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CAT 2025 Slot 2 QA

Quantitative Ability · 22 questions · 40 minutes · +3 / −1 (no negative marking on type-in answers)

Questions

  1. Q1. If m and n are integers such that ( m + 2 n ) ( 2 m + n ) = 27 , then the maximum possible value of 2 m - 3 n …
  2. Q2. If \log _ { 64 } x ^ { 2 } + \log _ { 8 } \sqrt { y } + 3 \log _ { 512 } ( \sqrt { y } z ) = 4 , where x , y a…
  3. Q3. The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in …
  4. Q4. Let f ( x ) = \frac { x } { ( 2 x - 1 ) } and g ( x ) = \frac { x } { ( x - 1 ) } . Then, the domain of the fu…
  5. Q5. If 9 ^ { x ^ { 2 } + 2 x - 3 } - 4 \left( 3 ^ { x ^ { 2 } + 2 x - 2 } \right) + 27 = 0 , then the product of a…
  6. Q6. Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of th…
  7. Q7. If a , b , c and d are integers such that their sum is 46 , then the minimum possible value of ( a - b ) ^ { 2…
  8. Q8. Let a _ { n } be the n ^ { \text {th } } term of a decreasing infinite geometric progression. If a _ { 1 } + a…
  9. Q9. Suppose a , b , c are three distinct natural numbers, such that 3 a c = 8 ( a + b ) . Then, the smallest possi…
  10. Q10. Two tangents drawn from a point P touch a circle with center O at points Q and R . Points A and B lie on P Q a…
  11. Q11. The number of divisors of \left( 2 ^ { 6 } \times 3 ^ { 5 } \times 5 ^ { 3 } \times 7 ^ { 2 } \right) , which …
  12. Q12. Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start t…
  13. Q13. The ratio of expenditures of Lakshmi and Meenakshi is 2 : 3, and the ratio of income of Lakshmi to expenditure…
  14. Q14. The set of all real values of x for which \left( x ^ { 2 } - | x + 9 | + x \right) > 0 , is
  15. Q15. An item with a cost price of Rs. 1650 is sold at a certain discount on a fixed marked price to earn a profit o…
  16. Q16. The equations 3 x ^ { 2 } - 5 x + p = 0 and 2 x ^ { 2 } - 2 x + q = 0 have one common root. The sum of the oth…
  17. Q17. A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and coco…
  18. Q18. A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and secon…
  19. Q19. Rita and Sneha can row a boat at 5 km/h and 6 km/h in still water, respectively. In a river flowing with a con…
  20. Q20. The sum of digits of the number ( 625 ) ^ { 65 } \times ( 128 ) ^ { 36 } , is
  21. Q21. In a \triangle A B C , points D and E are on the sides BC and AC , respectively. BE and AD intersect at point …
  22. Q22. A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received 20% of the total amount…