Question Bank  Number Theory  Shashank Prabhu, CAT 100 Percentiler

Q57) If a = sqrt(3) + 1, then the value of a^4  6a^2 + 8a is
a. 12a  3
b. 12a
c. 4a
d. 8a  3

Q58) If the eightdigit number N = 76542a3b is divisible by 18, find the number of possible values of N.

Q66) If N = 1!  2! + 3!  4! + 5! ... + 47!  48! + 49! then what is the unit's place digit of N^N?

Q67) Two different two digit numbers are written beside each other to form a 4 digit number such that the smaller number is to the right. The difference between these two numbers when subtracted from the 4 digit number so formed is 5481. What is the sum of the two 2 digit numbers?

Q70) Given that 1/(2!17!) + 1/(3!16!) + 1/(4!15!) + 1/(5!14!) + 1/(6!13!) + 1/(7!12!) + 1/(8!11!) + 1/(9!10!) = N /(1!18!)
Find the greatest integer that is less than N/100. (in numerical value)

Q72) How many natural numbers exist which divide at least one among 28^12, 18^8 and 21^6?

Q73) All the twodigit natural numbers whose unit digit is greater than their ten’s digit are selected. If all these numbers are written one after the other in a series, how many digits are there in the resulting number?

Q74) The set X consists of m consecutive integers such that their sum is 2m. The set Y consists of 2m consecutive integers such that their sum is m. The difference between the largest elements of X and Y is 9. What is the value of m?
a) 17
b) 36
c) 9
d) 21

Q80) How many natural numbers less than 10000 are present such that the sum of the digits of any such number is 33 and the number is divisible by 6?

Q84) a and b are two positive numbers such that their sum is less than their product. The product of these two numbers would always be more than?

Q89) The largest possible number divides four numbers, 5688, 6552, 7848 and 8712 to leave the same remainder in each case. What is the remainder?

Q92) How many numbers less than 1000 have their sum of digits as 12?

Q100) What is the remainder when the sum of all the terms in the 1024th row of the pascal triangle is divided by 1000.

Q4) How many numbers greater than 13000 can be formed using the digits 5, 0, 8, 1 and 7 such that each digit is used exactly once?
[OA: 90]

Q20) The sum of a twodigit number and the number formed by interchanging the two digits is 45 more than twice the original number. If the sum of the digits of the number is 9, what is the original number?
[OA: 27]

Q21) A sixdigit number is formed by writing 3 consecutive twodigit number side by side in ascending order. If the number so formed is divisible by 2,3,4,5,6,8, then what is the hundreds digit of the number?
[OA: 9]

Q29) What is the digit at the hundredths place of the number N = 45^36 ?
[OA: 6]

Q36) What is the value of expression 1/2! + 2/3! + 3/4! + ... + 7/8!
[OA: 1  (1/8!)]

Q59) What is the sum of factors of each factor of 1024?
[OA: 4083]

Q70) A set N is formed by selecting some of the numbers from the first 110 natural numbers such that the GCD of any two numbers in the set is 5. What is the maximum number of elements that set N can have?
[OA: 9]