Cat 2018 Slot 2 Quant Answers

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CAT 2019 (Quantitative Aptitude) QA – Slot 2 (Afternoon Slot) – Questions, Answers & Solutions

CAT 2018 Question Paper Slot 2 - Speed, Time and Distance On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. CAT2018.SolQA/1 Solutions for CAT 2018 QA – Afternoon (SLOT – 2) Let a and b be the two numbers. We know that for any two numbers AM ≥ GM ⇒ 2 + 2 2. CAT 2018 exam was successfully conducted by IIM Calcutta on November 26, 2018. The exam was conducted in two slots i.e. Slot 1 or morning slot (9 AM to 12 PM) and slot 2 or afternoon slot (2:30 PM to 5:30 PM). The detailed CAT 2018 exam analysis of slot 1 and slot 2 are given below to help the test-takers and future aspirants get an overview of.

The CAT 2019, Slot-1 questions, answers, and solutions.

1. If 5^x – 3^y = 13438 and 5^(x-1) + 3^(y+1) = 9686, then x + y equals? (Watch video solutions to CAT 2019 – Slot-2 – QA -1)

2. Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest then the amount, in rupees, invested by Bimal is? (Watch video solutions to CAT 2019 – Slot-2 – QA -2)

3. The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20cm. The vertical height of the pyramid, in cm, is (Watch video solutions to CAT 2019 – Slot-2 – QA -3)

  1. 12
  2. 8 x (3)^(1/2)
  3. 5 x (5)^(1/2)
  4. 10x (2)^(1/2)

4. A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20% respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x-y)/p equals (Watch video solutions to CAT 2019 – Slot-2 – QA -4)

  1. 1
  2. 0.7
  3. 0.50
  4. 1.2

5. Let A be a real number. Then the roots of the equation x2 -4x – log2A = 0 are real and distinct if and only if (Watch video solutions to CAT 2019 – Slot-2 – QA -5)

  1. A > 1/16
  2. A < 1/16
  3. A < 1/8
  4. A > 1/8

6. The quadratic equation x^2 + bx +c =0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b^2 + c? (Watch video solutions to CAT 2019 – Slot-2 – QA -6)

  1. 427
  2. 3721
  3. 549
  4. 361

7. The strength of a salt solution is p% if 100ml of the solution contains p grams of salt. Each of the three vessels A, B, C contains 500ml of salt solution of strengths 10%,22%, and 32% respectively. Now, 100ml of the solution in vessel A is transferred to vessel B. Then, 100ml of the solution in vessel B is transferred to vessel C. Finally, 100ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in Vessel A is. (Watch video solutions to CAT 2019 – Slot-2 – QA -7)

  1. 15
  2. 14
  3. 13
  4. 12

8. The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers? (Watch video solutions to CAT 2019 – Slot-2 – QA -8)

  1. 5
  2. 4
  3. 3.5
  4. 4.5

9.

(Watch video solutions to CAT 2019 – Slot-2 – QA – 9)

  1. 1 ≤ x ≤ 3
  2. -1 ≤ x ≤ 3
  3. 1 ≤ x ≤ 2
  4. -3 ≤ x ≤ 3

10. In 2020, a library contained a total of 11500 books in two categories – fiction and non-fiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was a 10% increase in the fiction category while there was a 12% increase in the non – fiction category. How many fiction books were in the library in 2015? (Watch video solutions to CAT 2019 – Slot-2 – QA -10)

  1. 6160
  2. 5500
  3. 6600
  4. 6000

11. Let ABC be a right-angled triangle with hypotenuse BC of length 20cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is (Watch video solutions to CAT 2019 – Slot-2 – QA -11)

  1. 8*(2)^(1/2)
  2. 6*(2)^(1/2)
  3. 5
  4. 10

12. The number of common terms in the two sequences: 15,19,23,27…….415 and 14,19,24,29……,464 is (Watch video solutions to CAT 2019 – Slot-2 – QA -12)

  1. 18
  2. 20
  3. 21
  4. 19

13. A man makes complete use of 405cc of iron, 783cc of aluminum, and 351cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has a radius of 3cm. If the total number of cylinders is to be kept at a minimum, then the total surface of all these cylinders, in sq cm, is (Watch video solutions to CAT 2019 – Slot-2 – QA -13)

  1. 8464 π
  2. 928 π
  3. 1026(1+π)
  4. 1044 (4+π)

14. How many factors of 2^4 * 3^5 * 10^4 are perfect squares which are greater than 1? (Watch video solutions to CAT 2019 – Slot-2 – QA -14)

16. Two ants A and B start from point P on a circle at the same time, with A moving clock-wise and B moving anti-clock-wise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at (Watch video solutions to CAT 2019 – Slot-2 – QA -16)

  1. 10:18 am
  2. 10:27 am
  3. 10:45 am
  4. 10:25 am

15. John jogs on track A at 6kmph and Mary jogs on track 7.5Kmph. The total length of tracks A and B is 325metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A? (Watch video solutions to CAT 2019 – Slot-2 – QA -15)

17. In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12cm and 9cm, respectively. Then, the area of triangle ABC, in sq cm, is (Watch video solutions to CAT 2019 – Slot-2 – QA -17)

  1. 1. 72
  2. 78
  3. 68
  4. 80

18. John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. he works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime? (Watch video solutions to CAT 2019 – Slot-2 – QA -18)

19. What is the largest positive integer n such that (n^2 + 7n + 12)/(n^2 -n -12) is also a positive integer? (Watch video solutions to CAT 2019 – Slot-2 – QA -19)

  1. 12
  2. 8
  3. 16
  4. 6

20. In a six-digit number, the sixth, that is the rightmost digit is the sum of the first three digits, the fifth digit is the sum of the first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of the fifth and sixth digits. Then, the largest possible value of the fourth digit is? (Watch video solutions to CAT 2019 – Slot-2 – QA -20)

2018

21. Let a,b,x,y be real numbers such that a^2 + b^2 = 25, x^2 + y^2 = 169 , and ax + by = 65. If k = ay -bx, then (Watch video solutions to CAT 2019 – Slot-2 – QA -21)

  1. k = 5/13
  2. k < 5/13
  3. K = 0
  4. 0 < k ≤ 5/13

22. How many pairs (m,n) of positive integers satisfy the equation m^2+105=n^2? (Watch video solutions to CAT 2019 – Slot-2 – QA -22)

23. A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A and moves towards B. Forty-five such motorcycles reach B by 11 am. All motorcycles have the same speed. If the cyclist had doubled his speed, how many motorcycles would have reached B by the time the cyclist reached B? (Watch video solutions to CAT 2019 – Slot-2 – QA -23)

2. 23
4. 15
24. Let A and B be two regular polygons having a and b sides respectively. If b=2a and each of the interior angles of B is 3/2 times each interior angle of A, then each interior angle, in degrees of a regular polygon with a+b sides is (Watch video solutions to CAT 2019 – Slot-2 – QA -24)

25. The salaries of Ramesh, Ganesh, and Rajesh were in the ratio 6:5:7 in 2010, and in the ratio 3:4:3 in 2015. If Ramesh’s salary increase during 25% during 2010-2015, then the percentage increase in Rajesh’s salary during this period is closest to (Watch video solutions to CAT 2019 – Slot-2 – QA -25)

  1. 8
  2. 9
  3. 7
  4. 10

26. If (2n+1)+(2n+3)+(2n+5)+…+(2n+47)=5280, then what is the value of 1+2+3+… +n ? (Watch video solutions to CAT 2019 – Slot-2 – QA -26)

Cat 2018 Slot 2 Quant Answers Key

27. let a1 – a2 + a3 – a4 ….. + (-1)^(n-1) * aN =N, for all n>=1.Then a51 + a52 + … + a1023 equals (Watch video solutions to CAT 2019 – Slot-2 – QA -27)

  1. 10
  2. 1
  3. 0
  4. -1

28. Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining at a loss of 25%. If he made a total profit of Rs 2000, then his purchase price of a bicycle, in Rupees, was? (Watch video solutions to CAT 2019 – Slot-2 – QA -28)

  1. 4000
  2. 8000
  3. 6000
  4. 2000

29. In an examination, the score of A was 10% less than that of B, the score of B was 25% more than that of C and the score of C was 20% less than that of D. If A scored 72, then the score of D was? (Watch video solutions to CAT 2019 – Slot-2 – QA -29)

30. Two circles, each of radius 4cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle is. (Watch video solutions to CAT 2019 – Slot-2 – QA -30)

  1. 2^(1/2)
  2. Pi / {(3)^(1/2)}
  3. 1
  4. 1/{(2)^(1/2)}

31. The real root of the equation 2^(6x) + 2^(3x+2) – 21 =0 is (Watch video solutions to CAT 2019 – Slot-2 – QA -31)

32. Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done? (Watch video solutions to CAT 2019 – Slot-2 – QA -32)

  1. 15
  2. 13
  3. 12
  4. 14

Cat 2018 Slot 2 Quant Answers Questions

33. In an examination, Rama’s score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, the score of each of them increased by 6. The revised scores of Anjali, Mohan and Rama were in the ratio 11:10:3. Then Anjali’s score exceeded Rama’s score by? (Watch video solutions to CAT 2019 – Slot-2 – QA -33)

Cat 2018 Slot 2 Quant Answers Test

  1. 24
  2. 26
  3. 35
  4. 32

Cat 2018 Slot 2 Quant Answers Free

34. Let f be a function such that f(mn) = f(m) f(n) for every positive integer m and n. If f(1), f(2), f(3) are positive integers, f(1)< f(2), and f(24) =54, then f(18) equals. (Watch video solutions to CAT 2019 – Slot-2 – QA -34)