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CAT 2019 Question Paper Slot 2 | CAT Quants

CAT Quantitative Aptitude | CAT 2019 Question Paper

Are you a CAT aspirant, looking to ace your CAT preparation online so that you can go full blazing at the questions in the upcoming CAT exam? The one answer to your queries is CAT previous year paper! Solving these papers will give you a hang of the questions to expect in the CAT Question Paper and will help you not get knocked off by the googlies the CAT Exam throws at you! CAT 2019 Question Paper Slot 2 is a perfect mix of questions that test you on your ability to comprehend the concepts instead of just remembering and applying gazillion formulas! Level up in your preparation by solving CAT previous year paper and see your online CAT preparation go upwards and onwards! Start with CAT 2019 question paper right away!

CAT 2019 Question Paper Slot 2 - Logarithms

The real root of the equation 2^6x + 2^3x+2 - 21 = 0 is
1. \\frac{log_{2}3}{3})
2. log₂9
3. \\frac{log_{2}7}{3})
4. log₂27
Choice A
\\frac{log_{2}3}{3})
CAT 2019 Question Paper Slot 2 - Averages

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. 4
2. 5
3. 4.5
4. 3.5
Choice C
4.5
CAT 2019 Question Paper Slot 2 - Number theory

Let a, b, x, y be real numbers such that a² + b² = 25 , x² + y² = 169 and ax + by = 65. If k = ay - bx, then
1. k = 0
2. k > \\frac{5}{13})
3. k = \\frac{5}{13})
4. 0 < k ≤ \\frac{5}{13})
Choice A
k = 0
CAT 2019 Question Paper Slot 2 - Geometry

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. 68
3. 72
4. 78
Choice C
72
CAT 2019 Question Paper Slot 2 - Sequence & series

Let a₁ , a₂ be integers such that a₁ - a₂ + a₃ - a₄ + ........ +(-1)^n-1 a_n = n , for n ≥ 1. Then a₅₁ + a₅₂ + ........ + a₁₀₂₃ equals
1. -1
2. 1
3. 0
4. 10
Choice B
1
CAT 2019 Question Paper Slot 2 - Number theory

How many factors of 2⁴ × 3⁵ × 10⁴ are perfect squares which are greater than 1? [TITA]
44
CAT 2019 Question Paper Slot 2 - Geometry

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. \\frac{π}{3})
2. 1
3. \\frac{1}{\sqrt{2}})
4. \\sqrt{2})
Choice B
1
CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

What is the largest positive integer such that \\frac{n^2+7n+12}{n^2-n-12}) is also positive integer?
1. 6
2. 8
3. 16
4. 12
Choice D
12
CAT 2019 Question Paper Slot 2 - Percentages

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. 6000
4. 5500
Choice A
6600
CAT 2019 Question Paper Slot 2 - Functions

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 [TITA]
12
CAT 2019 Question Paper Slot 2 - Geometry

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 [TITA]
150
CAT 2019 Question Paper Slot 2 - Speed, Time & distance

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?
1. 22
2. 20
3. 15
4. 23
Choice C
15
CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

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 < \\frac{1}{16})
2. A > \\frac{1}{8})
3. A > \\frac{1}{16})
4. A < \\frac{1}{8})
Choice C
\\frac{1}{16})
CAT 2019 Question Paper Slot 2 - Races

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? [TITA]
48
CAT 2019 Question Paper Slot 2 - Work & time

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. 13
2. 12
3. 15
4. 14
Choice A
13
CAT 2019 Question Paper Slot 2 - Ratio & proportion

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. 26
2. 32
3. 24
4. 35
Choice B
32
CAT 2019 Question Paper Slot 2 - Percentages

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 [TITA]
80
CAT 2019 Question Paper Slot 2 - Mensuration

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. 10\\sqrt{2})
2. 8\\sqrt{3})
3. 12
4. 5\\sqrt{5})
Choice A
10\\sqrt{2})
CAT 2019 Question Paper Slot 2 - Logarithms

If x is a real number ,then \\sqrt{log_{e}\frac{4x - x^2}{3}}) is a real number if and only if
1. -3 ≤ x ≤ 3
2. 1 ≤ x ≤ 2
3. 1 ≤ x ≤ 3
4. -1 ≤ x ≤ 3
Choice C
1 ≤ x ≤ 3
CAT 2019 Question Paper Slot 2 - Geometry

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. 8\\sqrt{2})
3. 6\\sqrt{2})
4. 5
Choice A
10
CAT 2019 Question Paper Slot 2 - Speed, time & distance

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. 10:27 am
2. 10:25 am
3. 10:45 am
4. 10:18 am
Choice A
10:27 am
CAT 2019 Question Paper Slot 2 - Number theory

How many pairs (m,n) of positive integers satisfy the equation the equation m² + 105 = n²? [TITA]
4
CAT 2019 Question Paper Slot 2 - Ratios and proportions

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. 7
2. 8
3. 9
4. 10
Choice A
7
CAT 2019 Question Paper Slot 2 - Mensuration

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. 8464π
3. 928π
4. 1026(1 + π)
Choice D
1026(1 + π)
CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

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
Choice B
549
CAT 2019 Question Paper Slot 2 - Number theory

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 [TITA]
7
CAT 2019 Question Paper Slot 2 - Profit & loss

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. 2000
2. 6000
3. 8000
4. 4000
Choice D
4000
CAT 2019 Question Paper Slot 2 - - Sequence & series

The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is
1. 20
2. 18
3. 21
4. 19
Choice A
20
CAT 2019 Question Paper Slot 2 - Sequence & series

If (2n+1) + (2n+3) + (2n+5) + ... + (2n+47) = 5280 , then what is the value of 1+2+3+ ... +n ? [TITA]
4851
CAT 2019 Question Paper Slot 2 - Mixtures

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. 12
3. 13
4. 14
Choice D
14
CAT 2019 Question Paper Slot 2 - Exponents & Powers

If 5^x - 3^y = 13438 and 5^x-1 + 3^y+1 = 9686 , then x+y equals [TITA]
13
CAT 2019 Question Paper Slot 2 - Simple interest & Compound interest

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 [TITA]
20920
CAT 2019 Question Paper Slot 2 - Profit & loss

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. 1
2. 1.2
3. 0.7
4. 0.50
Choice A
1
CAT 2019 Question Paper Slot 2 - Work & time

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? [TITA]
12