othello, Brutus is the tragic hero who even though noble, falls prey to his own honesty. Another important point is that throughout the play it is through Brutus' dialogues that one gets to understand the essence of the Roman Kingdom. Even though Ceaser was the king, it was Brutus who imbibed the true Roman spirit. Hence the titular hero may be Julius Ceaser, but surely it is Brutus who is the real tragic hero of the magnum opus Julius Ceasar.
 
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 9
  • To answer such questions, we need to find the central idea of the passage.
  • The passage talks about how according to the author Brutus is the real hero of the play Julius Caesar
  • Brutus has more screen time and helps the viewers to feel the spirit of Rome
  • Just like Shakespeare's other works like Othello, Brutus meets a tragic end and hence is the tragic hero of the play
CAT Mock Test- 1 (October 13) - Question 10
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The passage given below is followed by four alternative summaries. Choose the option that best captures the essence of the passage.

There may be a plethora of ways to define a "classic", but for me, a "classic" means a work that challenges the notion of its contemporaries and was is inspire the common people to look at things from a different perspective. A work is classical by reason of it being universal, by virtue of its ability to stir human emotions in a revolutionary way. Most of the classical works can be considered revolutionary given the changes they could inspire over the course of time. The classic is what gives birth to radically different forms of human consciousness for any generation of its viewers. A classical work nurtures an alternate reality among the masses and transcends barriers of culture, society, geography, age, etc.
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 10

To answer such questions, we need to find the central idea of the passage.

  • The passage talks about how the author thinks a "classic" should be defined
  • According to the author, classical work is revolutionary and different from the contemporaries
  • Hence given its novelty and revolutionary nature, a classical work appeals to the masses and stirs the human consciousness over any period of time.
CAT Mock Test- 1 (October 13) - Question 11
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What is the number of male employees who do not like Italian?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 11

Clearly, we need to bifurcate the employees into males and females to proceed. 

> The number of women who like at least 2 out of 3 preferences are 65

>  55 Women only like Italian

> Overall 25 employees like only Chinese out of which 40% are male. Thus 10 male and 15 female employees only like Chinese

> The number of Employees liking only Continental is the same as the number of women liking only Italian = 55. Thus 25 are female and 30 are male


Let the total number of females be F. Then the number of females who do not like any of the 3 options = 0.2F.

Total number of Female = Females who like none + Females who like exactly one+ Female who like atleast 2

F = 0.2F + 15+25+55+65 or 0.8F = 160. Thus F = 200. Females who like none of the option = 0.2F = 40

Thus number of male employees who did not like any of the 3 options = 20 which is also equal to a number of females liking all 3 options.


> 175 of the employees like exactly one of the 3 options. Thus number of males liking only Italian = 175-(10+30+15+25+55) = 40

> Total number of male employees = 7 times the number of males liking only continental = 210

> Number of male employees like only Italian is same the number of male liking Chinese and Continental but not Italian = 40


Number of male employees not liking Italian = 10+40+30+20 = 100

CAT Mock Test- 1 (October 13) - Question 12
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Which of the following can not be a subject of the Optional Category?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 12

The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20
We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.

Then a+b+c = 6 ....(I)

Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.

when c= 1, then b=3 and a = 2

when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.

Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.

Let us start by filling in the known information.

> Painting was taught on Wednesday C slot

>Slot D of Monday was a free slot

> Week starts with teaching English


> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot

>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects

Thus Dance is not a subject of Optional Category.

CAT Mock Test- 1 (October 13) - Question 13
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Which of the following subject was not conducted in D slot?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 13

The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20
We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.

Then a+b+c = 6 ....(I)

Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.

when c= 1, then b=3 and a = 2

when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.

Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.

Let us start by filling in the known information.

> Painting was taught on Wednesday C slot

>Slot D of Monday was a free slot

> Week starts with teaching English


> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot

> On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects

> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.

> There were 2 instances that the free period was in the same slot as that of the preceding day.

From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.

Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English

Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English

We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.

>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot

Since Counting was taught on Monday, it has to be in B slot.

Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance

Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday

We can see that Counting was not taught in the D slot.

CAT Mock Test- 1 (October 13) - Question 14
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Which of the following is correct? Key in the option number.
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 14


where
G(F): Goals for the team
G(A): Goals against the team
It can be seen from the table that the only match that KEP lost was against CSK.
KKR scored 3 goals against MI.

CAT Mock Test- 1 (October 13) - Question 15
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Which of the following groups is that of strangers for Lisa?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 15

We know there are seven individuals, so every individual sum of number of friendly aliens, number of enemy aliens and number of strangers will be 6. Based upon this, the following can be obtained.

Olivia is a friendly alien of both Emily and David.

David, Michael, and Emily are strangers.

Michael and Sarah are friendly aliens but Sarah and David are enemy aliens.

James is an enemy alien of Emily and Olivia but a stranger for David.

All enemy aliens of James are strangers for Lisa and Michael.

From the above table, Emily should have four strangers, So Sarah and Lisa must be a stranger for her.

From the above table, David should have 2 enemy aliens, so Lisa must be an enemy alien of David.

From the above table, Olivia is a stranger for Michael, so Michael is also a stranger for Olivia.

Michael needs one enemy alien and one stranger.
Out of Lisa and James, only Lisa can be the enemy alien of Michael because James' enemy alien already has completed.

From the above table, only one out of Sarah and Lisa can be a stranger for James, but Sarah has only one stranger, so Lisa will be a stranger for James and Sarah will be a friendly alien of James.

Now, Sarah can be a friendly alien of Lisa or a stranger for Lisa, but Sara does not need a stranger. So, Lisa will be a friendly alien of Sarah.

CAT Mock Test- 1 (October 13) - Question 16
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Which of the following groups is that of enemy aliens of Olivia?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 16

We know there are seven individuals, so every individual sum of number of friendly aliens, number of enemy aliens and number of strangers will be 6. Based upon this, the following can be obtained.

Olivia is a friendly alien of both Emily and David.

David, Michael, and Emily are strangers.

Michael and Sarah are friendly aliens but Sarah and David are enemy aliens.

James is an enemy alien of Emily and Olivia but a stranger for David.

All enemy aliens of James are strangers for Lisa and Michael.

From the above table, Emily should have four strangers, So Sarah and Lisa must be a stranger for her.

From the above table, David should have 2 enemy aliens, so Lisa must be an enemy alien of David.

From the above table, Olivia is a stranger for Michael, so Michael is also a stranger for Olivia.

Michael needs one enemy alien and one stranger.
Out of Lisa and James, only Lisa can be the enemy alien of Michael because James' enemy alien already has completed.

From the above table, only one out of Sarah and Lisa can be a stranger for James, but Sarah has only one stranger, so Lisa will be a stranger for James and Sarah will be a friendly alien of James.

Now, Sarah can be a friendly alien of Lisa or a stranger for Lisa, but Sara does not need a stranger. So, Lisa will be a friendly alien of Sarah.

*Answer can only contain numeric values
CAT Mock Test- 1 (October 13) - Question 17
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Butler reached point (9, 7) when a sequence of five instructions GOTO(x,y), WalkNX(1), WalkNY(3), WalkPY(7), WalkPX(4) are executed in the given order. Find the remainder when x is divided by y.

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 17

We know that Butler reached point (9, 7) after the last instruction. After the 1st instruction {GOTO(x,y)}, Butler should have moved to point (y, x) by the definition given in the table.
Butler's position just after the 2nd instruction = (y - 1, x)
Butler's position just after the 3rd instruction = (y - 1, x - 3)
Butler's position just after the 4th instruction = (y - 1, x - 3 + 7) = (y - 1, x + 4)
Butler's position just after the 5th instruction = (y - 1 + 4, x + 4) = (y + 3, x + 4)
Given: Butler's position after the 5th instruction = (9, 7) = (y + 3, x + 4)
Hence, Remainder = 3

CAT Mock Test- 1 (October 13) - Question 18
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Butler is initially at (x, y) where x, y > 0. In how many ways can it reach the billing counter if it responds only to WalkNX(1) and WalkNY(1) instructions?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 18

It is given that Butler is at (x, y). It will move by 1 unit towards the billing counter.

If Butler responds only to WalkNX(1), it means Butler has to move parallel to the x-axis for a distance 1 unit in negative x direction.
If Butler responds only to WalkNY(1), it means Butler has to move parallel to the y-axis for a distance 1 unit in negative y direction.
Given (x, y) > 0; so Butler's position is greater than 0.
Here, two coordinates x and y are involved. Therefore, we can use the formula for finding the number of ways of dividing m + n things into two groups containing 'm' and 'n' things, respectively.

We can see that in this case, Butler can reach the billing counter in ways. Hence, option 4 is the correct answer.

CAT Mock Test- 1 (October 13) - Question 19
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Butler reached point (-4, 2) when a sequence of six instructions WalkNX(1), GOTO(1,7), WalkNX(1), WalkNY(4), WalkPY(5), WalkNX(6) is executed in the given order. If point A(a, b) is the starting point of Butler, then what is the value of (a + b)?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 19

We can see that one out of the six instructions is GOTO. Hence, a new sequence will start from the GOTO instruction. We cannot backtrack the starting point since the continuity is lost.
Hence, the initial position of Butler cannot be determined. Therefore, option 4 is the correct answer.

CAT Mock Test- 1 (October 13) - Question 20
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Average of 20 distinct natural number are 19.25. 10 more natural numbers are added such that each of the newly added number is greater than 19 and the average increases to 20.1. What is the maximum possible value of the number which is added to the original set?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 20

Average of 20 distinct natural numbers = 19.25

Sum of those 20 numbers = 19.25 × 20 = 385 ....(I)

When 10 more numbers were added, the average becomes 20.1

Sum of all the 30 numbers = 20.1 × 30 = 603 ...(II)

Sum of the 10 numbers added = (II) -(I) = 218

All of these numbers are greater than 19. Thus the number to me maximum, 9 of them has to be 20 and tenth number will be the maximum

9 × 20 + n = 218

180 + n = 218 or n = 38

CAT Mock Test- 1 (October 13) - Question 21
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Solution A and solution B are 2 solutions of orange such that the concentration of orange juice is 64% in solution A and the concentration of water is 20% in solution B. Solution A and B are mixed in a ratio x:y such they form a 20 liter solution which has 6 litres of water. What is the value of 3x+2y if it is known that x and y are co-prime?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 21

The concentration of orange juice in solution A = 64%

The concentration of orange juice in solution B = 100-20 = 80%

The resultant solution obtained by mixing is of volume 20L out of which 6 L is water.

Quantity of orange juice = 20L - 6L =14L

Concentration of orange = 14/20 ​× 100% = 70%

As per question 0.64x + 0.8y = 0.7(x+y)

0.1y = 0.06x

x​/y = 0.1​/0.06 = 35​

x = 5 and y = 3

3x + 2y = 3(5) + 2(3) = 15 + 6 = 21

CAT Mock Test- 1 (October 13) - Question 22
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Ram bought 3 types of wheat flour which are type A, type B and type C. The cost of type A flour is Rs 38/kg. The cost of type B is flour is Rs 45/kg and the cost of type C flour is Rs 50/kg. He mixes flour of each type in such a way that he gets a profit of 14 2/7 % when he sells it for  Rs 48/kg. If a sample of the mixture is taken such that amount of type B is 12 kgs and the amount of the other two types of flour are also positive integers, then which of the following can not be the weight of the sample?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 22

Profit of 14 2/7 ​% is received when the mixture is sold at Rs 48/ kg. Let the cost price of the mixture be CP

Then, (1+14 2/7 ​%) CP =48

(8/7) CP = 48

CP = Rs 42/kg

Since Rs 38 < Rs 42 < Rs 45.

We have to take 2 mixtures, 1 of type A+ type B and another one of type A + type C as per the allegations.

Mixture 1: type A and type B

Let the ratio be a:b, then

38a + 45b = 42 (a+b)

3b = 4a or a:b = 3:4....(I)

Mixture 2: type A and type C

Let the ratio be a1​ : c, then

38a1​ + 50c = 42(a+c)

8c = 4a1​ or a1​ : c = 2:1 ....(II)

If mixture 1 and mixture 2 are mixed in ratio x:y then

a:b:c = 3x + 2y : 4x: y

4x=12 thus x=3

Weight of overall mixture = 3x+2y+4x+y = 21+ + 3y

When y = 1, the weight of mixture = 24 kg

when y = 2, the weight of mixure = 27kgs

when y = 3, the weight of mixture = 30 kgs

When y = 4, the wight of mixture = 33kgs

Option A is not possible.

*Answer can only contain numeric values
CAT Mock Test- 1 (October 13) - Question 23
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Find the number of integral values of x that satisfy

|x2 + 3x - 1| < 2|x| + 5

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 23

|x2 + 3x - 1| < 2|x| + 5

We have to find out the boundary points for each modulus and adjust the + or - sign after removing the modulus.

For the left expression,  x2 + 3x  - 1y = x, the roots are 
√13 ≈ 3.6
So, the approx roots are -3.3 and +0.3.

For the right side of the expression, the boundary point is 0

Let us denote the same in the number line.


For R1,

|x2 + 3x - 1| < 2|x| + 5

x2 + 3x - 1 < 2x + 5

x2+ x - 6 < 0

(x-2) (x +3) < 0

x ∈ (-3,2)

Overlapping region is 

For R2,

|x2 + 3x - 1| < 2|x| + 5

-x2 - 3x + 1 < 2x + 5

-x2 - 5x - 4 < 0

x2 + 5x + 4 > 0

(x + 1) (x + 4) > 0

x ∈ R −(−4,−1)

Overlapping region is

For R3,

|x2 + 3x - 1| < 2|x| + 5

-x2 - 3x + 1 < - 2x + 5

- x2 - x - 4 < 0

- x2 + x + 4 > 0
This is possible for all values of x. Therefore the overlapping region is

For R4,

|x2 + 3x - 1| < 2|x| + 5

-x2 - 3x + 1 < - 2x + 5

x2 + 5x - 6 < 0

(x + 6) (x -1) < 0

x ∈ (−6, 1)

Hence, the overall overlapping region is

Integral values are {-5, -4, -3, -2, -1, 0, 1}

CAT Mock Test- 1 (October 13) - Question 24
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The following figure depicts 2 circles C1​ and C2​ which touch at C. AC is the diameter of C1​ and BC is the diameter of C2​. A tangent is drawn from A to a point D on C2​, such that AD = 12 metres. Also, the radii of the circles(in metres)  are integer values and the difference between their radii is at least 4 metres. 

2 athletes A and B start running from C along the circumferences of C_1C1​ and C_2C2​ such that both reach C for the first time simultaneously. Find the ratio of speeds of A and B.
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 24

Let the radius of the larger circle be R and the radius of the smaller circle be r.


Hence, applying the tangent-chord theorem, we get,

2R x 2(R-r) = 144

R ( R - r ) = 36

Possibilities are 

1 x 36, R = 36, r = 35

2 x 18, R = 18, r = 16

3 x 12, R = 12, r = 9

4 x 9, R = 9, r = 5

6 x 6, R = 6, r = 0, not possible since the second circle can not be a point circle.

Difference in their radii > = 4, hence only possible case is R = 9 and r = 5.

Now, if they want to cover the circumference such that they take equal time to cover the circumference, ratio of speeds = ratio of circumferences = 9:5

CAT Mock Test- 1 (October 13) - Question 25
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Let (a,b) be 2 numbers such that their lcm is  300. How many such ordered pairs are possible?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 25

300 can be written 22 × 3 × 52

Thus aa and bb should also have 2,3 and 5 as their prime factors only.

For two such numbers a,b the number of ordered pairs whose LCM = N = 2p3q5r will be

(2p+1) (2q+1) (2r+1)

Thus number of ordered pairs such that LCM 300 = 22 × 3 × 52 is their lcm =

(2(2)+1) (2(1) + 1)(2 (2)+1)

Thus number of ordered pairs = 5  × 3  × 5 = 75

*Answer can only contain numeric values
CAT Mock Test- 1 (October 13) - Question 26
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Find the number of unordered pairs of 2-digit numbers, such that their LCM is twice their HCF.

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 26

Let the HCF be h. Hence, LCM = 2h.

Hence, product of the numbers = LCM X HCF = 2h2

Let the numbers be hx and hy, such that x and y are co-prime.

Hence, product = h2xy

Equating, we get xy = 2.

It is only possible when one of the numbers is twice the other.

Hence, the lowest possible group of such numbers is (10, 20), and the highest is (49, 98).

Hence, total possible unordered pairs = 49 - 10 + 1 = 40.

CAT Mock Test- 1 (October 13) - Question 27
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Series 1: 11, 2, -7, -16, -25,...... upto 1000 terms

Series 2: 25, 15, 5, -5, -15,........ upto 1000 terms

What is the sum of all the terms common to both series?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 27

The first common term of the 2 series is -25.

The first series has a common difference of -9, the second series has a common difference of -10.

Hence, common terms will be found at a common difference of -LCM(9,10) = -90.

Hence, the next common term is -115.

It continues in a similar way. 

The last term of this new series must be present in both series.

Let us find out the last term of both series.

t1000​ = 11 - 999 x 9 = 11 - 8991 = -8980 for the first series.

t1000​ = 25 - 999 x 10 = 25 - 9990 = -9965 for the second series.

Hence, the last term of the new series must be greater than or equal to -8980.

-25 - 90 x (n-1) ≥ − 8980

-25 - 90n + 90 ≥ −8980

65 - 90n ≥ −8980

-90n ≥ −9045

90n ≤ 9045

n ≤ 100.5

n = 100

100 terms in the new series.

Sum = n/2 ​[2a + (n−1) d] = 100​/2 [2 × −25 − 99 × 90] = -448000

CAT Mock Test- 1 (October 13) - Question 28
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A dishonest cloth merchant marks up the price of his cloth by 20%, and does not offer any discount unless asked for. Also, while selling, he uses a metre scale, whose actual length is 80cm. One fine day, an old woman visits his shop to buy some cloth. She is good at bargaining and consequently manages to buy the cloth at a price such that the merchant's net profit or loss is zero. What is the discount percentage she managed to get on the marked price while buying the cloth?
Detailed Solution for CAT Mock Test- 1 (October 13) - Question 28

Let the CP of 1 cm of cloth be Rs. 1.

Hence MP of 1 metre cloth = Rs. 100 x 1.2 = Rs 120

CP of the same amount of cloth = CP for 80cm cloth = Rs 80

Since there was no profit or no loss, SP = Rs 80.

Hence, discount = MP - SP = 120 - 80 = 40

Hence, discount % = 40​/120 × 100 = 33.33%

*Answer can only contain numeric values
CAT Mock Test- 1 (October 13) - Question 29
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Find the highest power of 30 in 50!

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 29

30=2×3×5.
Now 5 is the largest prime factor of 30, therefore, the powers of  5 in 50! will be less than those of 2 and 3. Therefore, there cannot be more 30 s than there are 5 in 50! So we find the highest power of 5 in 50! The highest power of 5 in 50! Hence the highest power of 30 in 50! = 12

*Answer can only contain numeric values
CAT Mock Test- 1 (October 13) - Question 30
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A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is (time in seconds)?

Detailed Solution for CAT Mock Test- 1 (October 13) - Question 30

D = 540 + 180 = 720 m

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