CAT Number system Practice Problems Set 14

Question 1:
The remainder, when (15²³ + 23²³) is divided by 19, is

[1] 4
[2] 15
[3] 0
[4] 18
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Question 2:
If \(x = \left( {{{16}^3} + {{17}^3} + {{18}^3} + {{19}^3}} \right)\), then x divided by 70 leaves a remainder of

[1] 0
[2] 1
[3] 69
[4] 35
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Question 3:
Let n! = 1 × 2 × 3 × … × n for integer n ≥ If p = 1! + (2 × 2!) + (3 × 3!) + … + (10 × 10!), then p + 2 when divided by 11! Leaves a remainder of

[1] 10
[2] 0
[3] 7
[4] 1
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Question 4:
The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B-A is perfectly divisible by 7, then which of the following is necessarily true?

[1] 100 < A < 299
[2] 106 < A < 305
[3] 112 < A < 311
[4] 118< A < 317
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Question 5:
The rightmost non-zero digits of the number 30²⁷²⁰ is

[1] 1
[2] 3
[3] 7
[4] 9
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