CAT 2018QASlot 1 · Morning

CAT 2018 Slot 1 QA Question Paper with Solutions

60 Minutes34 QuestionsNov 25, 20183 marks correct · −1 wrong

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Q1CAT 2018 Slot 1 QA

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is

Q2CAT 2018 Slot 1 QA

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A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

Q3CAT 2018 Slot 1 QA

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Raju and Lalitha originally had marbles in the ratio 4 : 9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5 : 6. What fraction of her original number of marbles was given by Lalitha to Raju?

Q4CAT 2018 Slot 1 QA

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In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

Q5CAT 2018 Slot 1 QA

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When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

Q6CAT 2018 Slot 1 QA

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If x is a positive quantity such that

2^{x} = 3^{\log_{5} 2}

, then x is equal to

Q7CAT 2018 Slot 1 QA

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Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

Q8CAT 2018 Slot 1 QA

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Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

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Q9CAT 2018 Slot 1 QA

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Given that

x^{2018}y^{2017} = \dfrac{1}{2}

and

x^{2016}y^{2019} = 8

, the value of

x^{2} + y^{3}

Q10CAT 2018 Slot 1 QA

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Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is

Q11CAT 2018 Slot 1 QA

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Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is

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Q12CAT 2018 Slot 1 QA

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f(x + 2) = f(x) + f(x + 1)

for all positive integers

x

, and

f(11) = 91

f(15) = 617

, then

f(10)

equals

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Q13CAT 2018 Slot 1 QA

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u^{2} + (u - 2v - 1)^{2} = - 4v(u + v)

, then what is the value of

u + 3v

Q14CAT 2018 Slot 1 QA

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A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

Q15CAT 2018 Slot 1 QA

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How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

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Q16CAT 2018 Slot 1 QA

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A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With

\pi = \dfrac{22}{7}

, the volume, in cubic ft, of the remaining part of the cone is

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Q17CAT 2018 Slot 1 QA

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\log_{2}(5 + \log_{3}a) = 3

and

\log_{5}(4a + 12 + \log_{2}b) = 3

, then

a + b

is equal to

Q18CAT 2018 Slot 1 QA

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If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be

Q19CAT 2018 Slot 1 QA

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In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

Q20CAT 2018 Slot 1 QA

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In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

Q21CAT 2018 Slot 1 QA

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Given an equilateral triangle T₁ with side 24 cm, a second triangle T₂ is formed by joining the midpoints of the sides of T₁. Then a third triangle T₃ is formed by joining the midpoints of the sides of T₂. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T₁, T₂, T₃,... will be

Q22CAT 2018 Slot 1 QA

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The number of integers x such that

0.25 < 2^{x} < 200

, and

2^{x} + 2

is perfectly divisible by either 3 or 4, is

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Q23CAT 2018 Slot 1 QA

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Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y?

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Q24CAT 2018 Slot 1 QA

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John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is

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Q25CAT 2018 Slot 1 QA

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Let

f(x) = \min\{2x^{2}, 52 - 5x\}

, where

x

is any positive real number. Then the maximum possible value of

f(x)

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Q26CAT 2018 Slot 1 QA

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Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

Q27CAT 2018 Slot 1 QA

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A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

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Q28CAT 2018 Slot 1 QA

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Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

Q29CAT 2018 Slot 1 QA

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In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

Q30CAT 2018 Slot 1 QA

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\log_{12} 81 = p

, then

3(\dfrac{4 - p}{4 + p})

is equal to

Q31CAT 2018 Slot 1 QA

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In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

Q32CAT 2018 Slot 1 QA

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Let

x, y, z

be three positive real numbers in a geometric progression such that

x < y < z

. If

5x

16y

, and

12z

are in an arithmetic progression then the common ratio of the geometric progression is

Q33CAT 2018 Slot 1 QA

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While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

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Q34CAT 2018 Slot 1 QA

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A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is

About CAT 2018 Slot 1 QA

The QA section of CAT 2018 Slot 1 was conducted on November 30, 2018, the last Sunday of November — consistent with IIM's scheduling across all recent years. The section contains 24 questions to be answered in 40 minutes, carrying 72 marks in total. There is no sectional time limit within the overall exam, but students choosing to switch sections mid-paper lose the ability to return — making pacing within QA critical.

Passage Topics in CAT 2018 Slot 1 QA

CAT 2018 Slot 1 QA featured four reading comprehension passages and a standalone Verbal Ability block. The RC passages spanned complexity theory and global systems, the aesthetics of electronic music, the economics of income inequality, and the legal history of criminal responsibility — a typical CAT spread across the sciences, humanities, and social sciences. The VA section included Para Jumbles, Para Summary, and Odd Sentence Out questions, consistent with the pattern since CAT 2019.

CAT 2018 QA Marking Scheme

Correct answer (MCQ): +3 marks
Wrong answer (MCQ): −1 mark
Unattempted (MCQ): 0 marks
TITA questions (if any): +3 correct, no negative marking

How to Use This Question Paper

Click any answer option to immediately check your answer. The correct option is highlighted in green; if you selected the wrong option, it is shown in red and the correct answer is revealed. A detailed explanation appears below each question after you answer it, along with statistics showing what percentage of students answered correctly in the actual exam.

The question navigator at the top of the page updates in real time — green bubbles indicate correct answers and red indicate wrong. Use this to spot weak areas at a glance. To practice under timed conditions, use the Take Full Mock button to attempt the complete CAT 2018 Slot 1 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QAsection. The passages in CAT are dense and argumentative — they reward close reading of the author's position rather than skimming for facts. Practising on past papers is the most reliable way to calibrate your reading speed, improve inference accuracy, and recognise the types of questions IIM setters favour. Use the answer statistics on this page to benchmark yourself; questions where more than 50% of test-takers answered correctly are ones you should aim to get right every time.