Number Theory Questionbank - CAT 2007 Sample Questions
An oft repeated topic in CAT since CAT 2000. Questions include simple word
problems testing one's understanding of appli class="text"cation of LCM, HCF, Factors,
Divisibili class="text"ty 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
Answer and Explanation �
- 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?
Answer and Explanation �
- Question 3 How many keystrokes are needed to type
numbers from 1 to 1000?
Answer and Explanation �
- 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?
Answer and Explanation �
- 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?
Answer and Explanation �
- Question 6 What number should be subtracted from x3
+ 4x2 - 7x + 12 if it is to be perfectly divisible by x + 3?
Answer and Explanation �
- 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?
Answer and Explanation �
- 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?
Answer and Explanation �
- Question 9 For what value of 'n' will the remainder of
351^n and 352^n be the same when divided by 7?
Answer and Explanation �
- Question 10 What is the remainder when 9^1 + 9^2 + 9^3
+ .... + 9^8 is divided by 6?
Answer and Explanation �
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