CAT Number system Practice Problems Set 03

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?

[1] 289
[2] 367
[3] 453
[4] 307
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Question 2:
Each of the numbers x₁, x₂,, x_n,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

[1] n is even
[2] n is odd
[3] n is an odd multiple of 3
[4] n is prime
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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

[1] / (@ (A, B), 2)
[2] × (@ (A, B), 2)
[3] @ (/ A, B), 2)
[4] @ (× (A, B), 2)
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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

[1] @ (/ (@ (/ (B, A), 2), C), 3)
[2] × (@ (/ (@ (B, A), 3), C), 2)
[3] / (×(× (@ (B, A), 2), C), 3)
[4] / (× (@ (/ (@ (B, A) 2), C), 3), 2)
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Question 5:
Let N = 55³+ 17³– 72³. N is divisible by

[1] both 7 and 13
[2] both 3 and 13
[3] both 17 and 7
[4] both 3 and 17
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