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CAT 2019 Quant - Slot 2 Past Year Questions

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1. CAT 2019 Quant - Slot 2

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is

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

Vessel A Contains 50 gm of salt and 450 ml water vessel B contains 110 gm of salt and 390 ml water vessel C contains 160 gm of salt & 340 ml water After the transfer of 100 ml from A to B A will contain 360 ml water & 40 gm salt and B will contain 120 gm of salt and 480 ml water which makes B having 20% salt strength. After the transfer of 100 ml from B to C, C will Contain 180 gm of salt & 420 ml of water making it have salt strength = 30% After the final transfer of 100 ml from C to A, A will contain 70 gm of salt and 430 ml water making the salt strength in A = 14%
Alternate method:- CAT 2019 Slot 2 Quant Answer 1 Answer = 14%

Correct Answer

Option 3
Video Explanation

2. CAT 2019 Quant - Slot 2

The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?

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

CAT 2019 Slot 2 Quant Answer 2

Correct Answer

Option 2
Video Explanation

3. CAT 2019 Quant - Slot 2

Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. 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

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

Let the circumference = 100m. Let the meeting point is X. The Distance P to X clockwise is 60 m and distance P to X anti-clockwise is 40 m. A Travelled 40 m in 12 min, so he can cover 60 m in Speeds of A and B are in the ratio 6:4 (Because A and B covered 60 m & 40 m respectively in the same time so their speeds are in the ratio 6:4) So the time taken by B to cover 60 m = min., So 10:27 am is the answer.

Correct Answer

Option 3
Video Explanation

4. CAT 2019 Quant - Slot 2

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 20 cm. The vertical height of the pyramid, in cm, is

  1. 12
  2. 10√2
  3. 8√3
  4. 5√5

CAT 2019 Slot 2 Quant Answer 4

Correct Answer

Option 2
Video Explanation

5. CAT 2019 Quant - Slot 2

CAT 2019 Slot 2 Quant Ques 5
  1. 6
  2. 16
  3. 12
  4. 8

CAT 2019 Slot 2 Quant Answer 5

Correct Answer

Option 3
Video Explanation

6. CAT 2019 Quant - Slot 2

Let A be a real number. Then the roots of the equation x2 – 4x – log2A = 0 are real and distinct if and only if

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

CAT 2019 Slot 2 Quant Answer 6

Correct Answer

Option 3
Video Explanation

7. CAT 2019 Quant - Slot 2

Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was

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

Profit from six of the bicycles = 6 × 25 % of x (where x is the purchase price of a bicycle) Loss from four of the bicycles = 4 × 25% of x Total net profit = 2000 = 6 × 25% of x – 4 × 25 % of x ⇒ 1.5 x – x = 2000 ⇒ x = 4000

Correct Answer

Option 1
Video Explanation

8. CAT 2019 Quant - Slot 2

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?

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

The sum of integers is 30 x 5 = 150. According to the question, exactly 20 integers do not exceed 5. Since the question is asking about the maximum value of the average of 20 integers, so we will find the minimum value of the remaining 10 integers which have to be greater than 5. So the sum of 10 integers each of them having value 6 is = 10 x 6 = 60. So remaining sum = 150 - 60 = 90. Hence the maximum value of the average of the remaining 20 integers is 90/20 = 4.5

Correct Answer

Option 3
Video Explanation

9. CAT 2019 Quant - Slot 2

Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f (2), and f (24) = 54, then f (18) equals (type in box)

f (1×2) = f(1) f(2) f (2) = f(1) f(2) ⇒ f (1) = 1 Also, f(2) > f(1) Let f(2) = a, f(3)=b. f(4) = f(2) × f(2) = a2 f(6) = f(2) × f(3) = ab f(24) = a3 b = 54 ⇒ a = 3, b=2 So f (18) = f(3) ×f(6) = ab2 = 12.

Correct Answer

12
Video Explanation

10. CAT 2019 Quant - Slot 2

Let a1, a2, ….. be integers such that

a1 – a2+ a3 – a4 + … + (-1)n-1an = n, for all n ≥ 1.

Then a51 + a52+ …+ a1023 equals

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

CAT 2019 Slot 2 Quant Answer 10

Correct Answer

Option 2
Video Explanation

11. CAT 2019 Quant - Slot 2

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

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

Let the scores of Rama, Mohan and Anjali are R,M and A respectively. R = (M+A) After the score of each of them increased by 6, the ratio of their scores are 11:10:3 fo Anjali, Mohan & Rama respectively. Let their scores are 11x, 10x, 3x. Their original scores before the increase were 11x-6, 10x-6, 3x-6 respectively So 3x-6 = (11x-6 + 10x -6) 3x – 6 = (21x -12) ⇒ x = 4 Anjali’s score exceeded Rama’s score by (11x-6)-(3x-6)=8x=32

Correct Answer

Option 1
Video Explanation

12. CAT 2019 Quant - Slot 2

A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?

  1. 20
  2. 23
  3. 15
  4. 22

Since cyclist takes one hour to reach from A to B and 45 motor cycles starting from 10:01,10:02,----------,10:45 am leave from A to reach B by 11 am, So the last motorcycle takes 15 min to reach from A to B. Hence every motorcycle takes 15 min to reach from A to B. If the cyclist doubles his speed then he will reach B at 10:30 am and hence the last motorcyclist who will reach B at 10:30 am has to leave from A at 10:15. Therefore 15 motorcycles will reach B in the given time. Answer= 15

Correct Answer

Option 3
Video Explanation

13. CAT 2019 Quant - Slot 2

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

  1. 10
  2. 6√2
  3. 5
  4. 8√2

For the maximum possible value of AP, x =y=⇒ maximum (in cm) AP = 10

Correct Answer

Option 1
Video Explanation

14. CAT 2019 Quant - Slot 2

In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

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

BF = 6 cm, FE = 3cm, AF = 8cm, FD = 4 cm Area of triangle ABE = So area of triangle ABC = 72 cm2

Correct Answer

Option 2
Video Explanation

15. CAT 2019 Quant - Slot 2

How many pairs (m, n) of positive integers satisfy the equation m2 + 105 = n2 ? (type in box)

105 = n2 – m2 = (n-m) (n+m) 31×71×51 = (n-m) (n+m) Number of factors of 105 = (1+1) (1+1) (1+1) = 8 So possible pairs for (n-m) & (n+m) are four (Answer = 4.)

Correct Answer

4
Video Explanation

16. CAT 2019 Quant - Slot 2

The real root of the equation 26x+ 23x+2– 21 = 0 is

CAT 2019 Slot 2 Quant Ques 16

Let 23x = y ⇒ y2 +22 y-21 = 0 ⇒ y2+4y-21=0 ⇒ y = 3, -7. The only possible value is y = 3 ⇒ 23x = 3 ⇒ 3x = log23 ⇒ x = log23/3

Correct Answer

Option C
Video Explanation

17. CAT 2019 Quant - Slot 2

CAT 2019 Slot 2 Quant Ques 17
  1. – 3 ≤ x ≤ 3
  2. 1 ≤ x ≤ 2
  3. – 1 ≤ x ≤ 3
  4. 1 ≤ x ≤ 3

CAT 2019 Slot 2 Quant Answer 17

Correct Answer

Option 4
Video Explanation

18. CAT 2019 Quant - Slot 2

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? (type in box)

Let number of regular working hours = x hours and number of overtime working hours = y hours. x+y = 172 15% of 57x = 114 y 57 × 15 % of (172 –y ) = 114 y ⇒ y = 12

Correct Answer

12
Video Explanation

19. CAT 2019 Quant - Slot 2

Two circles, each of radius 4 cm, 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, in cm, is

  1. π/3
  2. 1
  3. 1/√2
  4. √2

CAT 2019 Slot 2 Quant Answer 19 Considers ∆ APB having right angle at B AP = 4 + r BP = 4 – r AB = 4 Applying Pythagoras theorem (4+r)2 = ( 4 –r)2 + 42 ⇒ (4+r)2 – (4-r)2=16 ⇒ 16r=16 ⇒ r= 1 cm

Correct Answer

Option 2
Video Explanation

20. CAT 2019 Quant - Slot 2

If 5x– 3y= 13438 and 5x-1+ 3y+1 = 9686, then x + y equals (type in box)

CAT 2019 Slot 2 Quant Answer 20

Correct Answer

13
Video Explanation

21. CAT 2019 Quant - Slot 2

A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc 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 radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is

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

CAT 2019 Slot 2 Quant Answer 21

Correct Answer

Option 2
Video Explanation

22. CAT 2019 Quant - Slot 2

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 (type in box)

Let the score of D = 100 Then Score of C = 80 ⇒ Score of B = 100 ⇒ Score of A = 90 So if A scores 90 then D scores 100 ⇒ if A scores 72 then D scores 80 (Answer = 80)

Correct Answer

80
Video Explanation

23. CAT 2019 Quant - Slot 2

How many factors of 24 x 35 x 104are perfect squares which are greater than 1? (type in box)

CAT 2019 Slot 2 Quant Answer 23

Correct Answer

44
Video Explanation

24. CAT 2019 Quant - Slot 2

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. 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? (type in box)

CAT 2019 Slot 2 Quant Answer 24

Correct Answer

48
Video Explanation

25. CAT 2019 Quant - Slot 2

Let a, b, x, y be real number such that a2 + b2 = 25, x2 + y2 = 169, and ax + by = 65. If k = ay – bx, then

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

Lets try Hit and trial approach: Take a = 5 then b = 0, x = 13 and y = 0. So, k = ay-bx = 0 The only option that works here is 1st option. Technical approach: ax + by = 65 and –bx + ay = k , solving these two equations for x and y , we get , x = (65a – kb ) / 25 and y = ( 65b + ak ) / 25 By substituting these values in x2 + y2 = 169, we get k = 0.

Correct Answer

Option 1
Video Explanation

26. CAT 2019 Quant - Slot 2

The number of common terms in the two sequences: 15, 19, 23, 27,……., 415 and 14, 19, 24, 29,……..,464 is

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

15,19,23,27,--------415 A.P. with common difference = 4 14,19,24,29,----------- 464 A.P. with common difference = 5 LCM of 4 & 5 = 20 which has to be the common difference in the sequence of common terms. So, Common terms are : 19 , 39, 59 ----- 415 19 + 20(n-1) ≤ 415 20(n-1) ≤ 396 n ≤ 20.8 So, n = 20

Correct Answer

Option 2
Video Explanation

27. CAT 2019 Quant - Slot 2

In 2010, 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 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

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

Let the number of Fiction books = x and the number of Non-fiction books = y Given that, x+y = 11500 1.1x+1.12y = 12760 Solving the above two equations by multiplying the first one by 1.1 and then subtracting from the second equation: we get .02 y = 110 So y = 5500 and x = 6000 So, 1.1 x = 6000 × 1.1= 6600

Correct Answer

Option 1
Video Explanation

28. CAT 2019 Quant - Slot 2

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 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 fifth and sixth digits. Then, the largest possible value of the fourth digit is (type in box)

Let the six digit number be 100000a + 10000b+1000c+100d+10e+f Where a,b,c,d,e and f are digits. Given that, f= a+b+c ⇒f = a+2a+a=4a e = a+b ⇒ e = a+2a=3a c = a ⇒d = 7a b = 2a d= e+f ⇒ largest value possible for d is 7

Correct Answer

7
Video Explanation

29. CAT 2019 Quant - Slot 2

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 increased by 25% during 2010-2015, then the percentage increase in Rajesh’s salary during this period is closest to:

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

Let the salaries of Ramesh , Ganesh and Rajesh were 6x,5x,7x respectively in 2010. Let the salaries of Ramesh , Ganesh and Rajesh were 3y,4y,3y respectively in 2015. Salary of Ramesh in 2010 = 6x Salary of Ramesh in 2015 = 3y = 6x × 1.25 = 7.5x So y = 2.5 x Salary of Rajesh in 2010 = 7x and that in 2015 = 3y = 7.5 x CAT 2019 Slot 2 Quant Answer 29 ≈ 7%

Correct Answer

Option 2
Video Explanation

30. CAT 2019 Quant - Slot 2

If (2n + 1) + (2n + 3) + (2n + 5) + …. + (2n + 47) = 5280, then what is the value of 1 + 2 + 3 + …+ n? (type in box)

The given series has 24 terms and hence can be written as: 48 n + [ 1+3+5+--------47] = 5280 48 n + 576 = 5280 So, n = 98

Correct Answer

4851
Video Explanation

31. CAT 2019 Quant - Slot 2

Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle 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 (type in box)

CAT 2019 Slot 2 Quant Answer 31

Correct Answer

150
Video Explanation

32. CAT 2019 Quant - Slot 2

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?

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

CAT 2019 Slot 2 Quant Answer 32

Correct Answer

Option 3
Video Explanation

33. CAT 2019 Quant - Slot 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 (type in box)

CAT 2019 Slot 2 Quant Answer 33

Correct Answer

20920
Video Explanation

34. CAT 2019 Quant - Slot 2

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

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

CAT 2019 Slot 2 Quant Answer 34

Correct Answer

Option 2
Video Explanation
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