### Number Systems, Number Theory sample practice questions & Answers. LCM, HCF, Remainders, Remainder theorem - 2IIM : MBA Entrance Preparation

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# Number Theory Questionbank - CAT 2013 Sample Questions

###### Number Theory is an oft repeated topic in the Quant section of CAT
An oft repeated topic in CAT since CAT 2000. Questions include simple word problems testing one's understanding of application of LCM, HCF, Factors, Divisibility to questions that would require knowledge of remainders, remainder theorem, factorials, different bases to which numbers can be expressed.
1. Question 1  The largest number amongst the following that will perfectly divide 101100 - 1 is
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2. Question 2  A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
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3. Question 3  How many keystrokes are needed to type numbers from 1 to 1000?
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4. Question 4  When 242 is divided by a certain divisor the remainder obtained is 8. When 698 is divided by the same divisor the remainder obtained is 9. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 4. What is the value of the divisor?
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5. Question 5  Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?
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6. Question 6  What number should be subtracted from x3 + 4x2 - 7x + 12 if it is to be perfectly divisible by x + 3?
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7. Question 7  What is the minimum number of square marbles required to tile a floor of length 5 metres 78 cm and width 3 metres 74 cm?
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8. Question 8  A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?
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9. Question 9  For what value of 'n' will the remainder of 351n and 352n be the same when divided by 7?
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10. Question 10  What is the remainder when 91 + 92 + 93 + .... + 98 is divided by 6?
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11. Question 11  Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?
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12. Question 12  N is the smallest number that has 5 factors. How many factors does N - 1 have?
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13. Question 13  What is the smallest number that has exactly 12 factors?
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14. Question 14  If f(x) is the number of primes less than or equal to x, find the value of f(90) - f(80).
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15. Question 15  The difference between the ages of two brothers is a prime number. Sum of their ages is also a prime number. If the elder brother is 28 years old, how many different values can the age of the younger brother take?
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16. Question 16  A number N2 has 15 factors. How many factors can N have?
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17. Question 17  If a three digit number abc has 2 factors, how many factors does the 6-digit number abcabc have?
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18. Question 18  Find the smallest number that has exactly 18 factors.
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## CAT Practice Questions and Answers : Listed Topicwise

 Number Theory Permutation & Probability Data sufficiency Inequalities Geometry Mensuration Trigonometry Coordinate Geometry Percentages Profit Loss Ratio Proportion Mixtures Alligation Speed Time Distance Pipes Cisterns Linear Quadratic Races Progressions, AP & GP New Topic New Topic New Topic

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