CAT Number system Practice Problems Set 01

Question 1:
Let a, b, c be distinct digits. Consider a two-digit number ‘ab’ and a three-digit number ‘ccb’, both defined under the usual decimal number system, if (ab)²= ccb > 300, then the value of b is

[1] 1
[2] 0
[3] 5
[4] 6
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Question 2:
The remainder when 7⁸⁴ is divided by 342 is

[1] 0
[2] 1
[3] 49
[4] 341
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Question 3:
If n = 1+ x where x is the product of four consecutive positive integers, then which of the following is/are true?

A. n is odd

B. n is prime

C. n is a perfect square

[1] A and C only
[2] A and B only
[3] A only
[4] None of these
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Question 4:
For two positive integers a and b define the function h(a,b) as the greatest common factor (G.C.F) of a, b. Let A be a set of n positive integers. G(A), the G.C.F of the elements of set A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is

[1] \(\frac{1}{2}n\)
[2] \(\left( {n - 1} \right)\)
[3] N
[4] None of these
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Question 5:
Let D be a recurring decimal of the form D = 0. abababab ..., where digits a and b lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D?

[1] 18
[2] 108
[3] 198
[4] 288
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