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# 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
Topic: Digits

 1
 0
 5
 6

Question 2:
The remainder when 784 is divided by 342 is
Topic: Remainders

 0
 1
 49
 341

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

Topic: Basics

 A and C only
 A and B only
 A only
 None of these

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
Topic: HCF LCM

 $\frac{1}{2}n$
 $\left( {n - 1} \right)$
 N
 None of these

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?
Topic: Digits

 18
 108
 198
 288

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