CAT 2019 Slot 2 QA

Quantitative Ability · 34 questions · 60 minutes · +3 / −1 (no negative marking on type-in answers)

Questions

Q1. The real root of the equation 2 6x + 2 3x+2 - 21 = 0 is
Q2. The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is …
Q3. 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, th…
Q4. In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respect…
Q5. Let a 1 , a 2 be integers such that a 1 - a 2 + a 3 - a 4 + ........ +(-1) n-1 a n = n , for n ≥ 1. Then a 51 …
Q6. How many factors of 2 4 × 3 5 × 10 4 are perfect squares which are greater than 1? [TITA]
Q7. Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third…
Q8. What is the largest positive integer such that \frac{n^2+7n+12}{n^2-n-12} is also positive integer?
Q9. In 2010, a library contained a total of 11500 books in two categories - fiction and non-fiction. In 2015, the …
Q10. 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 …
Q11. Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B…
Q12. A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motorcycle leaves A…
Q13. Let A be a real number. Then the roots of the equation x 2 - 4x - log 2 A = 0 are real and distinct if and onl…
Q14. 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…
Q15. 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 da…
Q16. In an examination, Rama's score was one-twelfth of the sum of the scores of Mohan and Anjali. After a review, …
Q17. 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…
Q18. The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length …
Q19. If x is a real number ,then \sqrt{log_{e}\frac{4x - x^2}{3}} is a real number if and only if
Q20. Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the …
Q21. 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…
Q22. How many pairs (m,n) of positive integers satisfy the equation the equation m 2 + 105 = n 2 ? [TITA]
Q23. 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 …
Q24. A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of soli…
Q25. The quadratic equation x 2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following…
Q26. In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fift…
Q27. Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the r…
Q28. The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464…
Q29. If (2n+1) + (2n+3) + (2n+5) + ... + (2n+47) = 5280 , then what is the value of 1+2+3+ ... +n ? [TITA]
Q30. The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessel…
Q31. If 5 x - 3 y = 13438 and 5 x-1 + 3 y+1 = 9686 , then x+y equals [TITA]
Q32. Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annual…
Q33. A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a los…
Q34. John gets Rs 57 per hour of regular work and Rs 114 per hour of overtime work. He works altogether 172 hours a…