CAT 2023 Slot 1 - Quantitative Aptitude Test

1. If x and y are real numbers such that x² + (x - 2y - 1)² = -4y(x + y), then the value of x - 2y is:

A) 1
B) 2
C) 0
D) -1

2. Let n be the least positive integer such that 168 is a factor of 1134n. If m is the least positive integer such that 1134n is a factor of 168m, then m + n equals:

A) 12
B) 13
C) 15
D) 17

3. If √(5x + 9) + √(5x - 9) = 3(2 + √2), then √(10x + 9) is equal to:

A) √7
B) 2√7
C) 3√7
D) √21

4. If x and y are positive real numbers such that log_x(x² + 12) = 4 and 3log_y(x) = 1, then x + y equals:

A) 8
B) 9
C) 10
D) 11

5. The number of integer solutions of the equation 2|x|(x² + 1) = 5x² is:

A) 2
B) 3
C) 4
D) 5