TCS NQT Aptitude Practice Questions
Introduction
The TCS National Qualifier Test (NQT) is a comprehensive assessment used by Tata Consultancy Services for recruiting fresh graduates across various roles. The Aptitude section forms a critical component of this test, evaluating candidates' mathematical reasoning, analytical thinking, and problem-solving abilities.
This guide provides an in-depth exploration of all topics covered in the TCS NQT Aptitude section, along with detailed preparation strategies and high-quality resources to help you maximize your score.
Test Pattern and Structure
TCS NQT follows an integrated test pattern that evaluates candidates across various competencies. Understanding this structure is essential for effective preparation.
| Section | Duration (mins) |
|---|---|
| Part A - Foundation Section | 75 |
| Numerical Ability | 25 |
| Verbal Ability | 25 |
| Reasoning Ability | 25 |
| Part B - Advanced Section | 115 |
| Advanced Quantitative & Reasoning Ability | 25 |
| Advanced Coding | 90 |
| Total Duration | 190 |
Hiring Categories
Based on test performance, candidates will qualify for one of the following hiring categories:
- Prime
- Top tier; requires excellent performance in both Foundation and Advanced sections
- Digital
- Middle tier; requires good performance in both Foundation and Advanced sections
- Ninja
- Entry tier; can be achieved with good performance in just the Foundation section
Important: While all candidates are encouraged to attempt both sections, the Advanced section is mandatory for those aspiring for Digital or Prime offers.
Foundation Section (75 Minutes)
1. Numerical Ability (25 Minutes)
The Numerical Ability section tests your mathematical aptitude and problem-solving skills within a 25-minute timeframe.
Core Topics in Numerical Ability
- Number Systems and Arithmetic
- HCF and LCM problems
- Prime numbers and factorization
- Divisibility rules and remainder problems
- Number properties (even, odd, prime, composite)
- Unit digit calculations
- Factorial problems
- Percentage, Ratio, and Proportion
- Percentage calculations and conversions
- Percentage increase/decrease
- Ratio simplification and division
- Direct and inverse proportion
- Mixture and alligation problems
- Partnership calculations
- Profit, Loss, and Discount
- Profit and loss percentage calculations
- Marked price vs. selling price problems
- Discount calculations
- Successive discounts
- Cost price and selling price relationships
- Time, Speed, and Distance
- Speed, time, and distance relationships
- Relative speed (same/opposite directions)
- Average speed calculations
- Boats and streams
- Trains crossing platforms/bridges
- Race problems
- Time and Work
- Work rate calculations
- Time to complete work together
- Work efficiency comparisons
- Pipes and cisterns
- Work done in partial time
- Algebra and Sequences
- Linear and quadratic equations
- Sequences and series (AP, GP, HP)
- Word problems requiring algebraic modeling
- Function problems
- Pattern recognition
- Geometry and Mensuration
- Properties of triangles, circles, quadrilaterals
- Area and perimeter of 2D shapes
- Volume and surface area of 3D objects
- Coordinate geometry basics
- Pythagorean theorem applications
- Data Interpretation
- Tables and charts analysis
- Percentage and ratio calculations from data
- Trend analysis
- Comparative data analysis
- Inferential questions based on data
2. Verbal Ability (25 Minutes)
The Verbal Ability section assesses your English language proficiency, reading comprehension, and grammatical knowledge.
Core Topics in Verbal Ability
- Reading Comprehension
- Passage-based questions
- Inference drawing
- Author's tone/attitude identification
- Main idea and supporting details
- Fact vs. opinion distinction
- Vocabulary
- Synonyms and antonyms
- Contextual meaning of words
- Word usage in sentences
- Idioms and phrases
- Foreign words commonly used in English
- Grammar
- Parts of speech
- Subject-verb agreement
- Tenses and their usage
- Articles and prepositions
- Common grammatical errors
- Sentence Completion
- Fill in the blanks
- Sentence improvement
- Error identification and correction
- Coherence and cohesion
- Para Jumbles
- Rearranging sentences to form coherent paragraphs
- Identifying opening and closing sentences
- Logical flow of ideas
- Transition words and their usage
- Verbal Reasoning
- Analogy
- Odd one out
- Word relationships
- Logical deduction from textual information
3. Reasoning Ability (25 Minutes)
The Reasoning Ability section evaluates your logical thinking, pattern recognition, and problem-solving capabilities.
Core Topics in Reasoning Ability
- Logical Reasoning
- Syllogisms
- Statement and assumptions
- Statement and conclusions
- Logical deductions
- Strong and weak arguments
- Analytical Reasoning
- Seating arrangements (linear and circular)
- Blood relations
- Direction sense
- Ordering and ranking
- Time sequences and temporal reasoning
- Data Arrangement
- Tabulation
- Classification
- Sequential ordering
- Matrix arrangements
- Distribution problems
- Pattern Recognition
- Number series
- Letter series
- Mixed series
- Coding-decoding
- Symbol-based patterns
- Verbal Reasoning
- Analogies
- Classifications
- Logical word sequence
- Logical word grouping
- Word puzzles
- Non-verbal Reasoning
- Figure series
- Mirror images
- Paper folding and cutting
- Pattern completion
- Rule detection in figures
Advanced Section (115 Minutes)
The Advanced Section is mandatory for candidates aspiring for Digital or Prime offers and consists of two parts.
1. Advanced Quantitative & Reasoning Ability (25 Minutes)
This section includes more challenging mathematical and logical reasoning problems. It builds upon the foundation section but with increased complexity and depth.
Core Topics in Advanced Quantitative Ability
- Probability and Statistics
- Probability of events (simple, compound, conditional)
- Permutation and combination
- Binomial distribution basics
- Data interpretation using statistical measures
- Expected value problems
- Advanced Algebra
- Quadratic and higher degree equations
- Logarithms and exponential equations
- Functions and relations
- Inequalities and absolute values
- Complex numbers basics
- Advanced Geometry
- Coordinate geometry (lines, circles, parabola)
- 3D geometry problems
- Trigonometric applications
- Area and volume optimization problems
- Vectors basics
- Advanced Number Theory
- Modular arithmetic
- Diophantine equations
- Advanced divisibility and remainders
- Number theoretic functions
- Congruence relations
Core Topics in Advanced Reasoning
- Complex Logical Reasoning
- Multi-level syllogisms
- Complex logical deductions
- Conditional reasoning problems
- Logical puzzles with multiple variables
- Truth-teller and liar puzzles
- Advanced Analytical Reasoning
- Complex scheduling problems
- Multi-dimensional arrangement puzzles
- Network and route problems
- Game theory basics
- Decision trees and probability
- Advanced Pattern Recognition
- Complex number and letter series
- Multi-rule patterns
- Integrated visual-verbal patterns
- Pattern transformation rules
- Predictive sequence problems
2. Advanced Coding (90 Minutes)
The Advanced Coding section evaluates your programming skills and algorithm development abilities. This section is crucial for Digital and Prime hiring categories.
Core Topics in Advanced Coding
- Programming Fundamentals
- Data types and variables
- Control structures (loops, conditionals)
- Functions and recursion
- Input/output handling
- Basic OOP concepts
- Data Structures
- Arrays and strings
- Linked lists
- Stacks and queues
- Trees and graphs
- Hash tables
- Algorithms
- Searching and sorting
- Recursion and dynamic programming
- Greedy algorithms
- Graph algorithms
- Time and space complexity analysis
- Problem-Solving Approaches
- Brute force solutions
- Optimization techniques
- Edge case handling
- Multiple approach comparison
- Test case development
Common Programming Languages Accepted
- Java
- C/C++
- Python
- JavaScript
- C#
TCS NQT Aptitude Practice Question
1- A sum of Rs. 3000 is distributed amongst A, B, and C. A gets 2/3 of what B and C got together and C gets 1/3 of what A and B got together. C's share is?
- a) Rs. 1200
- b) Rs. 2250
- c) Rs. 750
- d) Rs. 1050
2- How many 5's will be there in the number 121122123... till 356?
- a) 51
- b) 54
- c) 50
- d) 49
3- If 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a day, for how many hours a day would 2 examiners have to work in order to examine twice the number of answer books in 20 days?
- a) 6 hours
- b) 7 hours
- c) 15/2 hours
- d) 8 hours
4- The HCF of 2472, 1284 and a third number 'N' is 12. If their LCM is 2^3 × 3^2 × 5 × 103 × 107, then the number 'N' is:
- a) 2^2 × 3^2 × 7
- b) 2^2 × 3^3 × 103
- c) 2^2 × 3 × 5
- d) None of these
5- A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days A alone can finish the remaining work?
- a) 7
- b) 6
- c) 5
- d) 10
6- A child is looking for his father. He went 90 meters in the east before turning to his right. He went 20 meters before turning to his right again to look for his father at his uncle's place 30 meters from this point. His father was not there. From there, he went 100 meters to his north before meeting his father in a street. How far did the son meet his father from the starting point?
- a) 80 meter
- b) 90 meter
- c) 100 meter
- d) 110 meter
7- A, B and C are three sisters. The oldest is Aasha, and she always tells the truth. The next oldest is Usha, and Usha always tells a lie. Eesha is the youngest, and she sometimes lies and sometimes tells the truth.
Mukund asked the sister sitting on the left: "Which sister is in the middle of you three?" and received the answer, "That's Aasha." Mukund then asked the sister in the middle: "What is your name?" The response was, "I'm Eesha." Mukund turned to the sister on the right and asked: "Who is that in the middle?" The sister replied, "She is Usha."
Who was in the middle?
- a) Aasha
- b) Eesha
- c) Usha
- d) Cannot be determined
8- Three cars A, B and C are participating in a race. A is twice as likely as B to win and B is thrice as likely as C to win. What is the probability that B will win, if only one of them can win the race?
- a) 1/2
- b) 2/5
- c) 3/10
- d) 1/10
9- In how many ways can 2310 be expressed as product of three factors?
- a) 41
- b) 56
- c) 23
- d) 46
10- At the end of 1994, Rohit was half as old as his grandmother. The sum of years in which they were born is 3844. How old was Rohit at the end of 1999?
- a) 48
- b) 55
- c) 49
- d) 53
11- 60 men can complete a piece of work in 40 days. 60 men start the work but after every 5 days, 5 people leave. In how many days will the work be completed?
- a) 60
- b) 80
- c) 120
- d) None of these
12- A shop sells chocolates. It used to sell chocolates for Rs. 2 each but there were no sales at that price. When it reduced the price, all the chocolates sold out, enabling the shopkeeper to realize Rs. 164.90 from the chocolates alone. If the new price was not less than half the original price quoted, how many chocolates were sold?
- a) 39
- b) 97
- c) 37
- d) 71
13- 4, 20, 35, 49, 62, 74, ?
- a) 76
- b) 79
- c) 78
- d) 85
14- A truck and a car start simultaneously from two points 105 km apart and travel toward each other. They meet after 1 hour and 10 min. The truck covers the distance at a speed of 70 km/hr. The speed of the car is:
- a) 20 km/hr
- b) 30 km/hr
- c) 40 km/hr
- d) 25 km/hr
15- Find the sum of the series 1(1!) + 2(2!) + 3(3!) + ... + 2012(2012!)
- a) 2013! + 1
- b) 2013! - 1
- c) 2012! + 1
- d) 2013! - 1
16- Find the number of ways a team of 11 must be selected from 5 men and 11 women such that the team must comprise of not more than 3 men.
- a) 1565
- b) 2256
- c) 2456
- d) 1243
17- The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas.
- a) 3:2
- b) 2:3
- c) 1:6
- d) 6:1
18- On a 26-question test, five points were deducted for each wrong answer and eight points were added for each correct answer. If all the questions were answered, how many were correct if the score was zero?
- a) 10
- b) 11
- c) 12
- d) 13
19- A man buys a certain number of marbles at rate of 59 marbles for rupees 2 times M, where M is an integer. He divided these marbles into two parts of equal numbers, one part of which he sold at the rate of 29 marbles for Rs. M, and the other at a rate 30 marbles for Rs. M. He spent and received an integral number of rupees but bought the least possible number of marbles. How many did he buy?
- a) 870
- b) 102660
- c) 1770
- d) 1740
20- Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5:3 and 1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4:3. What is the ratio of the composition of the two basic elements in alloy X?
- a) 1:1
- b) 2:3
- c) 5:2
- d) 4:32
21- How many 6-digit even numbers can be formed from digits 1, 2, 3, 4, 5, 6, 7 so that the digit should not repeat and the second last digit is even?
- a) 6480
- b) 320
- c) 2160
- d) 720
22- A circle has 29 points arranged in a clockwise manner numbered from 0 to 28. A bug moves clockwise around the circle according to the following rule: If it is at a point i on the circle, it moves clockwise in 1 second by (1 + r) places, where r is the remainder when i is divided by 11. If it starts at point 23, at what point will it be after 2012 seconds?
- a) 1
- b) 7
- c) 15
- d) 20
23- If a lemon and an apple together cost Rs. 12.00, a tomato and a lemon cost Rs. 4.00, and an apple cost Rs. 8.00 more than a tomato or a lemon, then what is the cost of a lemon?
- a) Rs. 2
- b) Rs. 4
- c) Rs. 1
- d) Rs. 3
24- In how many ways can 2310 be expressed as product of three factors?
- a) 41
- b) 56
- c) 23
- d) 46
25- A series of book was published at 7 year intervals. When the 7th book was issued, the sum of publication years is 13524. When was the 1st book published?
- a) 1911
- b) 1910
- c) 2002
- d) 1932
26- The average marks of A, B, C is 48. When D joins, the average becomes 47. E has 3 more marks than D. Average marks of B, C, D, E is 48. What are the marks of A?
- a) 42
- b) 43
- c) 53
- d) 56
27- How many lattice points are there between (2,0) and (16,203)?
- a) 8
- b) 10
- c) 14
- d) 15
28- The ratio of radii of cylinder to that of cone is 1:2. Heights are equal. Find ratio between volumes.
- a) 3:4
- b) 1:2
- c) 1:4
- d) 4:1
29- In a single toss of two dice, find the probability of getting a sum which is a multiple of 3 or 4.
- a) 5/9
- b) 4/9
- c) 2/9
- d) 1/9
30- A city has a basketball league with three teams: the Aretes, the Braves, and the Deities. A sports writer notices that the tallest player of the Aretes is shorter than the shortest player of the Braves. The shortest of the Deities is shorter than the shortest of the Aretes, while the tallest of the Braves is taller than the tallest of the Aretes. Which of the following can be judged with certainty? X) Paul, a Brave, is taller than David, an Arete. Y) David, a Deity, is shorter than Edward, an Arete.
- a) X only
- b) Both X and Y
- c) Neither X nor Y
- d) Y only
31- What is the value of (32^31^301) when it is divided by 9?
- a) 3
- b) 5
- c) 2
- d) 1
32- Find no. of ways in which 4 particular persons A, B, C, D and 6 more persons can stand in a queue so that A always stands before B, B always stands before C, and C always stands before D.
- a) 6!
- b) 7!
- c) 10! ÷ 6!
- d) 10! ÷ 4!
33- 100 students appeared for two different examinations. 60 passed the first, 50 the second, and 30 passed both examinations. Find the probability that a student selected at random failed in both examinations.
- a) 5/6
- b) 1/5
- c) 1/7
- d) 5/7
34- There are 10 points on a straight line AB and 8 on another straight line AC, none of them being point A. How many triangles can be formed with these points as vertices?
- a) 680
- b) 720
- c) 816
- d) 640
35- From a bag containing 8 green and 5 red balls, three are drawn one after the other. The probability of all three balls being green if the balls drawn are replaced before the next ball pick and the balls drawn are not replaced, are respectively:
- a) 512/2197, 336/2197
- b) 512/2197, 336/1716
- c) 336/2197, 512/2197
- d) 336/1716, 512/1716
36- Find the greatest number that will divide 148, 246, and 623 leaving remainders 4, 6, and 11 respectively.
- a) 20
- b) 12
- c) 6
- d) 48
37- A mother, her little daughter, and her just born infant boy together stood on a weighing machine which shows 74 kg. How much does the daughter weigh if the mother weighs 46 kg more than the combined weight of daughter and the infant, and the infant weighs 60% less than the daughter?
- a) 9 kg
- b) 11 kg
- c) Cannot be determined
- d) 10 kg
38- Find the number of ways a batsman can score a double century (200 runs) only in terms of 4's and 6's.
- a) 15
- b) 16
- c) 17
- d) 18
39- Thomas takes 7 days to paint a house completely whereas Raj would require 9 days to paint the same house completely. How many days will it take to paint the house if both of them work together? (Give answers to the nearest integer)
- a) 4
- b) 2
- c) 5
- d) 3
40- How many positive integers less than 4300 have digits only from 0-4?
- a) 560
- b) 565
- c) 575
- d) 625
41- A person travels from Chennai to Pondicherry by cycle at 7.5 kmph. Another person travels the same distance by train at a speed of 30 kmph and reached 30 mins earlier. Find the distance.
- a) 5 km
- b) 10 km
- c) 15 km
- d) 20 km
42- A bag contains 8 white balls and 3 blue balls. Another bag contains 7 white, and 4 blue balls. What is the probability of getting a blue ball?
- a) 3/7
- b) 7/22
- c) 7/25
- d) 7/15
43- In a 3×3 square grid comprising 9 tiles, each tile can be painted in red or blue color. When the grid is rotated by 180 degrees, there is no difference which can be spotted. How many such possibilities are there?
- a) 16
- b) 32
- c) 64
- d) 256
44- Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in:
- a) 48 days
- b) 96 days
- c) 24 days
- d) 32 days
45- For any two numbers we define an operation $ yielding another number, X $ Y such that following condition holds: • X $ X = 0 for all X • X $ (Y $ Z) = X $ Y + Z Find the Value of 2012 $ 0 + 2012 $ 1912
- a) 2112
- b) 100
- c) 5936
- d) Cannot be determined
46- On a toss of two dice, A throws a total of 5. Then the probability that he will throw another 5 before he throws 7 is:
- a) 40%
- b) 45%
- c) 50%
- d) 60%
47- 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, ... What is the 2320th position of the number in the sequence?
- a) 2
- b) 1
- c) 3
- d) 4
48- In 2003, there are 28 days in February and there are 365 days in the year. In 2004, there are 29 days in February and there are 366 days in the year. If the date March 11, 2003 is a Tuesday, then which one of the following would the date March 11, 2004 be?
- a) Wednesday
- b) Tuesday
- c) Thursday
- d) Monday
49- How many 6-digit even numbers can be formed from digits 1, 2, 3, 4, 5, 6, 7 so that the digit should not repeat and the second last digit is even?
- a) 6480
- b) 320
- c) 2160
- d) 720
50- There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that all the letters may be placed in wrongly addressed envelopes is:
- a) 11/9
- b) 44/120
- c) 53/120
- d) 44/120
51- How many liters of a 90% concentrated acid needs to be mixed with a 75% solution of concentrated acid to get a 30-liter solution of 78% concentrated acid?
- a) 8
- b) 9
- c) 7
- d) 6
52- Average marks of A, B, C is 48. When D joins, average becomes 47. E has 3 more marks than D. Average marks of B, C, D, E is 48. What is the marks of A?
- a) 42
- b) 43
- c) 53
- d) 56
53- On a certain assembly line, the rejection rate for Hyundai i10's production was 4 percent, for Hyundai i20's production 8 percent, and for the 2 cars combined 7 percent. What was the ratio of Hyundai i10 production to i20 production?
- a) 3/1
- b) 2/1
- c) 1/1
- d) 1/2
54- For a car, there are 5 tires including one spare tire. All tires are equally used. If the total distance traveled by the car is 40000 km, then what is the average distance traveled by each tire?
- a) 10000 km
- b) 40000 km
- c) 32000 km
- d) 8000 km
55- If A = x^3 y^2 and B = xy^3, then find the HCF of A, B.
- a) x^4 y^5
- b) xy^2
- c) xy
- d) x^3
56- In a clock, the long hand is of 8 cm and the short hand is of 7 cm. If the clock runs for 4 days, find out the total distance covered by both the hands.
- a) 1824π cm
- b) 1648π cm
- c) 1724π cm
- d) 2028π cm
57- A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days A alone can finish the remaining work?
- a) 7
- b) 6
- c) 5
- d) 10
58- In how many possible ways can you write 1800 as a product of 3 positive integers a, b, c?
- a) 350
- b) 360
- c) 380
- d) 450
59- In a horse racing competition, there were 18 horses numbered 1 to 18. The organizers assigned a probability of winning the race to each horse based on the horse's health and training. The probability that horse 1 would win is 1/7, that 2 would win is 1/8, and that 3 would win is 1/7. Assuming that a tie is impossible, find the chance that one of these three will win the race.
- a) 22/392
- b) 1/392
- c) 23/56
- d) 391/392
60- Apples cost L rupees per kilogram for first 30 kg and Q rupees per kilogram for each additional kilogram. If the price of 33 kilograms is 11.67 and for 36 kg of apples is 12.48, then the cost of first 10 kg of apples is:
- a) 3.50
- b) 10.53
- c) 1.17
- d) 2.8
61- How many vehicle registration plate numbers can be formed with digits 1, 2, 3, 4, 5 (no digits being repeated) if it is given that registration number can have 1 to 5 digits?
- a) 205
- b) 100
- c) 325
- d) 105
62- Jake and Paul each walk 10 km. Jake's speed is 1.5 times faster than Paul's speed. What is Jake's speed?
- a) 4 km/h
- b) 6 km/h
- c) 7 km/h
- d) 8 km/h
63 If m+n is divided by 12 and leaves a remainder 8, and if m-n is divided by 12 and leaves a remainder 6, then if mn is divided by 6, what is the remainder?
- a) 4
- b) 3
- c) 2
- d) 1
64- Complete the series: 4, 20, 35, 49, 62, 74, ?
- a) 76
- b) 79
- c) 78
- d) 85
65- The sum of 5 numbers in an Arithmetic Progression is 30 and the sum of their squares is 190. Which of the following is the third term?
- a) 5
- b) 6
- c) 8
- d) 9
66- A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
- a) 12 days
- b) 15 days
- c) 16 days
- d) 18 days
67- The least number which when divided by 48, 60, 72, 108 and 140 leaves 38, 50, 62, 98 and 130 as remainders respectively, is:
- a) 4562
- b) 15110
- c) 2135
- d) 7589
68- A sum of money is borrowed and paid back in two annual installments of Rs. 882 each, allowing 5% compound interest. The sum borrowed was:
- a) Rs. 1680
- b) Rs. 1642
- c) Rs. 640
- d) Rs. 1640
69- How many parallelograms are formed by a set of 4 parallel lines intersecting another set of 7 parallel lines?
- a) 125
- b) 126
- c) 127
- d) 128
70- A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long would it take for B if he alone completes the work?
- a) 37½ days
- b) 32 days
- c) 32½ days
- d) 37 days
71- A person starts writing all 4-digit numbers. How many times had he written the digit 2?
- a) 4200
- b) 4700
- c) 3700
- d) 3200
72- There is a tank, and two pipes A and B. A can fill the tank in 25 minutes and B can empty the tank in 20 minutes. If both pipes are opened at the same time, how much time is required to fill the tank?
- a) 15 min
- b) 18 min
- c) 13 min
- d) Never be filled
73- An old man and a young man are working together in an office and staying together in a nearby apartment. The old man takes 30 minutes and the young man takes 20 minutes to walk from the apartment to office. If one day the old man started at 10:00 AM and the young man at 10:05 AM from the apartment to the office, when will they meet?
- a) 10:15 AM
- b) 10:30 AM
- c) 10:45 AM
- d) 10:00 AM
74- The shopkeeper charged 12 rupees for a bunch of chocolates, but I bargained with the shopkeeper and got two extra ones, and that made them cost one rupee for a dozen less than the first asking price. How many chocolates did I receive for 12 rupees?
- a) 10
- b) 16
- c) 14
- d) 18
75- There are 16 teams divided into 4 groups. Every team from each group will play with each other once. The top 2 teams will go to the next round and so on. The top two teams will play the final match. Minimum how many matches will be played in that tournament?
- a) 43
- b) 40
- c) 14
- d) 50
76- A sealed envelope contains a card with a single digit written on it. Three of the following statements are true and one is false. I. The digit is 1. II. The digit is not 2. III. The digit is not 9. IV. The digit is 8. Which one of the following must necessarily be correct?
- a) II is false
- b) III is true
- c) IV is false
- d) The digit is even
- e) I is true
77- Tickets are numbered from 1, 2, ..., 1100 and one card is drawn randomly. What is the probability of having 2 as a digit?
- a) 29/110
- b) 32/110
- c) 30/110
- d) 22/110
We need to count numbers from 1 to 1100 that have the digit 2:
- Numbers with 2 in the ones place: 2, 12, 22, ..., 1092 (110 numbers)
- Numbers with 2 in the tens place: 20-29, 120-129, ..., 1020-1029 (110 numbers)
- Numbers with 2 in the hundreds place: 200-299, including 1200 if it exists (100 numbers)
- Numbers with 2 in the thousands place: None (as we only go up to 1100)
However, we've double-counted numbers with multiple 2s, such as 22, 212, etc.
- Numbers with 2 in both ones and tens place: 2 in every 100 numbers (11 numbers)
- Numbers with 2 in both ones and hundreds place: 2 in every 1000 numbers (1 number)
- Numbers with 2 in both tens and hundreds place: 10 in every 1000 numbers (1 number)
Total count = 110 + 110 + 100 - 11 - 1 - 1 = 307 Probability = 307/1100 = 29/110
78- How many 2's are there between the terms 112 to 375?
- a) 313
- b) 159
- c) 156
- d) 315
79- Ram and Shakil run a race of 2000 meters. First, Ram gives Shakil a start of 200 meters and beats him by one minute. If Ram gives Shakil a start of 6 minutes, Ram is beaten by 1000 meters. Find the time in minutes in which Ram and Shakil can run the races separately.
- a) 12, 18
- b) 10, 12
- c) 11, 18
- d) 8, 10
80- The average temperature of June, July and August was 31 degrees. The average temperature of July, August and September was 30 degrees. If the temperature of June was 30 degrees, find the temperature of September (in degrees).
- a) 25
- b) 26
- c) 27
- d) 28
81- Three generous friends, each with some money, redistribute the money as follows: Sandra gives enough money to David and Mary to double the amount of money each has. David then gives enough to Sandra and Mary to double their amounts. Finally, Mary gives enough to Sandra and David to double their amounts. If Mary had 11 rupees at the beginning and 17 rupees at the end, what is the total amount that all three friends have?
- a) 105
- b) 60
- c) 88
- d) 71
82- George walks 36 km partly at a speed of 4 km per hour and partly at 3 km per hour. If he had walked at a speed of 3 km per hour when he had walked at 4 and 4 km per hour when he had walked at 3, he would have walked only 34 km. The time (in hours) spent by George in walking was:
- a) 8
- b) 12
- c) 5
- d) 10
83- The sum of the four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can be one of these four numbers?
- a) 21
- b) 25
- c) 41
- d) 67
84- Consider the sequence of numbers 0, 2, 2, 4, ... where for n > 2 the nth term of the sequence is the unit digit of the sum of the previous two terms. Let sn denote the sum of the first n terms of this sequence. What is the smallest value of n for which sn > 2771?
- a) 692
- b) 693
- c) 694
- d) 700
85- A number plate can be formed with two alphabets followed by two digits with no repetition. Then how many possible combinations can we get?
- a) 52500
- b) 58500
- c) 56500
- d) 56800
86- I bought a certain number of marbles at rate of 59 marbles for rupees 2 times M, where M is an integer. I divided these marbles into two parts of equal numbers, one part of which I sold at the rate of 29 marbles for Rs. M, and the other at a rate 30 marbles for Rs. M. I spent and received an integral number of rupees but bought the least possible number of marbles. How many did I buy?
- a) 870
- b) 102660
- c) 1770
- d) 1740
87- Cara, a blue whale participated in a weight loss program at the biggest office. At the end of every month, the decrease in weight from original weight was measured and noted as 1, 2, 6, 21, 86, 445, 2676. While Cara made a steadfast effort, the weighing machine showed an erroneous weight once. What was that?
- a) 2676
- b) 2
- c) 445
- d) 86
88- How many different integers can be expressed as the sum of three distinct numbers from the set {3, 8, 13, 18, 23, 28, 33, 38, 43, 48}?
- a) 421
- b) 20
- c) 10
- d) 22
89- Aman walking at the speed of 4 km/h crosses a square field diagonally in 3 minutes. The area of the field (in m²) is:
- a) 20000
- b) 21000
- c) 25000
- d) 26000
90- A cow and a horse are bought for Rs. 200000. The cow is sold at a profit of 20% and the horse is sold at a loss of 10%. The overall gain is Rs. 4000. The cost price of the cow is:
- a) Rs. 130000
- b) Rs. 80000
- c) Rs. 70000
- d) Rs. 120000
91- Raj drives slowly along the perimeter of a rectangular park at 24 kmph and completes one full round in 4 mins. The ratio of length to breadth is 3:2. What are its dimensions?
- a) 450m × 300m
- b) 150m × 100m
- c) 480m × 320m
- d) 100m × 100m
92- For which of the following n is the number 2^74 + 2^2058 + 2^2n a perfect square?
- a) 2010
- b) 2018
- c) 2012
- d) 2020
92- A certain function f satisfies the equation f(x) + 2·f(6-x) = x for all real numbers x. The value of f(1) is:
- a) 2
- b) Can't determine
- c) 1
- d) 3
93- What is the value of [77!·(77!-2·54!)³]/[(77!+54!)³] + [54!·(2·77!-54!)³]/[(77!+54!)³]?
- a) 2·77! + 2·54!
- b) 77! - 54!
- c) 77! + 54!
- d) 2·77! - 2·54!
94- Find the sum of the series 1-2+3-4+...-98+99.
- a) -49
- b) 0
- c) 50
- d) -50
95- In a city, there are few engineering, MBA and CA candidates. Sum of four times the engineering, three times the MBA and 5 times CA candidates is 3650. Also, three times CA is equal to two times MBA and three times engineering is equal to two times CA. In total, how many MBA candidates are there in the city?
- a) 200
- b) 300
- c) 450
- d) 400
96- Find the sum of angles 1, 2, 3, 4, 5 in a star.
- a) 180°
- b) 300°
- c) 360°
- d) 400°
97- Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is:
- a) 780
- b) 800
- c) 820
- d) 741
98- The marked price of a coat was 40% less than the suggested retail price. Eesha purchased the coat for half of the marked price at the 15th anniversary sale. What percent less than the suggested retail price did Eesha pay?
- a) 60%
- b) 20%
- c) 70%
- d) 30%
99- There is a school where 60% are girls and 35% of the girls are poor. If students are selected at random, what is the probability of selecting a poor girl out of the total strength?
- a) 21%
- b) 27%
- c) 28%
- d) 29%
100- If m+n is divided by 12 leaves a remainder 8, if m-n is divided by 12 leaves a remainder 6, then if mn is divided by 6, what is the remainder?
- a) 4
- b) 3
- c) 2
- d) 1
101- There is a conical tent in which 10 persons can stand. Each person needs 6m² to stand and 60m³ air to breathe. What is the height of the tent?
- a) 60 m
- b) 30 m
- c) 20 m
- d) 45 m
102- In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
- a) 17.05
- b) 27.85
- c) 22.45
- d) 26.25
103- A rectangle is divided into four rectangles with areas 70, 36, 20, and X. The value of X is:
- a) 350/90
- b) 350/7
- c) 350/11
- d) 350/13
104- The ratio of radii of cylinder to that of cone is 1:2. Heights are equal. Find the ratio between volumes.
- a) 3:4
- b) 1:2
- c) 1:4
- d) 4:1
105- A hollow pipe has circumference 14 cm. A bug is on its wall at a distance of 48 cm from the top. A drop of honey is on the wall at 24 cm from the top but diametrically opposite to the bug. Find the shortest distance the bug has to travel to reach the honey.
- a) 25 cm
- b) 39 cm
- c) 21 cm
- d) 24 cm
106- If a ladder is 100m long, and the distance between the bottom of the ladder and the wall is 60m. The top side of the bottom and wall are joined. What is the maximum size of cube that can be placed between them?
- a) 34.28 cm
- b) 24.28 cm
- c) 21.42 cm
- d) 28.56 cm
107- What are the next three numbers for the given series? 11, 23, 47, 83, 131
- a) 145, 178, 231
- b) 178, 225, 272
- c) 176, 217, 280
- d) 191, 263, 347
108- A series of books was published at 7-year intervals. When the 7th book was issued, the sum of publication years is 13524. When was the 1st book published?
- a) 1911
- b) 1910
- c) 2002
- d) 1932
109- There are 14 digits of a credit card number to be filled. Each of the below three boxes contains continuous digits with a sum of 18. Given: 4th digit is 7 and 7th digit is x. Then what is the value of x?
- a) 1
- b) 7
- c) 4
- d) 2
110- Crusoe, hatched from a mysterious egg discovered by Angus, was growing at a fast pace that Angus had to move it from home to the lake. Given the weights of Crusoe in its first weeks of birth as 5, 15, 30, 135, 405, 1215, 3645. Find the odd weight out.
- a) 3645
- b) 135
- c) 30
- d) 15
111- Arun makes a popular brand of ice-cream in a rectangular shaped bar 6 cm long, 5 cm wide and 2 cm thick. To cut costs, the company had decided to reduce the volume of the bar by 19%. The thickness will remain the same, but the length and width will be decreased by the same percentage. The new width will be:
- a) 4.5 cm
- b) 5.5 cm
- c) 6.5 cm
- d) 7.5 cm
112- A can complete a piece of work in 8 hours, B can complete in 10 hours and C in 12 hours. If A, B, C start the work together but A leaves after 2 hours, find the time taken by B and C to complete the remaining work.
- a) 2 (1/11) hours
- b) 4 (1/11) hours
- c) 2 (6/11) hours
- d) 2 hours
113- What is the greatest possible positive integer n if 8^n divides (44)^44 without leaving a remainder?
- a) 14
- b) 28
- c) 29
- d) 15
114- A tree of height 36m is on one edge of a road of width 12m. It falls such that the top of the tree touches the other edge of the road. Find the height at which the tree breaks.
- a) 16 m
- b) 24 m
- c) 12 m
- d) 18 m
115- How many 6 digit even numbers can be formed from digits 1, 2, 3, 4, 5, 6, 7 so that the digit should not repeat and the second last digit is even?
- a) 6480
- b) 320
- c) 2160
- d) 720
116- At the end of 1994, Rohit was half as old as his grandmother. The sum of years in which they were born is 3844. How old was Rohit at the end of 1999?
- a) 48
- b) 55
- c) 49
- d) 53
117- Find the number of divisors of 1728.
- a) 28
- b) 21
- c) 24
- d) 18
118- A 17m × 8m rectangular ground is surrounded by a 1.5m width path. The depth of the path is 12 cm. Gravel is filled in the path. Find the quantity of gravel required.
- a) 5.5 m³
- b) 7.5 m³
- c) 6.05 m³
- d) 10.08 m³
119- Ashok, Eesha, Farookh, and Gowri ran a race. Ashok said, "I did not finish 1st or 4th". Eesha said, "I did not finish 4th". Farookh said, "I finished 1st". Gowri said, "I finished 4th". There were no ties in the competition, and exactly three of the children told the truth. Who finished 4th?
- a) Farookh
- b) Eesha
- c) Gowri
- d) Ashok
120- A circle has 29 points arranged in a clockwise manner numbered from 0 to 28, as shown in the figure below. A bug moves clockwise around the circle according to the following rule. If it is at a point i on the circle, it moves clockwise in 1 second by (1 + r) places, where r is the reminder (possibly 0) when i is divided by 11. Thus if it is at position 5, it moves clockwise in one second by (1 + 5) places to point 11. Similarly if it is at position 28 it moves (1 + 6) or 7 places to point 6 in one second. If it starts at point 23, at what point will it be after 2012 seconds?
- a) 1
- b) 7
- c) 15
- d) 20