# CAT 2018 Question Paper Slot 1 | CAT Quants

###### CAT Quantitative Aptitude | CAT 2018 Question Paper

The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for Free) head out here: CAT Official Question Mocks. In CAT 2018 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

1. #### CAT 2018 Question Paper Slot 1 - Mixtures and Alligations

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

1. 20
2. 16
3. 22
4. 26

2. #### CAT 2018 Question Paper Slot 1 - Geometry

In a circle with centre 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

4. #### CAT 2018 Question Paper Slot 1 - Speed Time Distance

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

1. 6
2. 3
3. 4
4. 5

5. #### CAT 2018 Question Paper Slot 1 - Averages

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 [TITA]

6. #### CAT 2018 Question Paper Slot 1 - Ratio & Proportions

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

1. 21 : 25
2. 19 : 24
3. 18 : 25
4. 17 : 25

7. #### CAT 2018 Question Paper Slot 1 - Mixtures

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?

1. 84
2. 86
3. 96
4. 98

8. #### CAT 2018 Question Paper Slot 1 - Work and Time

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?

1. 16
2. 22
3. 20
4. 18

9. #### CAT 2018 Question Paper Slot 1 - Geometry

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

1. 192√3
2. 164√3
3. 248√3
4. 188√3

10. #### CAT 2018 Question Paper Slot 1 - Number Theory

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: [TITA]

11. #### CAT 2018 Question Paper Slot 1 - Logarithm

If x is a positive quantity such that 2x = 3log52 , then x is equal to

1. log59

1. 32
2. 59
3. 67
4. 40

28. #### CAT 2018 Question Paper Slot 1 - Work and Time

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?

1. 40
2. 32
3. 36
4. 45

29. #### CAT 2018 Question Paper Slot 1 - Mensuration

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

1. 18√3
2. 24√3
3. 32√3
4. 12√3

30. #### CAT 2018 Question Paper Slot 1 - Geometry

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

1. √13
2. √14
3. √11
4. √12

31. #### CAT 2018 Question Paper Slot 1 - Pipes & Cisterns

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? [TITA]

32. #### CAT 2018 Question Paper Slot 1 - Set Theory

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

1. 26
2. 23
3. 96
4. 93

33. #### CAT 2018 Question Paper Slot 1 - Functions

Let f(x)=min{2x2, 52 - 5x}, where x is any positive real number.Then the maximum possible value of f(x) is [TITA]

34. #### CAT 2018 Question Paper Slot 1 - Averages

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?

1. 25
2. 26
3. 27
4. 28

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