IBPS PO Prelims Memory Based Paper (Held on:4 December 2021 Shift 1) (Previous Year Paper)

The correct answer is 'Facebook'.

Key Points

• As stated in the passage:
• 'Facebook is the most common activity that university students switch to when studying'.
• Thus, making option 2 the correct answer.

The correct answer is 2 and 3.

Key Points

• As mentioned in the passage: 'There is no official medical term that identifies addiction and social networking because it cannot be deemed as a disease or disorder as cases are not severe and the habit can easily be maintained or prevented'.
• Thus making option 5 the correct answer.

The correct answer is 1 and 2.

Key Points

• As mentioned in the above passage:
• 'Scientists believed some years ago that, dopamine was simply a pleasure chemical in the brain' eliminating option 3 as the correct answer.
• While 'Recent studies have shown that; dopamine actually produces the desire in people to 'want' by drawing out the need for us to -seek and search. Creating the ultimate drive to find what is that what we want' makes option 1 the correct answer.

Also,

• 'It’s stimulated by unpredictability and small bits of information as well as reward cues which are the same conditions that social media presents to all users' making option 2 also the correct answer.
• Thus, option 4 is the correct answer.

The correct answer is '1 and 2'

Key Points

• As mentioned in the above passage:
• 'Many call it the cuddle chemical because the brain releases pleasure chemicals that transpire usually when you kiss and hug- or tweet. It is also known as the hormone that builds the strong yet unique bond between mothers and their babies. Oxytocin is now regarded as the human stimulant of empathy, generosity, trust, and more
• Thus, making option 4 the correct answer.

The correct answer is 'Malignant'.

Key Points

• 'Contagiously' means (an emotion, feeling, or attitude) likely to spread to and affect others.
• Out of the options mentioned above:
• 'Assail' means to criticize strongly.
• 'Ambivalent' means having mixed feelings or contradictory ideas about something or someone.
• 'Arboreal' is related to trees.
• 'Cogent' means clear, logical, and convincing.
• While 'Malignant' means very virulent or infectious which is the most similar to the word Contagiously making option 4 the correct answer.

The correct answer is 'Relinquish'.

Key Points

• 'Confiscated' means to steal or seize.
• Out of the options mentioned above:
• 'Cognizant' means having knowledge or awareness.
• 'Covet' means yearning to possess.
• 'Expiate' means to make amends or reparation for (guilt or wrongdoing).
• 'Pithy' means terse and vigorously expressive.
• While 'Relinquish' means voluntarily cease to keep or claim or give up which is the opposite of the word Confiscated making option 5 the correct answer.

The correct answer is 1 and 3.

Key Points

• As mentioned in the above passage:
• 'Researchers at Chicago University studied the effects of social media. They concluded quite quickly that people presented higher levels of addiction to social media than the need to smoke or drink. Media cravings ranked higher'.
• Thus, option 1 and option 3 are the correct options making option 5 the right answer.

The correct answer is 2 and 3.

Key Points

• As mentioned in the above passage:
• 'Schools in many westernized countries have had to take drastic action- banning smartphones, iPad, and most portable devices from school premises- as it is claimed to be a huge distraction. Whereas, other schools use it for educational purposes and as a rewards system for their pupils'.
• Thus, option 5 is the correct answer as it includes both options 2 and 3.

The correct answer is 'Someone who spends too much time on social websites'.

Key Points

• Of all the options mentioned above,
• Option 1, Option 2, Option 3 are the activities that can be done by a person who is socially active.
• Option 5 is the phrase that is totally opposite to Social Addiction.
• Hence, Option 4, i.e., Someone who spends too much time on social websites fits the best to the meaning of Social Networking Addiction making it the correct answer.

The correct answer is 'The Psychology of Social Addiction'.

Key Points

• The passage can be divided into four subheadings:
• It begins with the Science behind Social Addiction talking about how it interferes with the basic aspects of our life.
• It continues telling that there is no medical term that identifies addiction and social networking.
• Furthermore, it talks about Dopamine and Oxytocin and how they contribute to social media addiction.
• The passage ends with a brief discussion of addiction in students nowadays.
• Thus, all these subsections can be put together into one major heading which would be 'The Psychology of Social Addiction' making option 1 the correct answer.

The correct answer is A.

Key Points

• The given paragraph is about integrity.
• Sentence B talks about a famous phrase that describes integrity.
• Sentence D mentions the phrase "Honesty is telling the truth to other people; integrity is telling the truth to myself.”
• Sentence C talks about the main word that the phrase focuses on.
• Sentence F is a continuation of sentence C as it talks more about the origin of the word integrity i.e., from where that word is derived from.
• Sentence E is at the correct place so it follows sentence F.
• After explaining the meaning of integrity, sentence A talks about how a person who has integrity should act.
• So, sentence A should be the sixth sentence after rearranging the paragraph.
• The correct sequence is BDCFEA.

Additional Information

• The word morally is an adverb form of the word moral that means with reference to the principles of right and wrong behaviour.
• For example, He believed the war was morally justified.

The correct answer is F.

Key Points

• The given paragraph is about integrity.
• Sentence B talks about a famous phrase that describes integrity.
• Sentence D mentions the phrase "Honesty is telling the truth to other people; integrity is telling the truth to myself.”
• Sentence C talks about the main word that the phrase focuses on.
• Sentence F is a continuation of sentence C as it talks more about the origin of the word integrity i.e., from where that word is derived.
• Sentence E is at the correct place so it follows sentence F.
• After explaining the meaning of integrity, sentence A talks about how a person who has integrity should act.
• So, sentence F should be the fourth sentence after rearranging the paragraph as it continues sentence C in describing the origins of the word.
• The correct sequence is BDCFEA.

Additional Information

• The word togetherness is the noun form of the word together that means a state or feeling of closeness and happiness among people who are together as friends, family members.
• For example, The way they were defending their lives shows togetherness.

The correct answer is C.

Key Points

• The given paragraph is about integrity.
• Sentence B talks about a famous phrase that describes integrity.
• Sentence D mentions the phrase "Honesty is telling the truth to other people; integrity is telling the truth to myself.”
• Sentence C talks about the main word that the phrase focuses on.
• Sentence F is a continuation of sentence C as it talks more about the origin of the word integrity i.e., from where that word is derived from.
• Sentence E is at the correct place so it follows sentence F.
• After explaining the meaning of integrity, sentence A talks about how a person who has integrity should act.
• So, sentence C should be the third sentence after rearranging the paragraph as it explains more on the word mentioned in the phrase in sentence D.
• The correct sequence is BDCFEA.

Additional Information

• The word completeness is the noun form of the word complete which means the state or condition of having all the necessary or appropriate parts.
• ​​For example, For the sake of completeness, all names are given in full.

The correct answer is D.

Key Points

• The given paragraph is about integrity.
• Sentence B talks about a famous phrase that describes integrity.
• Sentence D mentions the phrase "Honesty is telling the truth to other people; integrity is telling the truth to myself.”
• Sentence C talks about the main word that the phrase focuses on.
• Sentence F is a continuation of sentence C as it talks more about the origin of the word integrity i.e., from where that word is derived from.
• Sentence E is at the correct place so it follows sentence F.
• After explaining the meaning of integrity, sentence A talks about how a person who has integrity should act.
• So, sentence D should be the second sentence after rearranging the paragraph as it mentions the phrase that was mentioned in sentence B.
• The correct sequence is BDCFEA.

Additional Information

• The word perfectly is an adverb of the word perfect that means in a manner or way that could not be better. 
• ​For example, They're perfectly suited.

The correct answer is B.

Key Points

• The given paragraph is about integrity.
• Sentence B talks about a famous phrase that describes integrity.
• Sentence D mentions the phrase "Honesty is telling the truth to other people; integrity is telling the truth to myself.”
• Sentence C talks about the main word that the phrase focuses on.
• Sentence F is a continuation of sentence C as it talks more about the origin of the word integrity i.e., from where that word is derived.
• Sentence E is at the correct place so it follows sentence F.
• After explaining the meaning of integrity, sentence A talks about how a person who has integrity should act.
• So, sentence B should be the first sentence after rearranging the paragraph as it introduces the topic of the paragraph i.e., integrity.
• The correct sequence is BDCFEA.

Additional Information

• The word integrity means the quality of being honest and having strong moral principles.
• ​For example, A gentleman of complete integrity.

The correct answer is CAB

Key Points

• 'Approved' is a verb and is not a physical entity that can 'do' something or take any action as it by itself is an action. Thus, this blank requires a noun, this could be 'Russia'.
• 'Said' is not an action a country can take, it has to be replaced by a doable action like 'approved'.
• 'Russia' is not something that can be 'on' state TV, it is not an action that can be done by Prime Minister Mikhail Mishustin. The blank requires a verb, like 'said'.

Thus, the correct sentence will be: Russia on Saturday approved a third coronavirus vaccine for domestic use, Prime Minister Mikhail Mishustin said on state TV.

The correct answer is BAC

Key Points

• 'Mind' is not something that can be done, the blank requires a verb. Thus, 'asserted' is appropriate for the blank.
• 'Asserted' is an action, it is not a physical entity in which something can be 'kept'. This blank requires a noun. Thus, the appropriate word is 'mind'.
• 'Behaviour' can be appropriate, and since it has been established that A and B need to be interchanged, blank C remains unchanged.

Thus, the correct sentence will be: It is asserted that people should keep in mind the importance of adherence to COVID-19 appropriate behaviour.

The correct answer is BAC

Key Points

• 'Vaccine' is a noun, it is not an action that someone can 'do'. The blank requires a verb in the present tense.  Thus, the correct answer is 'produce'.
• 'Produce' is a verb it cannot be a type of something, it is an action and hence cannot have 'doses'. 'Product' is the noun form and can be a type of coronavirus vaccine. The blank requires a noun and thus the answer is 'vaccine'.
• We've already established that A and B will be interchanged and also '40 million' is a quality that can be used to describe people. Thus, the answer will be 'people'.

Hence, the final sentence will be: The AstraZeneca company is going to produce in Japan doses of the coronavirus vaccine enough for 40 million people, the executive director of the Japanese department of the firm said.

The correct answer is option 3 i.e. BCA

We can look at the sentence in the following way:

The _______ (A) birthday party was the best _______ (B) Andrew could have _______ (C). 

• Received: Given or presented with something. A 'birthday party' is not an object that can be 'received'.
• Surprise: An unexpected or astonishing thing - object or event.
• Gift: A present that is willingly given to someone without any payment. The sentence requires a verb in the past tense and 'gift' is in the present tense. 
  

Hence, we need to replace B with A and then replace C with A in order to make the sentence contextually correct. 

Correct Sentence: The surprise (B) birthday part was the best gift (C) Andrew could have received. (A).

The correct answer is option 3 i.e. CAB

We can look at the sentence in the following way:

The _______ (A) parlor's owner _______ (B) really loud music all _______ (C) long. 

• Blared: Made or caused a loud noise. 'Blared' is a verb (an action), it is grammatically and contextually incorrect to say "blared parlour".
• Night: The time between the sunset and the sunrise every day. 'Night' is a noun and not a verb, so it cannot cause loud music.
• Tattoo: An ink mark made on the body that is permanent and is done by puncturing the skin. A 'tattoo' is a noun and not a time period (like night) during which one can do anything. 
  

Hence, we need to replace A with B and then replace B with C, thereby making CAB the correct answer.

Correct Sentence: The tattoo (A) parlour's owner blared (B) really loud music all night (C) long.

The correct answer is the physical and mental changes that occurs in one's body- the error lies in this part only.

Key Points

For the sentence to be grammatically correct the word 'occurs' should be replaced with 'occur'.

The corrected form of the sentence is:

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Therefore, option 2) is the correct answer.

Thus, the correct sentence is: Psychiatrists feel that having a knowledge of the physical and mental changes that occur in one's body and the reasons behind them has become essential for all teenagers.

Additional Information

According to the subject and verb concord(agreement), when two singular nouns joined by 'and' refer to the same person or thing, the verb used is singular.

For e.g. The secretary and treasurer has been arrested.

The correct answer is we seldom or ever- the error lies in this part only.

Key Points

For the sentence to be grammatically correct the word ever should be replaced with never.

The corrected form of the sentence is:

<br>

Therefore, option 3) is the correct answer.

Thus, the correct sentence is: As these books on science are published only in English, we seldom or never find them in regional languages.

Additional Information

The use of “Seldom or never”: The word “Seldom” is an adverb and when a sentence begins with “seldom”, the law of inversion will be followed. For e.g.

• Seldom or never he comes to my recital. [Incorrect]
• Seldom or ever he comes to my recital. [Incorrect]
• Seldom, if ever does he come to my recital. [Correct]
• Seldom or never does he come to my recital. [Correct]

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Important Points

We can either use “Seldom or never” or “Seldom, if ever”, but we cannot use “Seldom or ever”.

The correct answer is option 3.

Key Points

• Whomsoever is an object pronoun and works like him, her and them.
• Whosoever is a subject pronoun and works like he, she and they.
• The given sentence states that the subject 'him', has set apart one evening of each week if anyone chose to visit him.
• In such sentences we always say if they/he/she chose to visit him and not if them/him/her chose to visit him.
• So, we must use 'whosoever' to maintain the subject-verb agreement.
• Therefore, the error lies in part C of the sentence.

The correct sentence will be: One evening of each week was set apart by him for the reception of whosoever chose to visit him.

The Correct answer is option A

Key Points 

• The error in part A of a sentence, the error is in usage 'Mysterious'
• Here, we need to use the adverb form of 'mysterious'
• Hence we need to replace 'Mysterious' with 'Mysteriously'

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Correct answer - Reports of researchers mysteriously falling ill at the Wuhan Institute in late 2019, and other reports of a researcher who has reportedly gone missing.

Additional Information

• Adverbs usually end with 'ly'.
• If any additional information is given regarding verbs then it is considered as an adverb.
• In the given sentence the adverb Mysteriously Describes the verb falling.

The correct answer is Only A. 

Key Points

• The error lies in Part A in the wrong usage of the preposition 'among' which is used to refer to when 'surrounded by somebody/something or in the middle of somebody/something'.
• The correct preposition to be used here is 'around' as we are referring populist politics of many different parts or areas.
• Therefore, the correct sentence is 'Populist politics around the world has sought to privilege national sovereignty over universal values and commitments, slacking off efforts to tackle critical challenges that are transnational'

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Therefore the correct answer is Only A.

The correct answer is 'All of the above'.

Key Points

• Let's understand the different ways in which the word 'wind' can be used:
• A current of air moving approximately horizontally, especially one strong enough to be felt.
• Example: There isn't enough wind to fly a kite.
• To make it difficult or temporarily impossible for someone to breathe, usually by hitting them in the stomach.
• To turn or cause something to turn.
• Example: Wind up your watch every day.
• By understanding the different meanings of the word 'wind' we can get that the usage of the word in all the given statements is correct.
• Hence, option 5 is the correct answer.

The correct answer is 'All of the above'.

Key Points

• Let's understand the different ways in which the word 'fellow' can be used:
• Used to refer to someone who has the same job or interests as you, or is in the same situation as you.
• Example: She introduced me to some of her fellow students.
• A man, used especially in the past by people in a higher social class.
• Example: He was an extremely obliging fellow.
• A member of a group of teachers of high rank at a particular college or university or of particular academic societies.
• Example: Georgia's a fellow of Clare College, Cambridge.
• By understanding the different meanings in which the word 'fellow', we can get that the usage of the word in all the given statements is correct.
• Hence, option 5 is the correct answer.

The correct answer is 'A and C'.

Key Points

• The word 'ascent' can be used to refer:
• The act of climbing or moving upwards.
• Example: The cart began its gradual ascent up the hill.
• The fact of starting to become successful.
• Example: His rapid ascent in the social scale was surprising.
• By understanding the different meanings of the word 'ascent' we can get that the usage of the word in statement A and C is correct.
• Sentence B is incorrect because it is talking about an approval of an idea, plan, or request, therefore the word 'ascent' is inappropriate according to the context of the given sentence.
• Hence, option 3 is the correct answer.

The correct answer is more leisurely pace.

​

Key Points

• In the sentence, more leisure pace is grammatically incorrect.
• In the emboldened part, the word leisure is a noun that is followed by another noun pace.
• Here, the adjective of leisure i.e. leisurely which means acting, proceeding, or done without haste must be used to describe the noun pace.
• So, more leisurely pace is the correct solution.

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So, the correct sentence is,  He slapped the team into action and they headed for the town at a more leisurely pace.

Additional Information

• many is incorrect because it is a determiner that means a large number of people or things.
• ​many leisured is also grammatically incorrect.
• paced is a verb that means to walk at a steady speed, especially without a particular destination and as an expression of anxiety or annoyance so it is contextually incorrect for the given sentence.

The correct answer is Option (2) i.e. India should side with the latter

Key Points

• The word ‘later’ means ‘at a time in the near future’ and is unsuitable in this sentence. The correct word to be used here is ‘latter’ which means ‘denoting the second or second mentioned of two people or things.’
• Hence ‘latter’ should be used in place of ‘later’ to make the sentence grammatically correct.
• Among the given choices, only option 2 replaces the given underlined part most appropriately.
• Hence, Option B is the correct answer.

<br>

Correct sentence: Although both the United States and China are formidable world powers, India should side with the latter.

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Additional Information

 

• Along(preposition): moving in a constant direction on (a road, path, or any more or less horizontal surface).
• Ex: "soon we were driving along a narrow road"
• There is no such word as 'side along'.
• Side with: to agree with or support the opinions or actions of (someone).
• Here, in the sentence, India needs to support someone's opinion, Hence, Side with should be used here.

Total number of male employees of five companies =

= 28000 × 3/7 + 25000 × 2/5 + 22000 × 5/11 + 30000 × 2/3 + 40000 × 5/8

= 12000 + 10000 + 10000 + 20000 + 25000

= 77000

Required average = 77000/5 = 15400

Total number of female employees of five companies =

= 28000 × 4/7 + 25000 × 3/5 + 22000 × 6/11 + 30000 × 1/3 + 40000 × 3/8

= 16000 + 15000 + 12000 + 10000 + 15000

= 68000

Total number of female workers of five companies =

= 10000 × 3/5 + 6000 × 1/3 + 8000 × ¾ + 5000 × 1/5 + 4000 × ½

= 6000 + 2000 + 6000 + 1000 + 2000

= 17000

Required ratio = 17000: 68000 = 1 : 4

Total number of male workers of five companies =

= 10000 × 2/5 + 6000 × 2/3 + 8000 × 1/4 + 5000 × 4/5 + 4000 × ½

= 4000 + 4000 + 2000 + 4000 + 2000

= 16000

Total workers of five companies =

= 10000 + 6000 + 8000 + 5000 + 4000 = 33000

Required percentage =

= 16000/33000 × 100

= 48.48% ≈ 48%

Female employees of company D =

= 30000 × 1/3 = 10000

Female workers of company D =

= 5000 × 1/5 = 1000

Required difference = 10000 – 1000 = 9000

 

Total number of female workers of five companies =

= 10000 × 3/5 + 6000 × 1/3 + 8000 × ¾ + 5000 × 1/5 + 4000 × ½

= 6000 + 2000 + 6000 + 1000 + 2000

= 17000

Total number of male workers of five companies =

= 10000 × 2/5 + 6000 × 2/3 + 8000 × 1/4 + 5000 × 4/5 + 4000 × ½

= 4000 + 4000 + 2000 + 4000 + 2000

= 16000

Required percentage = (17000 - 16000)/16000 × 100

⇒ Required percentage = (1000)/16000 × 100

⇒ Required percentage = 1/16 × 100

⇒ ? = 6.25%

I. x² – 37x + 330 = 0

⇒ x² – 15x – 22x + 330 = 0

⇒ x (x – 15) – 22 (x – 15) = 0

⇒ (x – 15) (x – 22) = 0

⇒ x = 15, 22

II. y² – 28y + 195 = 0

⇒ y² – 13y – 15y + 195 = 0

⇒ y (y – 13) – 15 (y – 13) = 0 

⇒ (y – 13) (y – 15) = 0

⇒ y = 13, 15  

 

 

Hence, x ≥ y

I. x² + 14x + 48 = 0

⇒ x² + 8x + 6x + 48 = 0

⇒ x(x + 8) + 6(x + 8) = 0

⇒ (x + 6) (x + 8) = 0

⇒ x = -6, -8

II. y² + 12y + 32 = 0

⇒ y² + 8y + 4y + 32 = 0

⇒ y(y + 8) + 4(y + 8) = 0

⇒ (y + 4) (y + 8) = 0

⇒ y= - 4,- 8

 

∴ Relationship between x and y can't be established

I. 16x² – 32x + 15 = 0

⇒ 16x² – 12x – 20x + 15 = 0

⇒ 4x(4x – 3) – 5(4x – 3) = 0

⇒ (4x – 3) (4x – 5) = 0

Thus, x = 3/4 or 5/4

II. 16y² – 48y + 35 = 0

⇒ 16y² – 20y – 28y + 35 = 0

⇒ 4y(4y – 5) – 7(4y – 5) = 0

⇒ (4y – 5) (4y – 7) = 0

Thus, y = 5/4 or 7/4

So, when x = 3/4, for y = 5/4, then x < y and when x = 3/4, for y = 7/4, then x < y

And when x = 5/4, for y = 5/4, then x = y and when x = 5/4, for y = 7/4, then x < y

∴ We can observe that x ≤ y

I. x² – 35x + 294 = 0

⇒ x² – 21x – 14x + 294 = 0

⇒ x (x – 21) – 14 (x – 21) = 0

⇒ (x – 21) (x – 14) = 0

⇒ x = 21, 14

 

II. y² – 68y + 1140 = 0

⇒ y² – 38y – 30y + 1140 = 0

⇒ y (y – 38) – 30 (y – 38) = 0

⇒ (y – 38) (y – 30) = 0

⇒ y = 38, 30

 

 

Hence x < y

i. x² - 12x + 35 = 0

⇒ x² - 5x - 7x + 35 = 0

⇒ (x - 5) (x - 7) = 0

⇒ x = 5, 7

ii. y² - 25y + 126 = 0

⇒ y² - 7y - 18y + 126 = 0

⇒ (y - 7) (y - 18) = 0

⇒ y = 7, 18

 

Hence, x ≤ y.

Total number of employees working in marketing department = (61.2/360) × 6000 = 1020

∴ Total number of men working in the marketing department = 1020 × (7/17) = 420

Total number of employees working in marketing department = (61.2/360) × 6000 = 1020

Total number of women working in the marketing department = 1020 × (10/17) = 600

Total number of employees working in HR department = (79.2/360) × 6000 = 1320

Total number of men working in the HR department = 1320 × (20/33) = 800

∴ Required ratio = 600 : 800

⇒ 3 : 4

total number of employees working in IT department = (97.2/360) × 6000 = 1620

total number of men working in the IT department of the Organisation = (5/9) × 1620 = 900

∴ Required percentage = (900/1620) × 100 = 55.55% ≈ 56%

Total number of employees working in Production department = (64.8/360) × 6000 = 1080

Total number of women working in the Production department = 1080 × (4/9) = 480

Totla number of employees working in organisation = 6000

∴ required percentage = (480/6000) × 100 = 8%

Total number of women working in Production department = (64.8/360) × 6000 × (4/9) = 480

Total number of women working in HR department = (79.2/360) × 6000 × (13/33) = 520

Total number of women working in IT department = (97.2/360) × 6000 × (4/9) = 720

Total number of women working in Marketing department = (61.2/360) × 6000 × (10/17) = 600

Total number of women working in Accounts department = (57.6/360) × 6000 × (17/32) = 510

∴ total number of women working in the organisation = 480 + 520 + 720 + 600 + 510 = 2830

Calculation:

Total number of students = 6300

Number of boys = 5/9 × 6300

⇒ 3500

∴ number of girls = (6300 - 3500)

⇒ 2800

Number of boys enrolled in Painting = 621

Number of students enrolled in Quiz = 36% of 6300 = 2268

Number of girls enrolled in Quiz = 640

∴ number of boys enrolled in quiz = 2268 – 640

⇒ 1628

Number of boys enrolled in Debating = 25% of 3500

⇒ 875

∴ Number of girls enrolled in Carom = 640 + 150 = 790

Number of students enrolled in Painting = 816

∴ Number of girls enrolled in painting = 816 – 621 = 195

Number of boys enrolled in Chess and Carom together = 3500 – (875 + 621 + 1628) = 376

∴ Number of boys enrolled in Chess = 5/(5 + 3) × 376

⇒ 235

Number of girls enrolled in Chess = 235 + 186 = 421

Number of boys enrolled in Carom = 376 – 235 = 141

Number of girls enrolled in Debating = 2800 – (640 + 790 + 195 + 421) = 754

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∴ total number of students enrolled in Chess = 656

∴ Required percentage = 656/6300 × 100

⇒ 10.41% ≈ 10%

The percentage of students from the university who are enrolled in Chess is approximately 10%.

Calculation:

Total number of students = 6300

Number of boys = 5/9 × 6300

⇒ 3500

∴ number of girls = (6300 - 3500)

⇒ 2800

Number of boys enrolled in Painting = 621

Number of students enrolled in Quiz = 36% of 6300 = 2268

Number of girls enrolled in Quiz = 640

∴ number of boys enrolled in quiz = 2268 – 640

⇒ 1628

Number of boys enrolled in Debating = 25% of 3500

⇒ 875

∴ Number of girls enrolled in Carom = 640 + 150 = 790

Number of students enrolled in Painting =816

∴ Number of girls enrolled in painting = 816 – 621 = 195

Number of boys enrolled in Chess and Carom together = 3500 – (875 + 621 + 1628) = 376

∴ Number of boys enrolled in Chess = 5/(5 + 3) × 376

⇒ 235

Number of girls enrolled in Chess = 235 + 186 = 421

Number of boys enrolled in Carom = 376 – 235 = 141

Number of girls enrolled in Debating = 2800 – (640 + 790 + 195 + 421) = 754

<br>

∴ required Ratio = 141 : 790

The ratio of the number of boys enrolled in Carom to the number of girls enrolled in the same activity is 141 : 790.

Calculation:

Total number of students = 6300

Number of boys = 5/9 × 6300

⇒ 3500

∴ number of girls = (6300 - 3500)

⇒ 2800

Number of boys enrolled in Painting = 621

Number of students enrolled in Quiz = 36% of 6300 = 2268

Number of girls enrolled in Quiz = 640

∴ number of boys enrolled in quiz = 2268 – 640

⇒ 1628

Number of boys enrolled in Debating = 25% of 3500

⇒ 875

∴ Number of girls enrolled in Carom = 640 + 150 = 790

Number of students enrolled in Painting = 816

∴ Number of girls enrolled in painting = 816 – 621 = 195

Number of boys enrolled in Chess and Carom together = 3500 – (875 + 621 + 1628) = 376

∴ Number of boys enrolled in Chess = 5/(5 + 3) × 376

⇒ 235

Number of girls enrolled in Chess = 235 + 186 = 421

Number of boys enrolled in Carom = 376 – 235 = 141

Number of girls enrolled in Debating = 2800 – (640 + 790 + 195 + 421) = 754

<br>

Difference in number of boys and girls enrolled in Painting = 621 – 195

⇒ 426

∴ Required percentage = 426/1629 × 100

⇒ 26.15% ≈ 26%

The difference in the number of boys and girls who are enrolled in painting is approximately 26% of the total number of students who are enrolled in Debating.

Calculation:

Total number of students = 6300

Number of boys = 5/9 × 6300

⇒ 3500

∴ number of girls = (6300 - 3500)

⇒ 2800

Number of boys enrolled in Painting = 621

Number of students enrolled in Quiz = 36% of 6300 = 2268

Number of girls enrolled in Quiz = 640

∴ number of boys enrolled in quiz = 2268 – 640

⇒ 1628

Number of boys enrolled in Debating = 25% of 3500

⇒ 875

∴ Number of girls enrolled in Carom = 640 + 150 = 790

Number of students enrolled in Painting = 816

∴ Number of girls enrolled in painting = 816 – 621 = 195

Number of boys enrolled in Chess and Carom together = 3500 – (875 + 621 + 1628) = 376

∴ Number of boys enrolled in Chess = 5/(5 + 3) × 376

⇒ 235

Number of girls enrolled in Chess = 235 + 186 = 421

Number of boys enrolled in Carom = 376 – 235 = 141

 

Number of girls enrolled in Debating = 2800 – (640 + 790 + 195 + 421)

⇒ 754

The number of girls who are enrolled in Debating is 754.

Calculation:

Total number of students = 6300

Number of boys = 5/9 × 6300

⇒ 3500

∴ number of girls = (6300 - 3500)

⇒ 2800

Number of boys enrolled in Painting = 621

Number of students enrolled in Quiz = 36% of 6300 = 2268

Number of girls enrolled in Quiz = 640

∴ number of boys enrolled in quiz = 2268 – 640

⇒ 1628

∴ Required percentage = 640/2268 × 100

⇒ 28.21% ≈ 28%

The total number of girls in Quiz is approximately 28% of the total number of students in Quiz.

Shortcut Trick

Ratio 10 years ago = 4 : 1 (Difference = 3)

Ratio 10 years later = 2 : 1 (Difference = 1)

Equating differences: Multiply second ratio by 3 → 6 : 3

Change in units = 6 − 4 = 2 units for 20 years (10 ago to 10 later)

1 unit = 10 years. Total units 10 years ago = 4 + 1 = 5 units.

Sum 10 years ago = 5 × 10 = 50 years. Present sum = 50 + 10 + 10 = 70 years.

∴ The correct answer is 70 years.

Alternate Method

Given: Ratio 10 years ago = 4 : 1, Ratio 10 years later = 2 : 1.

⇒ Let ages 10 years ago be 4x and 1x.

⇒ Ages 10 years later = (4x + 20) and (x + 20).

⇒ (4x + 20) / (x + 20) = 2 / 1

⇒ 4x + 20 = 2x + 40

⇒ 2x = 20 ⇒ x = 10

⇒ Present age of Mother = 4(10) + 10 = 50 years.

⇒ Present age of Daughter = 1(10) + 10 = 20 years.

⇒ Sum = 50 + 20 = 70 years.

∴ The correct answer is 70 years.

Additional Information

Ratio Difference Method

When the age gap remains constant, the numerical difference between the ratio parts must be made equal to simplify calculations.

Present Age Calculation

Always remember to add or subtract the time offset from the variable "x" to reach the Present Age from past or future ratios.

Shortcut Trick

Initial Savings = 30,000 − 20,000 = ₹10,000

New Income = 30,000 + 10,000 = ₹40,000

New Savings = 40,000 − 25,000 = ₹15,000

Percentage Increase = [(15,000 − 10,000) ÷ 10,000] × 100 = 50%

∴ The correct answer is 50%.

Alternate Method

Given:

Initial Income (I₁) = ₹30,000, Initial Expenditure (E₁) = ₹20,000

New Income (I₂) = 30,000 + 10,000 = ₹40,000, New Expenditure (E₂) = ₹25,000

Formula Used:

Savings = Income − Expenditure

Percentage Increase = (Increase ÷ Original Value) × 100

Calculations:

⇒ Initial Savings (S₁) = 30,000 − 20,000 = ₹10,000

⇒ New Savings (S₂) = 40,000 − 25,000 = ₹15,000

⇒ Increase in Savings = 15,000 − 10,000 = ₹5,000

⇒ Percentage Increase = (5,000 ÷ 10,000) × 100

⇒ Percentage Increase = 0.5 × 100 = 50%

∴ The correct answer is 50%.

Additional Information

Income-Expenditure Relation

Income is always the sum of Expenditure and Savings (I = E + S). Any change in one affects at least one other component.

Percentage Change

Percentage change = [(Final Value − Initial Value) ÷ Initial Value] × 100. Always ensure the denominator is the original/base value.

Base Shift

If expenditure increases at a higher rate than income, the savings percentage increase might be lower or even negative depending on the initial values.

Shortcut Trick

Rate of interest (R) = 80% ÷ 8 years = 10% per annum.

For 3 years at 10% rate, effective CI rate = 33.1%.

CI = 33.1% of ₹15,000 = 150 × 33.1 = ₹4,965.

∴ The correct answer is ₹4,965.

Alternate Method

Given: Increase in 8 years = 80%; Principal (P) = ₹15,000; Time (n) = 3 years.

Formula: SI = (P × R × T) ÷ 100 and CI = P[(1 + R/100)ⁿ − 1]

⇒ Let Principal be 100, then SI = 80 in 8 years.

⇒ R = (80 × 100) ÷ (100 × 8) = 10% per annum.

⇒ For Compound Interest: P = ₹15,000, R = 10%, n = 3 years.

⇒ Amount (A) = 15000 × (1 + 10/100)³

⇒ A = 15000 × (11/10) × (11/10) × (11/10)

⇒ A = 15 × 1331 = ₹19,965.

⇒ CI = A − P = 19965 − 15000 = ₹4,965.

∴ The correct answer is ₹4,965.

Additional Information

Effective Rate for Compound Interest

For 10% interest rate, effective CI rate for 2 years is 21% and for 3 years is 33.1%.

CI and SI Difference

Difference for 2 years = PR²/100². Difference for 3 years = [PR²(300 + R)] ÷ 100³.

Successive Percentage Method

Net change for two years at r% = (r + r + r²/100)%.

Shortcut Trick

Initial average of n students = 12 years.

Total age of 2 students leaving = 23 + 25 = 48 years.

Effective age loss compared to initial average = 48 − (2 × 12) = 48 − 24 = 24 years.

Due to this loss of 24 years, the average of remaining (n − 2) students drops by 12 − 11 = 1 year.

Number of remaining students = 24 ÷ 1 = 24.

Initial students (n) = 24 + 2 = 26.

∴ The correct answer is 26 students.

Alternate Method

Given: Initial average = 12 years, Ages of students leaving = 23 years and 25 years, Final average = 11 years.

Formula Used: Total Age = Number of students × Average age

⇒ Let the initial number of students be n.

⇒ Initial total age = 12n

⇒ New total age after 2 students leave = 12n − (23 + 25) = 12n − 48

⇒ New average = (New total age) ÷ (n − 2) = 11

⇒ 12n − 48 = 11 × (n − 2)

⇒ 12n − 48 = 11n − 22

⇒ 12n − 11n = 48 − 22

⇒ n = 26

∴ The correct answer is 26 students.

Additional Information

Basic Average Formula

Average = Sum of all observations ÷ Total number of observations.

Average Deviation Method

When members leave or join, the change in total sum = (New Average − Old Average) × New Quantity + (Difference in value of replaced item).

Weighted Average

Combined average of two groups = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is quantity and x is average.

Shortcut Trick Assume total students = 100. Girls = 45, Boys = 55. Students with > 75% marks: Girls = 80% of 45 = 36; Boys = 70% of 55 = 38.5. Total students with > 75% marks = 36 + 38.5 = 74.5. Probability (Boy | > 75% marks) = 38.5 ÷ 74.5 = 385/745 = 77/149. ∴ The correct answer is 77/149. Alternate Method

Given: Percentage of Girls (G) = 45%, Percentage of Boys (B) = 55%. Conditional Probabilities: P(>75%|G) = 80/100, P(>75%|B) = 70/100. Formula Used: Bayes Theorem: P(B|>75%) = [P(B) × P(>75%|B)] ÷ [P(G) × P(>75%|G) + P(B) × P(>75%|B)] ⇒ Numerator = 0.55 × 0.70 = 0.385 ⇒ Denominator = (0.45 × 0.80) + (0.55 × 0.70) ⇒ Denominator = 0.360 + 0.385 = 0.745 ⇒ Required Probability = 0.385 ÷ 0.745 ⇒ Probability = 385/745 = 77/149 ∴ The correct answer is 77/149. Additional Information Bayes Theorem It describes the probability of an event based on prior knowledge of conditions that might be related to the event. Conditional Probability P(A|B) is the probability of event A occurring given that B has already occurred. P(A|B) = P(A ∩ B) / P(B). Total Probability Rule The total probability of an outcome is the weighted average of its conditional probabilities across all mutually exclusive events.

46       187     284      345     378      391 

     +141     +97     +61      +33     +13

              -44     -36       -28       -20

                     +8      +8        +8

The given series,

⇒ 9 × 2 + 1 = 19

⇒ 19 × 2 + 2 = 40

⇒ 40 × 2 + 3 = 83

⇒ 83 × 2 + 4 = 170 = ?

⇒ 170 × 2 + 5 = 345

⇒ 345 × 2 + 6 = 696

As per the series given in the question, it is clear that it follows a pattern of:

17 × 2 + 1 = 35

35 × 3 + 1 = 106

106 × 4 + 1 = 425

425 × 5 + 1 = 2126

∴ Considering the above mention pattern, the missing term in the series is 425.

The pattern of the number series is -

7 × 2 - 1 = 13

13 × 2 - 1 = 25

25 × 2 - 1 = 49

49 × 2 - 1 = 97

97 × 2 - 1 = 193

Hence 25 will come in place of question mark.

The pattern of the number series is -

17 × 3 + 1 = 52

52 × 3 + 2 = 158

158 × 3 + 3 = 477

477 × 3 + 4 = 1435

Hence 1435 will come in place of question mark.

Shortcut Trick

Assume Total Work = 100 units (LCM of 25 and 20).

Efficiency of A = 100 ÷ 25 = 4 units/day; Efficiency of B = 100 ÷ 20 = 5 units/day.

Work done by A in first 7 days = 7 × 4 = 28 units.

Remaining work = 100 − 28 = 72 units. Days taken by (A + B) = 72 ÷ 9 = 8 days.

Total Days = 7 + 8 = 15 days.

∴ The correct answer is 15 days.

Alternate Method

Given: A finishes in 25 days, B finishes in 20 days. A starts and works for 7 days before B joins.

Formula Used: Total Work = Time × Efficiency

⇒ Work done by A alone in 7 days = 7 × 4 = 28 units

⇒ Remaining Work = 100 − 28 = 72 units

⇒ Combined efficiency of A + B = 4 + 5 = 9 units/day

⇒ Time taken to finish remaining work = 72 ÷ 9 = 8 days

⇒ Total time = Initial 7 days + Remaining 8 days = 15 days

∴ The correct answer is 15 days.

Additional Information

Efficiency and Time Relation

Efficiency is inversely proportional to the time taken. If time ratio is x : y, the efficiency ratio is y : x.

Pipes and Cisterns

This logic is identical to inlet pipes. If an outlet pipe is present, its efficiency is taken as negative.

Work and Wages

Wages are distributed in the ratio of work done or the ratio of efficiencies if all work for the same duration.

Shortcut Trick

Cost Price of mixture = 360 ÷ 1.25 = ₹288 per kg.

Apply Alligation: (Type 2 − Mean) : (Mean − Type 1)

Ratio = (300 − 288) : (288 − 220) = 12 : 68

Simplified Ratio = 3 : 17

∴ The correct answer is 3 : 17.

Alternate Method

Given: CP₁ = ₹220/kg, CP₂ = ₹300/kg, SP_mix = ₹360/kg, Profit = 25%.

Formula Used: CP = [SP × 100] ÷ [100 + Profit%]; Ratio = (CP₂ − CP_m) : (CP_m − CP₁)

⇒ Mean CP = (360 × 100) ÷ 125

⇒ Mean CP = 360 ÷ 1.25 = ₹288 per kg

⇒ Required Ratio = (300 − 288) : (288 − 220)

⇒ Ratio = 12 : 68

⇒ Ratio = 3 : 17

∴ The correct answer is 3 : 17.

Additional Information

Alligation Rule

It is used to find the ratio in which two ingredients at given prices must be mixed to produce a mixture at a given price. Always ensure all values (CP1, CP2, Mean) are Cost Prices.

Profit and Loss Relation

When Selling Price (SP) and Profit% are known, Cost Price (CP) is calculated as CP = SP ÷ (1 + P/100).

Weighted Average

The mean price can also be verified using the formula: C_m = (n₁c₁ + n₂c₂) ÷ (n₁ + n₂).

Shortcut Trick

Relative speed in opposite direction = 93 + 51 = 144 kmph = 144 × (5/18) = 40 m/s.

Total distance (Length A + Length B) = 40 × 18 = 720 m.

Since B = A/2, then A + A/2 = 720 ⇒ 1.5A = 720 ⇒ A = 480 m.

Distance covered by A in 42s = (93 × 5/18) × 42 = 1085 m.

Length of bridge = 1085 − 480 = 605 m.

∴ The correct answer is 605 m.

Alternate Method

Given: Speed of Train A = 93 km/hr, Speed of Train B = 51 km/hr, Crossing time = 18 s, Bridge crossing time = 42 s.

Formula Used: Relative Speed = S₁ + S₂ (Opposite); Distance = Speed × Time; 1 km/hr = 5/18 m/s.

⇒ Relative Speed = (93 + 51) × (5/18) = 144 × (5/18) = 40 m/s.

⇒ Let Length of Train A = 2x and Train B = x.

⇒ Total Length = 2x + x = 40 × 18 ⇒ 3x = 720 ⇒ x = 240 m.

⇒ Length of Train A = 2 × 240 = 480 m.

⇒ Speed of Train A in m/s = 93 × (5/18) = 15.5 × (5/3) = 25.833... or 310/12 = 155/6 m/s.

⇒ Total Distance for bridge crossing = Length A + Bridge = (155/6) × 42.

⇒ 480 + Bridge = 155 × 7 = 1085 m.

⇒ Bridge = 1085 − 480 = 605 m.

∴ The correct answer is 605 m.

Additional Information

Relative Speed Concept

When two objects move in the opposite direction, relative speed is S₁ + S₂. When they move in the same direction, it is |S₁ − S₂|.

Crossing a Bridge/Platform

When a train crosses a stationary object of length L, the total distance covered is the sum of the length of the train and the length of the object.

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Shortcut Trick

Investment ratio R : S : T = 25000 : 15000 : 30000 = 5 : 3 : 6.

Total shareable profit = 1/3 × 58800 = 19600.

Sum of ratio parts = 5 + 3 + 6 = 14 units.

14 units = 19600 ⇒ 1 unit = 1400.

T's share = 6 units = 6 × 1400 = 8400.

∴ The correct answer is 8400.

Alternate Method

Given → Investments: R = 25000, S = 15000, T = 30000. Total Profit = 58800. Formulas: Profit Ratio = Investment Ratio × Time Ratio | Share = (Individual Ratio ÷ Total Ratio) × Shareable Profit.

⇒ Calculate the ratio of investments of R, S, and T = 25 : 15 : 30 = 5 : 3 : 6. ⇒ The amount to be divided among them = 1/3 × 58800 = 19600. ⇒ Sum of the ratios = 5 + 3 + 6 = 14. ⇒ Share of T = (Ratio of T ÷ Sum of Ratios) × Dividable Profit. ⇒ Share of T = (6 ÷ 14) × 19600 = 6 × 1400 = 8400.

∴ The correct answer is 8400.

Additional Information

Partnership Basics

When time periods are the same, the profit is divided directly in the ratio of the capitals invested.

Working vs Sleeping Partner

A working partner often receives a percentage of the profit as a salary or management fee before the remaining profit is split.

Shortcut Trick

Net discount involves both cash discount and free articles: 1 dozen = 12 articles.

Total articles given = 12 + 4 = 16. Effective discount ratio = (12 ÷ 16) × 0.80 = 0.60.

Net selling price factor (0.60 MP) must equal profit factor (1.20 CP).

MP ÷ CP = 1.20 ÷ 0.60 = 2 ÷ 1.

Markup percentage = (2 − 1) ÷ 1 × 100% = 100%.

∴ The correct answer is 100%.

Alternate Method

Given → Profit = 20%, Cash Discount = 20%, Free Articles = 4 on 12. Formulas: Total Discount% = (1 − (Selling Price ÷ Marked Price)) × 100 | MP × (1 − D₁) × (Paid Qty ÷ Total Qty) = CP × (1 + P%)

⇒ Let Marked Price of 1 article be 100. ⇒ Customer pays for 12 articles, gets 16. Total revenue = 12 × 100 × (1 − 0.20) = 12 × 80 = 960. ⇒ This revenue is the Selling Price of 16 articles. SP per article = 960 ÷ 16 = 60. ⇒ Profit is 20%, so 1.20 × CP = 60 ⇒ CP = 60 ÷ 1.20 = 50. ⇒ Markup = MP − CP = 100 − 50 = 50. ⇒ Markup% = (50 ÷ 50) × 100 = 100%.

∴ The correct answer is 100%.

Additional Information

Successive Discounts with Free Items

When 'x' articles are bought and 'y' are given free, the discount% = [y ÷ (x + y)] × 100. If an additional cash discount d% is given, net multiplier = (1 − d/100) × [x ÷ (x + y)].

CP and MP Relationship

The ratio of MP to CP can be expressed as: MP ÷ CP = (100 + Profit%) ÷ (100 − Net Discount%).

According to the given information, we get the following figure,

So, U is in the south-east of M.

Hence, ‘South-East’ is the correct answer.

According to the given information, we get the following figure,

Shortest distance between N and Q = √ (4² + 3²) = √ (16 + 9) = √ 25 = 5

Hence, ‘5 m’ is the correct answer.

According to the given information, we get the following figure,

So, the perimeter of quadrilateral NYOM = 2 × (L + B) = 2 × (5 + 4) = 2 × 9 = 18 m.

Hence, ‘18 m’ is the correct answer.

1)Three persons are sitting between X and T, who are sitting adjacent to Q.

2. H is sitting 2nd to the right of Q. X is in left of Q.

3. Two persons are sitting between H and S who is sitting at one of the ends.

4. S is not sitting adjacent to Q, who is sitting 2nd to the right of L.

5. L is sitting exactly in the middle of the row.

6. J is sitting 6th from the left end.

7. X is not sitting to the right of J.Hence, Case-1 will be elliminated.

8. Two persons are sitting between J and R.

9. Two persons are sitting between X and K.

Therefore the final arrangement is, 

Hence, the persons are sitting between X and S are nine.

1)Three persons are sitting between X and T, who are sitting adjacent to Q.

2. H is sitting 2nd to the right of Q. X is on the left of Q.

3. Two persons are sitting between H and S who is sitting at one of the ends.

4. S is not sitting adjacent to Q, who is sitting 2nd to the right of L.

5. L is sitting exactly in the middle of the row.

6. J is sitting 6th from the left end.

7. X is not sitting to the right of J.Hence, Case-1 will be eliminated.

 

4. Two persons are sitting between J and R.

5. Two persons are sitting between X and K.

Therefore the final arrangement is, 

Hence, persons are sitting in the row are 15.

1)Three persons are sitting between X and T, who are sitting adjacent to Q.

2. H is sitting 2nd to the right of Q. X is on the left of Q.

3. Two persons are sitting between H and S who is sitting at one of the ends.

4. S is not sitting adjacent to Q, who is sitting 2nd to the right of L.

5. L is sitting exactly in the middle of the row.

6. J is sitting 6th from the left end.

7. X is not sitting to the right of J.Hence, Case-1 will be eliminated.

8. Two persons are sitting between J and R.

9. Two persons are sitting between X and K.

Therefore the final arrangement is, 

Hence**, the person is sitting to the left of Q is nine.**

1)Three persons are sitting between X and T, who are sitting adjacent to Q.

2. H is sitting 2nd to the right of Q. X is on the left of Q.

3. Two persons are sitting between H and S who is sitting at one of the ends.

4. S is not sitting adjacent to Q, who is sitting 2nd to the right of L.

5. L is sitting exactly in the middle of the row.

6. J is sitting 6th from the left end.

7. X is not sitting to the right of J.Hence, Case-1 will be eliminated.

8. Two persons are sitting between J and R.

9. Two persons are sitting between X and K.

Therefore the final arrangement is, 

Hence, the position of H with respect to T is 3rd to the right.

1)Three persons are sitting between X and T, who are sitting adjacent to Q.

2. H is sitting 2nd to the right of Q. X is on the left of Q.

3. Two persons are sitting between H and S who is sitting at one of the ends.

4. S is not sitting adjacent to Q, who is sitting 2nd to the right of L.

5. L is sitting exactly in the middle of the row.

6. J is sitting 6th from the left end.

7. X is not sitting to the right of J.Hence, Case-1 will be eliminated.

8. Two persons are sitting between J and R.

9. Two persons are sitting between X and K.

Therefore the final arrangement is, 

Hence, X sits exactly in the middle of K and L.

Correct Answer:- (5)

Given Statement: A < B ≤ C > D; C > E ≥ F; E > B

i) A < F: False ( A < B ≤ C > E ≥ F; There is no clear relation between A and F, hence can not conclude anything.)

ii) D < B: False ( B ≤ C > D; There is no clear relation between B and D, hence can not conclude anything.)

Hence, the correct answer is None follows.

Given statement: B > C = D ; E < F ; B ≤ A; D ≤ E

On Combining: A ≥ B > C = D ≤ E < F

Conclusions:

I. A > C - True ( as, A ≥ B > C; so A > C is true )

II. B = D - False ( as, B > C = D; So B > D )

Hence, only conclusion I follows

Given:

R ≥ T = Q < M; S ≥ R

On Combining:

S ≥ R ≥ T = Q < M

Conclusions:

I. M < R → False (as R ≥ T = Q < M; therefore,the relationship between M and R cannot be determined)

II. S ≥ Q → True (as S ≥ R ≥ T = Q; therefore S ≥ Q)

Hence, only conclusion II is true.

Given statements: M > N < O ≤ P; S ≥ R > Q = P

On combining: M > N < O < P = Q < R ≤ S

I. S ≥ M → False (as M > N < O < P = Q < R ≤ S) thus clear relation between S and M cannot be determined.

II. S < M → False (as M > N < O < P = Q < R ≤ S) thus clear relation between S and M cannot be determined.

A number can be either equal, less, or greater than another number.

Here, S ≥ M (S is greater than or equal to M).

S < M (S is smaller than M).

One statement must be true but can't say which statement.

Hence, Either I or II follows.

Given Statements: A > B, D ≤ E, D ≥ C ≤ B

On combining: A > B ≥ C ≤ D ≤ E

Conclusions:

I. C < A → True (as A > B ≥ C → A > C)

II. E ≥ C → True (as C ≤ D ≤ E → C ≤ E)

Hence, both I and II are true

Six persons: P, Q, R, S, T and U

Floors: 1, 2, and 3

Flat: X and Y

(1) P lives on an odd numbered floor in flat X. Therefore, we get two the following two cases here.

 

(2) The one who is from Kolkata lives immediately above U  in the same flat. .

(3) S lives to the west of U.

(4) P and the one who is from Kolkata do not live on the same floor.

 

(5) T does not live in flat Y.

(6) There is one floor between Q and the one who is from Delhi who lives above Q. Since, only flat Y of floor 3 is left for Q in case (I), case (I) eliminates here.

 

(7) Neither S nor Q is from Bangalore.

(8) U is either from Pune or from Agra (implies, P is from Bangalore).

(9) The one who is from Mumbai lives on the same floor on which the one who is from Agra lives (implies, S is from Mumbai and U is from Agra). Thus, the final arrangement is as follows:

 

We can see that, all T, R, P, and Q live in odd numbered floor and thus forms a group.

Hence, S does not belong to that group.

Six persons: P, Q, R, S, T and U

Floors: 1, 2, and 3

Flat: X and Y

(1) P lives on an odd numbered floor in flat X. Therefore, we get two the following two cases here.

 

(2) The one who is from Kolkata lives immediately above U  in the same flat. .

(3) S lives to the west of U.

(4) P and the one who is from Kolkata do not live on the same floor.

 

(5) T does not live in flat Y.

(6) There is one floor between Q and the one who is from Delhi who lives above Q. Since, only flat Y of floor 3 is left for Q in case (I), case (I) eliminates here.

 

(7) Neither S nor Q is from Bangalore.

(8) U is either from Pune or from Agra (implies, P is from Bangalore).

(9) The one who is from Mumbai lives on the same floor on which the one who is from Agra lives (implies, S is from Mumbai and U is from Agra). Thus, the final arrangement is as follows:

 

Hence, R lives to the east of T.

Six persons: P, Q, R, S, T and U

Floors: 1, 2, and 3

Flat: X and Y

(1) P lives on an odd numbered floor in flat X. Therefore, we get two the following two cases here.

 

(2) The one who is from Kolkata lives immediately above U  in the same flat. .

(3) S lives to the west of U.

(4) P and the one who is from Kolkata do not live on the same floor.

 

(5) T does not live in flat Y.

(6) There is one floor between Q and the one who is from Delhi who lives above Q. Since, only flat Y of floor 3 is left for Q in case (I), case (I) eliminates here.

 

(7) Neither S nor Q is from Bangalore.

(8) U is either from Pune or from Agra (implies, P is from Bangalore).

(9) The one who is from Mumbai lives on the same floor on which the one who is from Agra lives (implies, S is from Mumbai and U is from Agra). Thus, the final arrangement is as follows:

 

Hence, the one who is from Pune and P both live on bottom most floors.