Prepositions
1. I'll arrive sometime ___ 8 and 9 am.

A. in B. next to C. between D. on

Answer: Option C
2. She wants to stay ___ home tonight.

A. to B. of C. at D. in

Answer: Option C
3. Did you watch the football ___ TV last night?

A. by B. on C. in D. to

Answer: Option B
Active Voice and Passive Voice
1. Let her go out for a walk.

A. It has been suggested that she should go out for a walk. B. It had been suggested that she should go out for a walk. C. It was suggested that she should go out for a walk. D. It is suggested that she should go out for a walk.

Answer: Option D
2. Why are they laughing at you?

A. Why are they being laughed at by you? B. Why are you being laughed at by them? C. Why are all being laughed at by them? D. Why are you laughed at by them?

Answer: Option B
3. His pocket has been picked.

A. They have his pocket picked. B. Picking has been done to his pocket. C. Picked has been his pocket. D. Someone has picked his pocket.

Answer: Option D
Joining Sentences
1. He is, no doubt, very clever. He will fall into my trap. (A) Although he is clever..... (B) If he is clever, he will fall..... (C) In spite of being clever he.....

A. A and B B. Only A C. A and C D. Only C E. All the three

Answer: Option C
Explanation: The two sentences express contradictory ideas. Hence conjunctions like 'though' can combine the sentences meaningfully. 'Despite being ... or In spite of being' ... can also be used to express the same idea.
2. There is an increase in the incidents of violence these days. The police have tightened security. (A) Because there is an increase ..... (B) As there is an increase ..... (C) While there is an increase .....

A. Only A B. A and B C. Only B D. All the three E. None of these

Answer: Option B
Explanation: The reason for the security being tightened is because of the increase in the incidents of violence. This is conveyed in A and B.
3. The new principal is a well-read man. He can also speak many languages. (A) In spite of being well -read man ..... (B) Besides being a well-read man ..... (C) The new principal is not only a well-read man

A. A and B B. Only B C. B and C D. Only C E. All the three

Answer: Option C
Explanation: Apart from being a well-read man, the new principal can speak many languages, this meaning is conveyed using 'besides' and '... not only ... but also ...'
Spotting Errors
Read each sentence to find out whether there is any grammatical error in it. The error, if any will be in one part of the sentence. The letter of that part is the answer. If there is no error, the answer is 'D'. (Ignore the errors of punctuation, if any).
1. (solve as per the direction is given above)

A. We discussed the problem so thoroughly B. on the eve of the examination C. that I found it very easy to work it out. D. No error.

Answer: Option A
Explanation: We discussed the problem so thoroughly.
2. (solve as per the direction is given above)

A. If I had known B. this yesterday C. I will have helped him. D. No error.

Answer: Option C
Explanation: I would have helped him.
3. (solve as per the direction is given above)

A. The students were B. waiting for C. the arrival of the chief guest. D. No error.

Answer: Option B
Explanation: waiting
Synonyms
In the following, the questions choose the word which best expresses the meaning of the given word.
1. INEBRIATE

A. Dreamy B. Stupefied C. Unsteady D. Drunken

Answer: Option D
2. ABJECT

A. Challenge B. Miserable C. Deny D. Disobey

Answer: Option B
3. BARE

A. Uncovered B. Tolerate C. Clear D. Neat

Answer: Option A
Sentence Improvement
1. The workers are hell bent at getting what is due to them.

A. hell-bent on getting B. hell-bent forgetting C. hell-bent upon getting D. No improvement

Answer: Option C
2. The record for the biggest tiger hunt has not been met since 1911 when Lord Hardinge. then Viceroy of India, shot a tiger than measured 11 feet and 6 inches.

A. improved B. broken C. bettered D. No improvement

Answer: Option B
3.They are social insects, living in communities, regulated by definite laws, each member of society bearing well-defined and separate part in the work of a colony.

A. who are living in communities B. living among a community C. who lives with a community D. No improvement

Answer: Option D
Error Correction (Phrase in colour)
1. The organization aims "to providing" with satellite-based data on climate-relevant information with the highest possible levels of accuracy and reliability.

A. to provide with B. at providing with C. to provide D. to the provision of E. No correction required

Answer: Option C
Explanation: The organization aims 'at providing' or 'to provide' something. The use of 'with' is incorrect. It aims 'to provide' something not 'provide with something'.
2. Each galaxy is surrounded by a giant sphere of dark matter more than 10 times "so wide as" the visible portion of the galaxy.

A. the width of B. so wider than C. of the width to D. in width than E. No correction required

Answer: Option A
Explanation: It is 'more than 10 times the width of' something else. It has to take a noun and not an adjective. The comparison is between the width of the dark matter and the width of the visible portion of the galaxy. The comparison is brought out with the use of 'more than'. Hence the use of 'as wide as' or 'wider than' becomes absurd. The correction is '10 times of the width of'.
3. It might be located right in the capital's posh area but the moment you step into this famous restaurant," cozy and warm enfolding you."

A. cozy and warm enfolds you B. cozy and warmth enfolds you C. coziness and warmth enfolds you D. coziness and warmth is enfolding you E. No correction required

Answer: Option C
Explanation: The last part is the main clause of the second sentence 'the moment you'. Hence it needs a finite verb. The sentence needs a verb in the present tense. Hence 'enfolds' should replace 'enfolding'. Also 'cozy and warm' is the subject which has to be given in the noun form. The correction is 'coziness and warmth enfolds you'.
Para Completion
1. Providing benefits for women on maternity leave and children is a societal responsibility which can be funded in a large country through a combination of general taxation and contributory payments from those who have the means. Health care should be treated as a right and deliveries handled without cost to women. ______________________________. Such a policy would harmonise the varying maternity benefit provisions found in different laws that govern labour at present.

A. The income guarantees during the pregnancy period can be ensured through a universal social insurance system. B. Beneficiaries covered by the latest amendment must be protected from discrimination through clear provisions. C. Mandating creche facilities to help women workers under the changed law is a forward-looking move. D. Women’s empowerment can be achieved through universal initiatives, not by imposing conditionalities to avail benefits.a E. Access to welfare support has become even more critical as workers migrate frequently due to economic changes.

Answer: Option A
Explanation: The paragraph starts while quoting that providing benefits for women and children is a societal responsibility. The sentence further states how the funds can be collected for this purpose. Out of the choices available, the sentence A clearly fits the blank most appropriately and the usage of the phrase ‘income guarantees’ confirms the same.
2. With the direction of global headwinds remaining uncertain, growth in government spending budgeted to be lower this year compared to last year, and private investment virtually absent, the lowering GDP numbers should serve as a reality check. _____________________________. While the government has vigorously underlined its reform achievements of the last three years, such as the Goods and Services Tax that rolls out in July, a mission-mode reforms reboot is urgently needed. And that can only begin if the problem is suitably acknowledged by policymakers.

A. While lower inflation and growth may soften the RBI’s outlook, there is little that monetary policy alone can do at this juncture to revive animal spirits. B. Returning to the 8% growth mark is going to be a big challenge. C. In fact, the only reason the 7.1% estimate has held up is that growth for the previous quarters was revised upwards. D. Private consumption grew at the slowest pace in five quarters, even as construction and manufacturing activities dipped sharply. E. Yet, whichever way one looks at it, the note ban seems to have exacerbated the problem, particularly for India’s large informal economy that the poor depend on, as even the World Bank has now noted.

Answer: Option B
Explanation: As it clearly seen that the sentence preceding the blank show's concern regarding the lowering GDP, the only sentence that fits the blank coherently is option B. It aligns to the idea introduced in the first sentence and connects well to the sentences that follow.
3. Fringe elements affiliated with the Bharatiya Janata Party (BJP) have been in the news ever since the party came to power. Activists who pretend to be associated with the Trinamool Congress in West Bengal and the Samajwadi Party in Uttar Pradesh too have had their day in the news. _________________________. First, the “fringe” is encouraged by the party as a strategy to appeal to more extreme elements within the party and to polarise politics. Second, and more specifically to the right wing, some believe that these individuals’ provocative actions and remarks are indicative of the government’s tacit support for Hindutva principles.

A. There are two reasons for the palpable polarization in politics. B. There are also local politicians who have misperceived favorable responses or miscalculated the impacts of their actions. C. There are two widely held explanations for such activism. D. In our view, this results from a systemic problem with our politics. E. Their two actions have served to embarrass the BJP and the Central government.

Answer: Option C
Explanation: Out of all the sentences, option C fits the blank most appropriately as it takes the discussion started in the paragraph further in the most logical manner. Moreover, usage of the adjective ‘such’ before the word ‘activism’ indicates that the sentence preceding the blank must have a reference of ‘activism’ and the presence of ‘activists’ in the very beginning of the sentence validates it.
Sentence Completion
1. His ----------- in his family’s position is great but he does not boast about it.

A. status B. pride C. deceit D. presumption

Answer: Option A
2. It was through the Second World War that Russia ----------- herself increased ----------- in power and wealth and prestige.

A. saw, abundantly B. notice, gullibly C. witnessed prodigiously D. None of these

Answer: Option C
3. For nations conscious of the ----------- of modern war, peace must be the goal of their foreign policies.

A. incidence B. perils C. potentialities D. redundancies

Answer: Option C
Fill in the blanks
1. I ________ not visit her ______ she is discharged

A. Shall, since B. Shall, until C. Probably, since D. Probably, until E. Probably, until

Answer: Option B
2. Our classes will _______ ____ next week

A. Commence, on B. Commence, by C. Commence, at D. Over, on E. Over, at

Answer: Option B
3. We are _________ to you for _______ hard work.

A. Grateful, your B. Helpful, your C. Helpful, our D. Helpful, their E. Thankful, our

Answer: Option A
Error Correction (Underlined Part)
1. The prices of essential commodities has risen unprecedentedly, causing a lot of hardship to the common man.

A. has rosen B. has rising C. have risen D. have rose E. no correction required

Answer: Option C
Explanation: 'The prices' which is the subject of the sentence is in the plural and hence it has to take a plural verb. 'Has risen' has to be replaced with 'have risen'.
2. In spite of all odds he pursued with his goal with girl and determination

A. he pursued to his goal B. he pursued on his goal C. he pursued into his goal D. he pursued his goal E. No correction required

Answer: Option D
Explanation: The verb 'pursued' should not be followed by any preposition, this makes choices (A), (B) and (C) incorrect.
3. Yoga and meditation can relieve people of their mental stress and fatigues.

A. mental stress and fatigue B. mental stresses and fatigues C. mental stress or fatigue D. mental stress or fatigues E. No correction required

Answer: Option A
Explanation: 'Fatigue' means tiredness and it is not used in the plural form. 'Fatigues' is inappropriate usage. Yoga relieves one of both 'stress and fatigue' and not just 'stress or fatigue' and thus choice (C) can be eliminated.
Passage Completion
1. For Ms. Merkel, walking the tightrope between her principles and maintaining a good relationship with an important ally is a challenge. Germany and the U.S. have historically shared values, but the current U.S. President has his own. At the G7 summit, six nations reaffirmed their commitment to the Paris climate pact; the U.S. refrained. Mr. Trump’s immigration order is the antithesis of Germany’s immigration policy. ____________________________. In a nutshell, Mr. Trump’s worldview is everything that Ms. Merkel’s is not.

A. It’s time Germany faced up to the new situation – with realism and above all with self-confidence. B. He even declined to sign onto a G7 statement endorsing the Paris climate deal. C. During his first visit to Europe as US president, Mr. Trump slammed European nations for not spending enough on defense. D. He is pushing aggressively for an ‘America First’ policy, even as Germany remains at the forefront of keeping the European Union together. E. US president, Mr. Trump did not reaffirm the US commitment to NATO’s mutual defense clause.

Answer: Option D
Explanation: In the given paragraph, the contradictory viewpoints of Ms. Merkel and Mr. Trump have already been shared in the statements preceding the blank. Among the given choices, option D is the one that actually summarizes the conflict of viewpoints between Ms. Merkel and Mr. Trump.
2. state institution faces monetary constraints in its operations and must constantly balance the exigencies of cash inflows and cash outflows. Thus, money flows, including the accumulation of debt and the acquisition of financial assets, are the very lifeblood of the system. ___________________________. While highly useful, such an approach often misses or obscures underlying monetary relations.

A. Despite this fact, most of our understanding of the macro-economy is based on the national accounts system which foregrounds current expenditure by various sectors. B. Given such lacunae, an alternative approach was originally suggested in 1947 by Morris Copeland, who promoted the Flow of Funds (FoF) account approach. C. These accounts examine flows across six sectors — households, government, private corporations, banks, other financial institutions (OFIs) and the Rest of the World. D. Despite the availability of the data, there have been very few attempts to provide a description of the money flows in the economy. E. Despite this India is moving from a bank-based to a market-based financial system.

Answer: Option A
Explanation: As we can observe the whole paragraph talks about the Macroeconomic approach and its drawbacks, option A is the only sentence among the given ones that fit the blank most appropriately. Though the word ‘approach’ in the sentence following the blank and in the sentence given as option B indicates a possible link at the first glance, the usage of the word ‘lacunae’ in option B confirms that it must follow the last sentence of the given paragraph as the last sentence of the paragraph specifies what the macroeconomic approach lacks.
3. The Goods and Services Tax (GST) is being flaunted as the single-biggest economic reform since the economic liberalization of 1991. Even critics of the tax, who complain about its complex four-slab rate structure, agree that it is a step in the right direction. The primary reason is that it does away with the present system of multiple Central and State taxes, replacing it with a much simpler tax system. __________________________. In the process, it is said, the new tax system does away with the barriers to free trade within and between States, effectively turning India into a single free market for goods and services.

A. Two, the number of taxes does not necessarily reflect the actual burden imposed on businesses by any tax system. B. Another supposed benefit of GST is that it is a tax on consumption, which replaces the current web of ‘cascading’ taxes in the production chain that increases prices and distorts production. C. A single, low tax rate might also turn out to be more burdensome if the cost of bureaucratic compliance is higher than under multiple, higher tax rates. D. Such distortion of production can lead to the rise in the prices of certain goods due to lower supply and a fall in the prices of others due to greater supply, which is clearly not the same as a general increase in prices. E. For skeptics, there is a good reason to doubt all these claimed benefits of the GST.

Answer: Option B
Explanation: The sentences preceding the blank talk about the benefits of the implementation of the GST. The sentence immediately preceding the blank states the primary reason for the appreciation the GST is receiving even by its critics. Clearly, the sentence for the blank has to be in line with the same chain of thoughts. Among the sentences given as options, sentence B specifies another benefit of GST in the context. The sentence most appropriately fits the blank.
Substitution
1. A person who withdraws from the world to live in seclusion and often in solitude

A. priest B. sage C. recluse D. iconoclast

Answer: Option C
2. great person or event in people’s memory

A. commensurate B. commiserate C. communicate D. commemorate

Answer: Option D
3. Murder of a man

A. Genocide B. Homicide C. Fratricide D. Regicide

Answer: Option B
Idioms and Phrases
Some proverbs/idioms are given below together with their meanings. Choose the correct meaning of proverb/idiom, If there is no correct meaning given, E (i.e.) 'None of these' will be the answer.
1. To leave someone in the lurch

A. To come to a compromise with someone B. A constant source of annoyance to someone C. To put someone at ease D. To desert someone in his difficulties E. None of these

Answer: Option D
2. To hit the nail right on the head

A. To do the right thing B. To destroy one's reputation C. To announce one's fixed views D. To teach someone a lesson E. None of these

Answer: Option A
Explanation: To do exactly the right thing; to do something in the most effective and efficient way.
3. To pick holes

A. To find some reason to quarrel B. To destroy something C. To criticize someone D. To cut some part of an item E. None of these

Answer: Option C
Antonyms
In the following questions choose the word which is the exact OPPOSITE of the given words.
1. COMMISSIONED

A. Started B. Closed C. Finished D. Terminated

Answer: Option D
2. ARROGANT

A. Humble B. Cowardly C. Egotistic D. Gentlemanly

Answer: Option A
3. EXTRAVAGANCE

A. Luxury B. Poverty C. Economical D. Cheapness

Answer: Option C
Sentence Arrangement
Directions (1-3): In the following questions, the sentence is split into four parts & named A, B, C & D. These four parts are not given in their proper order. Read the sentence/passage and find out which of the four combinations is connect. Then find the correct answer and indicate it by blackening the appropriate circle in the Answer Sheet.
1. A. that was open to all castes B. in 1932, Gandhi, at the time imprisoned in India, C. in 1915 Gandhi founded an ashram in Ahmedabad, India, D. embarked on a six-day fast to protest the British decision.

(a) CABD (b) ABCD (c) CBAD (d) CDAB

Answer: Option a
2. A. for more than 400 years B. the works of William Shakespeare C. known throughout the world D. has been performed in countless hamlets, villages, and cities.

(a) ACDB (b) BDCA (c) CBDA (d) CDBA

Answer: Option c
3. A. of 1974 saw Dr. A.P.J Abdul Kalam in B. the Pokhran-II nuclear tests conducted in India C. in 1998 after the original nuclear test D. a pivotal political, organizational and technical role.

(a) BDAC (b) BCAD (c) BADC (d) CDBA

Answer:Option b

Inserting Correct Mathematical Sign
1. If × stands for ‘addition’, ÷ stands for ‘subtraction’, + stands for ‘multiplication’ and stands for ‘division’, then 20 × 8 ÷ 8 – 4 + 2 =?

A. 80 B. 25 C. 24 D. 5

Answer: Option C
Explanation: By the Given data , We have the expression: 20 + 8 – 8 ÷ 4 × 2 = 20 + 8 – 2 × 2 = 20 + 8 – 4 = 24.
2. Which one of the given interchange in signs would make the given equation correct?

A. 4 + 8 – 12 = 12 B. 4 – 8 + 12 = 0 C. 8 + 4 – 12 = 24 D. 8 – 4 + 12 = 8

Answer: Option B
Explanation: On interchanging + and – and 4 and 8 in (b), we get the equation as 8 + 4 – 12 = 0 or 12 – 12 = 0 or 0 = 0, which is true.
3. Find out the two signs to be interchanged for making following equation correct: 5 + 3 x 8 – 12 ÷ 4 = 3

A. + and – B. – and ÷ C. + and x D. + and ÷

Answer: Option B
Mutual Relation Problem
1. Veena who is the sister-in-law of Ashok is the daughter-in-law of Kalyani. Dheeraj is the father of Sudeep who is the only brother of Ashok. How Kalyani is related to Ashok?

A. Mother-in-law B. Aunt C. Wife D. None of these

Answer: Option D
Explanation: Ashok is the only brother of Sudeep and Veena is the sister-in-law of Ashok. Hence Veena is the wife of Sudeep. Kalyani is the mother-in-law of Veena. Kalyani is the mother of Ashok.
2. Pointing to a woman, Abhijit said, "Her granddaughter is the only daughter of my brother." How is the woman related to Abhijit?

A. Sister B. Grandmother C. Mother-in-law D. Mother

Answer: Option D
Explanation: Daughter of Abhijit's brother → niece of Abhijit. Thus the granddaughter of the woman is Abhijit's niece. Hence, the woman is the mother of Abhijit.
3. Pointing to a person, Deepak said, "His only brother is the father of my daughter's father". How is the person related to Deepak?

A. Father B. Grandfather C. Uncle D. Brother-in-law

Answer: Option C
Explanation: Father of Deepak's daughter's father → Deepak's father. Hence, the person in the brother of Deepak's father. Therefore, the person is the uncle of Deepak.
Number Puzzle
1. Which number replaces the question mark?

A. 4 B. 7 C. 9 D. 11

Answer: 4
Explanation: Working in columns, the sum of the numbers in each column is always 14.
2. Which number replaces the question mark?

A. 9 B. 34 C. 21 D. 11

Answer: 9
Explanation : In each square of the diagram, the sum of the numbers is always 22.
3. Which number replaces the question mark?

A. 12 B. 16 C. 23 D. 34

Answer: 16
Explanation: Moving clockwise, around alternate segments in the chain, one sequence decreases by 1, 2, 3 and 4 each time, while the other increases by 2, 3, 4 and 5.
Human Relation
1. If X + Y means X is the daughter of Y; X - Y means X is the brother of Y; X % Y means X is the father of Y and X x Y means X is the sister of Y. Which of the following means I is the niece of J?

A. J - N % C x I B. I x C - N % J C. J + M x C % I D. I x C + N - J

Answer: Option D
Explanation: I x C → I is the sister of C C + N → C is the daughter of N and N - J → N is the brother of I. Hence, I is niece of J.
2. If M x N means M is the daughter of N; M + N means M is the father of N; M % N means M is the mother of N and M - N means M is the brother of N then P % Q + R - T x K indicates which relation of P to K?

A. Daughter-in-law B. Sister-in-law C. Aunt D. None of these

Answer: Option D
Explanation: P % Q → P is the mother of Q Q + R → Q is the father of R R - T → R is the brother of T Hence, → Q is the father of T T x K → T is the daughter of K Hence, → Q is the husband of K. Therefore, P is the mother-in-law of K.
3. Anupam said to a lady sitting in a car, "The only daughter of the brother of my wife is the sister-in-law of the brother of your sister." How the husband of the lady is related to Anupam?

A. Maternal uncle B. Uncle C. Father D. Son-in-law

Answer: Option D
Explanation: Anupam's son-in-law is the brother of the lady who was sitting in the car. Hence, the husband is also the son-in-law of Anupam.
Non-Verbal Reasoning
1. Choose the figure which is different from the rest.

A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option A
Explanation: The pins, equal in number to the number of sides in the main figure are attached to the midpoint of a side of the main figure in case of figures (2), (3), (4) and (5). In fig. (1), these pins are attached to a vertex of the main figure.
2. Choose the figure which is different from the rest.

A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option A
Explanation: In all other figures, there are two small line segments towards the pin and three small line segments towards the arrow.
3. Choose the figure which is different from the rest.

A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option D
Explanation: Only in fig. (4), both the parallel lines are bent in the same direction {i.e. towards the left). Distance and Direction Sense Test
1. A man walks 5 km toward the south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?

A. West B. South C. North-East D. South-West

Answer: Option D
Explanation:
Hence required direction is South-West.
2. Rasik walked 20 m towards the north. Then he turned right and walks 30 m. Then he turns right and walks 35 m. Then he turns left and walks 15 m. Finally he turns left and walks 15 m. In which direction and how many meters is he from the starting position?

A. 15 m West B. 30 m East C. 30 m West D. 45 m East

Answer: Option D
Explanation:

3. Starting from the point X, Jayant walked 15 m towards west. He turned left and walked 20 m. He then turned left and walked 15 m. After this he turned to his right and walked 12 m. How far and in which directions is now Jayant from X?

A. 32 m, South B. 47 m, East C. 42 m, North D. 27 m, South

Answer: Option A
Explanation:

Dictionary Words
1. Arrange the following words according to the dictionary: (a) Trinity (b) Tool (c) Town (d) Twist (e)Type

A. b, c, a, d, e B. c, a, d, b, e C. b, c, a, e, d D. d, c, b, a, e

Answer: Option A
Solution: Dictionary Order: (b) Tool (c) Town (a) Trinity (d) Twist (e)Type So, the correct order is b, c, a, d, e.
2. Arrange the following words as per order in the dictionary 1. Dyke 2. Dwindle 3. Dwell 4. Dye

A. 3, 2, 4, 1 B. 1, 3, 4, 2 C. 2, 1, 3, 4 D. 4, 2, 1, 3

Answer: Option A
Solution: Arranging the given words as per the dictionary order, 3. Dwell 2. Dwindle 4. Dye 1. Dyke Hence the correct dictionary order is 3, 2, 4, 1
3. Arrange the following words according to the dictionary. 1. Horse 2. Harness 3. Horizon 4. Horlicks 5. Hormone

A. 5, 1, 2, 3, 4 B. 5, 1, 3, 2, 4 C. 2, 3, 4, 5, 1 D. 2, 5, 1, 4, 3

Answer: Option C
Solution: after arranging as per the order of dictionary we get; Harness, Horizon, Horlicks, Hormone, Horse Hence the correct sequence is 2, 3, 4, 5, 1
Mathematical Operations (Assigning Value to Arithmetic Sign)
1. If ÷ means ×, – means +, × means – & + means ÷, then what will be the value of the following? 20+4×6–5÷7=?

A. 28 B. 32 C. 34 D. 36

Answer: Option C
2. P $ Q means divide P # Q means subtract P % Q means add P @ Q means multiply then, 70 # 30% 80 $ 20 @ 10 = ?

A. 60 B. 80 C. 20 D. 10

Answer: Option C
3. Which of the following equation will be correct if ÷ & +, 12 & 18 are interchanged with each other?

A. (90×18) + 18 = 60 B. (18+6) ÷ 12 = 2 C. (72÷18) × 18 = 72 D. (12+6) × 18 = 36

Answer: Option D
Analogy
1. Select a suitable figure from the Answer Figures that would replace the question mark (?).

A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option C
Explanation: The half-shaded leaf rotates 135oACW and the unshaded leaf rotates 135oCW.
2. Select a suitable figure from the Answer Figures that would replace the question mark (?).

A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option A
Explanation: The upper element is converted to an element similar to the lower elements and each one of the lower element is converted to an element similar to the upper element.
3. Select a suitable figure from the Answer Figures that would replace the question mark (?).

A. 1 B. 2 C. 3 D. 4 E. 5

Answer: Option C
Explanation: Except for the dots, the remaining part of the figure rotates through 180o and shifts to the opposite side of the square boundary.
Numerical Series
Directions (1-3): These questions are based on the following five numbers. 714, 927, 175, 593, 398
1. If these numbers are written with their digits in the increasing order, which number among them will become 2nd lowest?

A. 927 B. 593 C. 714 D. 175 E. None of these

Answer: Option D
Solution: 147, 279, 157, 359, 389
2. If 3rd digit of a 2nd highest number is divided by 1st digit of the lowest number, then what will be the final answer?

A. 2 B. 1 C. 4 D. 5 E. None of these

Answer: Option C
3. If these numbers are written with their digits in the increasing order, which number among them will be the highest number?

A. 175 B. 593 C. 398 D. 714 E. None of these

Answer: Option C
Tallest, Youngest Relation
Direction(1-3) There are five friends Sachin, Kunal, Mohit, Anuj, and Rohan. Sachin is shorter than Kunal but taller than Rohan. Mohit is tallest. Anuj is a little shorter than Kunal a little taller than Sachin.
1. Who is the second tallest?

A. Sachin B. Kunal C. Anuj D. Rohan E. None of these

Answer: Option B
2. Who is the shortest?

A. Rohan B. Sachin C. Anuj D. Kunal E. None of these

Answer: Option A
3.If they stand in the order of their heights, who will be in the middle?

A. Kunal B. Rohan C. Sachin D. Anuj E. None of these

Answer: Option D
Number Ranking & Time Sequence Test
1. In a queue, Amrita is 10th from the front while Mukul is 25th from behind and Mamta is just in the middle of the two. If there were 50 persons in the queue, what position does Mamta occupy from the front?

A. 20th B. 19th C. 18th D. 17th E. 21th

Answer: Option C
Explanation: Number of persons between Amrita and Mukul = 50 -(10 + 25) = 15. Since Mamta lies in the middle of these 15 persons, so Mamta's position is 8th from Amrita i.e. 18th from the front.
2. In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, Rita and Monika occupy seventeenth place from the right and eighteenth place from the left, respectively. How many girls are there in the row?

A. 25 B. 26 C. 27 D. Data Inadequate E. None of these.

Answer: Option B
Explanation: Since Rita and Monika exchange places, so Rita's new position is the same as Monika's earlier position. This position is 17th from the right and 10th from the left. Number of girls in the row = (16 + 1 + 9) = 26.
3. Asish leaves his house at 20 minutes to seven in the morning, reaches Kunal's house in 25 minutes, they finish their breakfast another 15 minutes and leave for their office which takes another 35 minutes. At what time do they leave Kunal's house to reach their office?

A. 7.40 a.m. B. 7.20 a.m. C. 7.45 a.m. D. 8.15 a.m. E. 7.55 a.m.

Answer: Option B
Explanation: Asish leaves his house at 6.40 a.m. He reaches Kunal's house in 25 minutes i.e., at 7.05 a.m. Both leave for office 15 minutes after 7.05 a.m. i.e., at 7.20 a.m.
Coding and Decoding
1. In a certain code ‘RATIONAL’ is written as ‘TARNOILA’. How would ‘BRUTAL’ be written in that code?

A. UBRTAL B. URBLAT C. UBRATL D. URBTAL E. None of these

Answer: Option B
Explanation: Letters are reversed in groups of 3 which can be shown as: RAT = TAR, ION = NOI. etc. So for BRUTAL BRU = UBR TAL = LAT so code for BRUTAL = UBRLAT
2. In a certain code ‘FORGIVE’ is written as ‘DPPHGWC’. How would ‘REQUEST’ be written in that code?

A. PFOVCUR B. TFOVCRU C. POFCVUR D. TOFCVUR E. None of these

Answer: Option E
Explanation: The letters move –2, +1, alternately R-2=P, E+1=F, Q-2=O, U+1=V and so on. So the code of REQUEST is PFOVCTR
3. In a certain code ‘PURPOSE’ is written as ‘UPPRSOE’. How would ‘WATER’ be written in that code?

A. WATRE B. AWTRE C. AWETR D. WEATR E. TRWAE

Answer: Option C
Explanation: Interchange the letter in the pair of two and keep the last letter as it is. WA = AW TE = ET So code of WATER is AWETR.
Assign Artificial Values to Mathematical Digit
1. If + means –, – means x, x means ÷ and ÷ means +, then— 16 ÷ 4 x 2 – 5 + 8 = ?

A. 58 B. 50 C. 44 D. 42 E. None of these

Answer: Option E
2. If + means ÷, ÷ means –, – means x and x means +, then— 12 + 2 x 9 ÷ 4 = ?

A. 9 B. 11 C. 4 D. 15 E. None of these

Answer: Option B
3. If + means –, – means x, x means ÷ and ÷ means +, then— 12 x 4 ÷ 12 + 5 – 3 = ?

A. 4 B. 15 C. 30 D. 17 E. None of these

Answer: Option E

Simple Interest
1. What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 9 years?

A. 1 : 3 B. 1 : 4 C. 2 : 3 D. Data inadequate E. None of these

Answer: Option C
Explanation: Let the principal be P and rate of interest be R%. Required ratio =[latex]\frac{\frac{P\times R\times 6}{100}}{\frac{P\times R\times 9}{100}}[/latex] =[latex]\frac{ P\times R\times 6}{ P\times R\times 9}[/latex] = [latex]\frac{6}{9}[/latex] = 2 : 3.
2. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

A. 5% B. 7% C. 7[latex]\frac{1}8{}[/latex]% D. 10%

Answer: Option D
Explanation: Let the rate be R% p.a. Then, ([latex]\frac{5000 \times R \times 2}{100}[/latex]) + ([latex]\frac{3000 \times R \times 4}{100}[/latex]) = 2200. 100R + 120R = 2200 R = [latex]\frac{2200}{220}[/latex] = 10. Rate = 10%.
3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?

A. Rs. 4462.50 B. Rs. 8032.50 C. Rs. 8900 D. Rs. 8925 E. None of these

Answer: Option D
Explanation: Principal = Rs. [latex]\frac{100 \times 4016.25}{9 \times 5}[/latex] = Rs. [latex]\frac{401625}{45}[/latex] = Rs. 8925.
Height and Distance.
1. From a point P on level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

A. 149 m B. 156 m C. 173 m D. 200 m

Answer: Option C
Explanation: Let AB be the tower.
Then, APB = 30° and AB = 100 m. [latex]\frac{AB}{AP}[/latex] = tan 30° = [latex]\frac{1}{\sqrt 3}[/latex] AP = (AB x [latex]\sqrt 3[/latex]) m = 100 [latex]\sqrt 3[/latex] m = (100 x 1.73) m = 173 m.
2. The angle of elevation of the sun, when the length of the shadow of a tree 3 times the height of the tree, is:

A. 30° B. 45° C. 60° D. 90°

Answer: Option A
Explanation: Let AB be the tree and AC be its shadow.
Then, [latex]\frac{AC}{AB}[/latex] = [latex] \sqrt 3[/latex] = cot = [latex] \sqrt 3[/latex] = 30°.
3. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

A. 2.3 m B. 4.6 m C. 7.8 m D. 9.2 m

Answer: Option D
Explanation: Let AB be the wall and BC be the ladder.
Then, ACB = 60° and AC = 4.6 m. [latex]\frac{AC}{BC}[/latex] = cos 60° = [latex]\frac{1}{2}[/latex] BC = 2 x AC = (2 x 4.6) m = 9.2 m.
Volume and Surface Area
1. 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

A. 20 cm B. 25 cm C. 35 cm D. 50 cm

Answer: Option B
Explanation: Total volume of water displaced = (4 x 50) m[latex]^{3}[/latex] = 200 m[latex]^{3}[/latex]. Rise in water level = [latex]\frac{200}{40 \times 20}[/latex] m 0.25 m = 25 cm.
2. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of the ground is:

A. 75 cu. m B. 750 cu. m C. 7500 cu. m D. 75000 cu. m

Answer: Option B
Explanation: 1 hectare = 10,000 m[latex]^{2}[/latex] So, Area = (1.5 x 10000) m[latex]^{2}[/latex] = 15000 m[latex]^{2}[/latex]. Depth = [latex]\frac{5}{100}[/latex] m = [latex]\frac{1}{20}[/latex] m. Volume = (Area x Depth) = 15000 x [latex]\frac{1}{20}[/latex] m[latex]^{3}[/latex] = 750 m[latex]^{3}[/latex].
Logarithm
1. If log 27 = 1.431, then the value of log 9 is:

A. 0.934 B. 0.945 C. 0.954 D. 0.958

Answer: Option C
Explanation: log 27 = 1.431 log (3[latex]^{3}[/latex] ) = 1.431 3 log 3 = 1.431 log 3 = 0.477 log 9 = log(3[latex]^{2}[/latex] ) = 2 log 3 = (2 x 0.477) = 0.954.
2. If [latex]log_{10}[/latex] 2 = 0.3010, the value of [latex]log_{10}[/latex] 80 is:

A. 1.6020 B. 1.9030 C. 3.9030 D. None of these

Answer: Option B
Explanation: [latex]log_{10}[/latex] 80 = [latex]log_{10}[/latex] (8 x 10) = [latex]log_{10}[/latex] 8 + [latex]log_{10}[/latex] 10 = [latex]log_{10}[/latex] (2[latex]^{3}[/latex] ) + 1 = 3 [latex]log_{10}[/latex] 2 + 1 = (3 x 0.3010) + 1 = 1.9030.
Races and Games
1. A runs 1[latex]\frac {2}{3}[/latex] times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?

A. 200 m B. 300 m C. 270 m D. 160 m

Answer: Option A
Explanation: The ratio of the speeds of A and B = [latex]\frac {5}{3}[/latex] : 1 = 5 : 3. Thus, in the race of 5 m, A gains 2m over B. 2m is gained by A in a race of 5m. 80m will be gained by A in race of ([latex]\frac {5}{2}[/latex] x 80) m = 200 m. Winning post is 200 m away from the starting point.
2. In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:

A. 22.75 m B. 25 m C. 19.5 m D. 7[latex]\frac {4}{7}[/latex]m

Answer: Option B
Explanation: A : B = 200 : 169. A : C = 200 : 182. [latex]\frac {C}{B}[/latex] = ([latex]\frac {C}{A}[/latex] x [latex]\frac {A}{B}[/latex]) = ([latex]\frac {182}{200}[/latex] x [latex]\frac {200}{169}[/latex]) = 182 : 169. When C covers 182 m, B covers 169 m. When C covers 350 m, B covers ([latex]\frac {169}{182}[/latex] x 350) m = 325 m. Therefore, C beats B by (350 - 325) m = 25 m.
Simplification
1. If a - b = 3 and a[latex]^{2}[/latex] + b[latex]^{2}[/latex] = 29, find the value of ab.

A. 10 B. 12 C. 15 D. 18

Answer: Option A
Explanation: 2ab = (a[latex]^{2}[/latex] + b[latex]^{2}[/latex]) - (a - b)[latex]^{2}[/latex] = 29 - 9 = 20 ab = 10.
2. To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifths of its present?

A. 10 B. 35 C. 62.5 D. Cannot be determined E. None of these

Answer: Option C
Explanation: Let the capacity of 1 bucket = x. Then, the capacity of tank = 25x. New capacity of bucket = [latex]\frac {2}{5}[/latex]x Required number of buckets = [latex]\frac {25 \times x}{(2 \times x/5)}[/latex] = 25x x [latex]\frac {5}{2 \times x}[/latex] = [latex]\frac {125}{2}[/latex] = 62.5
Time and Distance
1. The ratio between the speeds of two trains is 7:8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

A. 70 km/hr B. 75 km/hr C. 84 km/hr D. 87.5 km/hr

Answer: Option D
Explanation: Let the speed of two trains be 7x and 8x km/hr. Then, 8x = [latex]\frac {400}{4}[/latex] = 100 x = [latex]\frac {100}{8}[/latex] = 12.5 Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
2. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

A. 5 kmph B. 6 kmph C. 6.25 kmph D. 7.5 kmph

Answer: Option A
Explanation: Let Abhay's speed be x km/hr. Then, [latex]\frac {30}{x}[/latex] - [latex]\frac {30}{2x}[/latex] = 3 6x = 30 x = 5 km/hr.
Chain Rule
1. If the cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?

A. Rs.[latex]\frac {xy}{d}[/latex] B. Rs. (xd) C. Rs. (yd) D. Rs. [latex]\frac {yd}{x}[/latex]

Answer: Option D
Explanation: Cost of x metres = Rs. d. Cost of 1 metre = Rs. [latex]\frac {d}{x}[/latex] Cost of y metres = Rs. ([latex]\frac {d}{x}[/latex] . y) = Rs. [latex]\frac {yd}{x}[/latex] .
2. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

A. 48 paise B. 54 paise C. 56 paise D. 72 paise

Answer: Option A
Explanation: Let the required weight be x kg. Less weight, Less cost (Direct Proportion) 250 : 200 :: 60 : x = 250 x x = (200 x 60) x= [latex]\frac {(200 \times 60)}{250}[/latex] x = 48.
Permutation and Combination
1. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

A. 360 B. 480 C. 720 D. 5040 E. None of these

Answer: Option C
Explanation: The word 'LEADING' has 7 different letters. When the vowels EAI are always together, they can be supposed to form one letter. Then, we have to arrange the letters LNDG (EAI). Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways. The vowels (EAI) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.
2. In how many ways can the letters of the word 'LEADER' be arranged?

A. 72 B. 144 C. 360 D. 720 E. None of these

Answer: Option C
Explanation: The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R. The required number of ways = [latex]\frac {6!}{(1!)(2!)(1!)(1!)(1!)}[/latex] = 360.
Surds and Indices
1. If 5[latex]^{a}[/latex] = 3125, then the value of 5[latex]^{(a - 3)}[/latex] is:

A. 25 B. 125 C. 625 D. 1625

Answer: Option A
Explanation: 5[latex]^{a}[/latex] = 3125 = 5[latex]^{a}[/latex] = 5[latex]^{5}[/latex] a = 5. 5[latex]^{(a-3)}[/latex] = 5[latex]^{(5 - 3)}[/latex] = 5[latex]^{2}[/latex] = 25.
2. If m and n are whole numbers such that m[latex]^{n}[/latex] = 121, the value of (m - 1)[latex]^{n + 1}[/latex] is:

A. 1 B. 10 C. 121 D. 1000

Answer: Option D
Explanation: We know that 11[latex]^{2}[/latex] = 121. Putting m = 11 and n = 2, we get: (m - 1)[latex]^{n + 1}[/latex] = (11 - 1)[latex]^{(2 + 1)}[/latex] = 103 = 1000.
Pipes and Cistern
1. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

A. [latex]\frac {5}{11}[/latex] B. [latex]\frac {6}{11}[/latex] C. [latex]\frac {7}{11}[/latex] D. [latex]\frac {8}{11}[/latex]

Answer: Option B
Explanation: Part filled by (A + B + C) in 3 minutes = 3 ([latex]\frac {1}{30} + \frac {1}{20} + \frac {1}{10}[/latex]) = 3 x [latex]\frac {11}{60}[/latex] = [latex]\frac {11}{20}[/latex] . Part filled by C in 3 minutes = [latex]\frac {3}{10}[/latex] . Required ratio =([latex]\frac {3}{10}[/latex] x [latex]\frac {20}{11}[/latex]) = [latex]\frac {6}{11}[/latex].
2. A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

A. 20 hours B. 25 hours C. 35 hours D. Cannot be determined E. None of these

Answer: Option C
Explanation: Suppose pipe A alone takes x hours to fill the tank. Then, pipes B and C will take [latex]\frac {x}{2}[/latex]and [latex]\frac {x}{4}[/latex] hours respectively to fill the tank. [latex]\frac {1}{x}[/latex] + [latex]\frac {2}{x}[/latex] + [latex]\frac {4}{x}[/latex] = [latex]\frac {1}{5}[/latex] [latex]\frac {7}{x}[/latex] = [latex]\frac {1}{5}[/latex] x = 35 hrs.
Boats and Streams
1. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

A. 4 km/hr B. 6 km/hr C. 8 km/hr D. Data inadequate

Answer: Option B
Explanation: Rate downstream = [latex]\frac {16}{2}[/latex] kmph = 8 kmph. Rate upstream = [latex]\frac {16}{4}[/latex] kmph = 4 kmph. Speed in still water = [latex]\frac {1}{2}[/latex](8 + 4) kmph = 6 kmph.
2. A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:

A. 2 mph B. 2.5 mph C. 3 mph D. 4 mph

Answer: Option A
Explanation: Let the speed of the stream x mph. Then, Speed downstream = (10 + x) mph, Speed upstream = (10 - x) mph. [latex]\frac {36}{(10 - x)}[/latex] - [latex]\frac {36}{(10 + x)}[/latex] = [latex]\frac {90}{60}[/latex] 72x x 60 = 90 (100 - x[latex]^{2}[/latex]) x[latex]^{2}[/latex] + 48x - 100 = 0 (x+ 50)(x - 2) = 0 x = 2 mph.
Numbers
1. 1397 x 1397 = ?

A. 1951609 B. 1981709 C. 18362619 D. 2031719 E. None of these

Answer: Option A
Explanation: 1397 x 1397 = (1397)[latex]^{2}[/latex] = (1400 - 3)[latex]^{2}[/latex] = (1400)[latex]^{2}[/latex] + (3)[latex]^{2}[/latex] - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609.
2. 72519 x 9999 = ?

A. 725117481 B. 674217481 C. 685126481 D. 696217481 E. None of these

Answer: Option A
Explanation: 72519 x 9999 = 72519 x (10000 - 1) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481.
Partnership
1. A, B and C enter into a partnership in the ratio [latex]\frac {7}{4}[/latex] :[latex]\frac {4}{3}[/latex] : [latex]\frac {6}{5}[/latex] . After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:

A. Rs. 2100 B. Rs. 2400 C. Rs. 3600 D. Rs. 4000

Answer: Option D
Explanation: Ratio of initial investments = [latex]\frac {7}{2}[/latex] : [latex]\frac {4}{3}[/latex] : [latex]\frac {6}{5}[/latex] = 105 : 40 : 36. Let the initial investments be 105x, 40x and 36x. A : B : C = (105x x 4 + [latex]\frac {150}{100}[/latex] x 105x x 8) : (40x x 12) : (36x x 12) = 1680x : 480x : 432x = 35 : 10 : 9. Hence, B's share = Rs. (21600 x [latex]\frac {10}{54}[/latex]) = Rs. 4000.
2. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?

A. Rs. 7500 B. Rs. 9000 C. Rs. 9500 D. Rs. 10,000

Answer: Option A
Explanation: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3. B's share = Rs. (25000 x [latex]\frac {3}{10}[/latex]) = Rs. 7,500.
Ratio and Proportion
1. In a mixture 60 liters, the ratio of milk and water 2: 1. If this ratio is to be 1: 2, then the quantity of water to be further added is:

A. 20 liters B. 30 liters C. 40 liters D. 60 liters

Answer: Option D
Explanation: Quantity of milk = (60 x [latex]\frac {2}{3}[/latex] litres = 40 litres. Quantity of water in it = (60- 40) litres = 20 litres. New ratio = 1 : 2 Let quantity of water to be added further be x liters. Then, milk : water = [latex]\frac {40}{20 + x}[/latex]. Now, [latex]\frac {40}{20 + x}[/latex] = [latex]\frac {1}{2}[/latex] 20 + x = 80 x = 60. The quantity of water to be added = 60 liters.
2. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40: 57. What is Sumit's salary?

A. Rs. 17,000 B. Rs. 20,000 C. Rs. 25,500 D. Rs. 38,000

Answer: Option D
Explanation: Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively. Then,[latex]\frac {2x + 4000}{3x + 4000}[/latex] = [latex]\frac {40}{57}[/latex] 57(2x + 4000) = 40(3x + 4000) 6x = 68,000 3x = 34,000 Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.
Problems on H.C.F and L.C.M
1. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:

A. 101 B. 107 C. 111 D. 185

Answer: Option C
Explanation: Let the numbers be 37a and 37b. Then, 37a x 37b = 4107 1369ab = 4107 ab = [latex]\frac { 4107}{1369}[/latex] ab = 3. Now, co-primes with product 3 are (1, 3). So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111). Greater number = 111.
2. The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:

A. 1677 B. 1683 C. 2523 D. 3363

Answer: Option B
Explanation: L.C.M. of 5, 6, 7, 8 = 840. The required number is of form 840k + 3 Least value of k for which (840k + 3) is divisible by 9 is k = 2. Required number = (840 x 2 + 3) = 1683.
3. 252 can be expressed as a product of primes as:

A. 2 x 2 x 3 x 3 x 7 B. 2 x 2 x 2 x 3 x 7 C. 3 x 3 x 3 x 3 x 7 D. 2 x 3 x 3 x 3 x 7

Answer: Option A
Explanation: Clearly, 252 = 2 x 2 x 3 x 3 x 7.
Banker’s Discount
1. The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:

A. Rs. 960 B. Rs. 840 C. Rs. 1020 D. Rs. 760

Answer: Option C
Explanation: T.D. = [latex]\frac {B.G. \times 100}{R \times T}[/latex] = Rs. [latex]\frac {270 \times 100}{12 \times 3}[/latex] = Rs. 750. B.D. = Rs.(750 + 270) = Rs. 1020.
2. The banker's discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:

A. Rs. 360 B. Rs. 432 C. Rs. 540 D. Rs. 1080

Answer: Option A
Explanation: Sum = [latex]\frac {B.D. \times T.D.}{B.D. - T.D.}[/latex] = Rs. [latex]\frac {72 \times 60}{72 - 60}[/latex] = Rs. [latex]\frac {72 \times 60}{12}[/latex]= Rs. 360.
Compound Interest
1. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?

A. Rs. 2160 B. Rs. 3120 C. Rs. 3972 D. Rs. 6240 E. None of these

Answer: Option C
Explanation: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years. R = [latex]\frac {100 \times 60}{100 \times 6}[/latex] = 10% p.a. Now, P = Rs. 12000. T = 3 years and R = 10% p.a. C.I. = Rs. (12000 x((1 + [latex]\frac {10}{100})^{3}[/latex] - 1)) = Rs. (12000 x [latex]\frac {331}{1000}[/latex]) = 3972.
2. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?

A. Rs. 8600 B. Rs. 8620 C. Rs. 8820 D. None of these

Answer: Option C
Explanation: Amount = Rs. (8000 x (1 + [latex]\frac {5}{100})^{2}[/latex]) = Rs. (8000 x [latex]\frac {21}{20}[/latex] x [latex]\frac {21}{20}[/latex]) = Rs. 8820.
Area
1. In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of the ground is:

A. 75 cu. m B. 750 cu. m C. 7500 cu. m D. 75000 cu. m

Answer: Option B
Explanation: 1 hectare = 10,000 m[latex]^{2}[/latex] So, Area = (1.5 x 10000) m[latex]^{2}[/latex] = 15000 m[latex]^{2}[/latex]. Depth = [latex]\frac {5}{100}[/latex] m = [latex]\frac {1}{20}[/latex] m. Volume = (Area x Depth) = 15000 x [latex]\frac {1}{20}[/latex] m[latex]^{3}[/latex] = 750 m[latex]^{3}[/latex].
2. A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

A. 720 B. 900 C. 1200 D. 1800

Answer: Option C
Explanation: 2(15 + 12) x h = 2(15 x 12) h = [latex]\frac {180}{27}[/latex]m = [latex]\frac {20}{3}[/latex]m. Volume = 15 x 12 x [latex]\frac {20}{3}[/latex]m[latex]^{3}[/latex] = 1200 m[latex]^{3}[/latex].
Time and Work
1. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A. 20 days B. 22 [latex]\frac {1}{2}[/latex]days C. 25 days D. 30 days

Answer: Option B
Explanation: The ratio of times taken by A and B = 1 : 3. The time difference is (3 - 1) 2 days while B takes 3 days and A takes 1 day. If the difference in time is 2 days, B takes 3 days. If difference of time is 60 days, B takes ([latex]\frac {3}{2}[/latex] x 60) = 90 days. So, A takes 30 days to do the work. A's 1 day's work = [latex]\frac {1}{30}[/latex] B's 1 day's work = [latex]\frac {1}{90}[/latex] (A + B)it's 1 day's work = [latex]\frac {1}{30}[/latex] + [latex]\frac {1}{90}[/latex] = [latex]\frac {4}{90}[/latex] = [latex]\frac {2}{45}[/latex] A and B together can do the work in [latex]\frac {45}{2}[/latex] = 22 [latex]\frac {1}{2}[/latex] days.
2. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

A. 11:30 A.M. B. 12 noon C. 12:30 P.M. D. 1:00 P.M.

Answer: Option D
Explanation: (P + Q + R)'s 1 hour's work = ([latex]\frac {1}{8}[/latex] + [latex]\frac {1}{10}[/latex] + [latex]\frac {1}{12}[/latex] = [latex]\frac {37}{120}[/latex] Work was done by P, Q, and R in 2 hours =([latex]\frac {37}{120}[/latex] x 2 )= [latex]\frac {37}{60}[/latex] Remaining work = ( 1 - [latex]\frac {37}{60}[/latex]) = [latex]\frac {23}{60}[/latex]. (Q + R)'s 1 hour's work = ([latex]\frac {1}{10}[/latex] + [latex]\frac {1}{12}[/latex] ) = [latex]\frac {11}{60} [/latex]. Now, [latex]\frac {11}{60}[/latex] work is done by Q and R in 1 hour. So, [latex]\frac {23}{60}[/latex] work will be done by Q and R in ( [latex]\frac {60}{11}[/latex] x [latex]\frac {23}{60}[/latex]) = [latex]\frac {23}{11}[/latex] hours = 2 hours. So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
Allegation or Mixture
1. A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

A. 4 litres, 8 litres B. 6 litres, 6 litres C. 5 litres, 7 litres D. 7 litres, 5 litres

Answer: Option B
Explanation: Let the cost of 1 litre milk be Re. 1 Milk in 1 litre mix. in 1st can = [latex]\frac {3}{4}[/latex] litre, C.P. of 1 litre mix. in 1st can Re. [latex]\frac {3}{4}[/latex] Milk in 1 litre mix. in 2nd can =[latex]\frac {1}{2}[/latex] litre, C.P. of 1 litre mix. in 2nd can Re. [latex]\frac {1}{2}[/latex] Milk in 1 litre of final mix. = [latex]\frac {5}{8}[/latex] litre, Mean price = Re. [latex]\frac {5}{8}[/latex] By the rule of alligation, we have:
Ratio of two mixtures = [latex]\frac {1}{8}[/latex] : [latex]\frac {1}{8}[/latex] = 1 : 1. So, quantity of mixture taken from each can = ([latex]\frac {1}{2}[/latex] x 12) = 6 litres.
2. A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

A. 4% B. 6[latex]\frac {1}{4}[/latex]% C. 20% D. 25%

Answer: Option C
Explanation: Let C.P. of 1 litre milk be Re. 1 Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%. C.P. of 1 litre mixture = Re.([latex]\frac {100}{125}[/latex] x 1) = [latex]\frac {4}{5}[/latex] By the rule of alligation, we have:
Ratio of milk to water = [latex]\frac {4}{5}[/latex] : [latex]\frac {1}{5}[/latex] = 4 : 1. Hence, percentage of water in the mixture = ([latex]\frac {1}{5}[/latex] x 100) % = 20%.
3. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

A. Rs. 18 B. Rs. 18.50 C. Rs. 19 D. Rs. 19.50

Answer: Option A
Explanation: Let the price of the mixed variety be Rs. x per kg. By rule of alligation, we have:
[latex]\frac {(20 - x)}{(x - 15)}[/latex] = [latex]\frac {2}{3}[/latex] 60 - 3x = 2x - 30 5x = 90 x = 18.
Decimal Fraction
1. [latex]\frac {4.2 \times 4.2 - 1.9 \times 1.9}{2.3 \times 6.1}[/latex] is equal to:

A. 0.5 B. 1.0 C. 20 D. 22

Answer: Option B
Explanation: Given Expression = [latex]\frac {a^{2} - b^{2} }{(a + b)(a - b)}[/latex]) = ([latex]\frac {a^{2} - b^{2}} {a^{2} - b^{2}}[/latex]) = 1.
2. If [latex]\frac {144}{0.144}[/latex] = [latex]\frac {14.4}{x}[/latex], then the value of x is:

A. 0.0144 B. 1.44 C. 14.4 D. 144

Answer: Option A
Explanation: [latex]\frac {144}{0.144}[/latex] = [latex]\frac {14.4}{x}[/latex] [latex]\frac {144 \times 1000}{144}[/latex] =[latex]\frac {14.4}{x}[/latex] x =[latex]\frac {14.4}{1000}[/latex] = 0.0144
Probability
1. What is the probability of getting a sum 9 from two throws of a dice?

A.[latex]\frac {1}{6}[/latex] B.[latex]\frac {1}{8}[/latex] C.[latex]\frac {1}{9}[/latex] D.[latex]\frac {1}{12}[/latex]

Answer: Option C
Explanation: In two throws of a dice, n(S) = (6 x 6) = 36. Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}. P(E) = [latex]\frac {n(E)}{n(S)}[/latex] = [latex]\frac {4}{36}[/latex] = [latex]\frac {1}{9}[/latex].
2. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A.[latex]\frac {1}{2}[/latex] B.[latex]\frac {3}{4}[/latex] C.[latex]\frac {3}{8}[/latex] D.[latex]\frac {5}{16}[/latex]

Answer: Option B
Explanation: In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36. Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} n(E) = 27. P(E) = [latex]\frac {n(E)}{n(S)}[/latex] = [latex]\frac {27}{36}[/latex] = [latex]\frac {3}{4}[/latex].
Average
1. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A. 23 years B. 24 years C. 25 years D. None of these

Answer: Option A
Explanation: Let the average age of the whole team by x years. 11x - (26 + 29) = 9(x -1) 11x - 9x = 46 2x = 46 x = 23. So, average age of the team is 23 years.
2. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

A. 3500 B. 4000 C. 4050 D. 5000

Answer: Option B
Explanation: Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) P + R = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv) Subtracting (ii) from (iv), we get P = 4000. P's monthly income = Rs. 4000.
Stocks and Share
1. A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:

A. 3 : 4 B. 3 : 5 C. 4 : 5 D. 16 : 15

Answer: Option D
Explanation: For an income of Re. 1 in 9% stock at 96, investment = Rs.[latex]\frac {96}{9}[/latex] = Rs.[latex]\frac {32}{3}[/latex] For an income Re. 1 in 12% stock at 120, investment = Rs.[latex]\frac {120}{12}[/latex] = Rs. 10. Ratio of investments = [latex]\frac {32}{3}[/latex] : 10 = 32 : 30 = 16 : 15.
2. The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being [latex]\frac {1}{4}[/latex] %, is:

A. Rs. 108.25 B. Rs. 112.20 C. Rs. 124.75 D. Rs. 125.25

Answer: Option C
Explanation: For an income of Rs. 756, investment = Rs. 9000. For an income of Rs.[latex]\frac {21}{2}[/latex], investment = Rs.([latex]\frac {9000}{756}[/latex] x [latex]\frac {21}{2}[/latex]) = Rs. 125. For a Rs. 100 stock, investment = Rs. 125. Market value of Rs. 100 stock = Rs. (125 - [latex]\frac {1}{4}[/latex]) = Rs. 124.75
Square Root and Cube Root
1. What should come in place of both x in the equation [latex]\frac {x}{\sqrt {128}}[/latex] = [latex]\frac {\sqrt {162}}{x}[/latex].

A. 12 B. 14 C. 144 D. 196

Answer: Option A
Explanation: Let[latex]\frac {x}{\sqrt {128}}[/latex] = [latex]\frac {\sqrt {162}}{x}[/latex] Then x[latex]^{2}[/latex] = [latex]\sqrt{128 \times 162}[/latex] = [latex]\sqrt{64 \times 2 \times 18 \times 9}[/latex] =[latex]\sqrt{82 \times 62 \times 32}[/latex] =[latex]\sqrt{8 \times 6 \times 3}[/latex] = [latex]\sqrt{144}[/latex]. x = [latex]\sqrt{144}[/latex] = 12.
2. If 3[latex]\sqrt{5}[/latex] + [latex]\sqrt{125}[/latex] = 17.88, then what will be the value of [latex]\sqrt{80}[/latex] + 6[latex]\sqrt{5}[/latex] ?

A. 13.41 B. 20.46 C. 21.66 D. 22.35

Answer: Option D
Explanation: 3[latex]\sqrt{5}[/latex]+ [latex]\sqrt{125}[/latex]= 17.88 3[latex]\sqrt{5}[/latex] + [latex]\sqrt{12 \times 5}[/latex] = 17.88 3[latex]\sqrt{5}[/latex] + 5[latex]\sqrt{5}[/latex] = 17.88 8[latex]\sqrt{5}[/latex] = 17.88 [latex]\sqrt{5}[/latex] = 2.235 = [latex]\sqrt{80}[/latex] + 6[latex]\sqrt{5}[/latex] = [latex]\sqrt{16 \times 5}[/latex] + 6[latex]\sqrt{5}[/latex] = 4[latex]\sqrt{5}[/latex] + 6[latex]\sqrt{5}[/latex] = 10[latex]\sqrt{5}[/latex] = (10 x 2.235) = 22.35
Problems on Ages
1. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?

A. 24 B. 27 C. 40 D. Cannot be determined E. None of these

Answer: Option A
Explanation: Let the present ages of Sameer and Anand be 5x years and 4x years respectively. Then,[latex]\frac {5x + 3}{4x + 3}[/latex] = [latex]\frac {11}{9}[/latex] 9(5x + 3) = 11(4x + 3) 45x + 27 = 44x + 33 45x - 44x = 33 - 27 x = 6. Anand's present age = 4x = 24 years.
2. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

A. 14 years B. 18 years C. 20 years D. 22 years

Answer: Option D
Explanation: Let the son's present age be x years. Then, man's present age = (x + 24) years. (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 x = 22.