Number Theory Questionbank - CAT 2008 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.
- Question 1 The largest number amongst the following that will perfectly divide 101100 - 1 is
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- 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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- Question 3 How many keystrokes are needed to type numbers from 1 to 1000?
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- 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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- 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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- 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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- 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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- 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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- Question 9 For what value of 'n' will the remainder of 351^n and 352^n be the same when divided by 7?
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- Question 10 What is the remainder when 9^1 + 9^2 + 9^3 + .... + 9^8 is divided by 6?
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