# CAT Number System Questions for Practice

Question 1:
The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder.

What is the value of n?

Topic: HCF LCM

 289
 367
 453
 307

Question 2:
Each of the numbers x1, x2,, xn,n ≥ 4, is equal to 1 or –1. Suppose

${x_1}{x_2}{x_3}{x_4} + {x_2}{x_3}{x_4}{x_5} + {x_{n - 3}}{x_{n - 2}}{x_{n - 1}}{x_n} + ... + {x_{n - 2}}{x_{n - 1}}{x_n}{x_1} + {x_{n - 1}}{x_n}{x_1}{x_2} + {x_n}{x_1}{x_2}{x_3} = 0,$ then

Topic: Basics

 n is even
 n is odd
 n is an odd multiple of 3
 n is prime

Question 3:
A, B and C are three numbers. Let

@ (A, B) = Average of A and B,

/ (A, B) = Product of A and B, and

× (A, B) = The result of dividing A by B.

The sum of A and B is given by

Topic: Basics

 / (@ (A, B), 2)
 × (@ (A, B), 2)
 @ (/ A, B), 2)
 @ (× (A, B), 2)

Question 4:
A, B and C are three numbers. Let

@ (A, B) = Average of A and B,

/ (A, B) = Product of A and B, and

× (A, B) = The result of dividing A by B.

Average of A, B and C is given by

Topic: Basics

 @ (/ (@ (/ (B, A), 2), C), 3)
 × (@ (/ (@ (B, A), 3), C), 2)
 / (×(× (@ (B, A), 2), C), 3)
 / (× (@ (/ (@ (B, A) 2), C), 3), 2)

Question 5:
Let N = 553+ 173– 723. N is divisible by
Topic: Divisibility

 both 7 and 13
 both 3 and 13
 both 17 and 7
 both 3 and 17 