Question Bank  Number Theory  Shashank Prabhu, CAT 100 Percentiler

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]

Q72) The number of 6digit numbers of the form ababab (where a and b are distinct, nonnegative integers) each of which is a product of exactly 6 district primes is
a. 11
b. 10
c. 14
d. None of these
[OA: Option a]

Q75) Find the sum of the series 6/6 + 12/15 + 12/35 + 24/77 + 12/143 + 24/221 + 12/323 + 24/437 + 36/667 + 12/899
[OA: 87/31]

Q80) There is a set of numbers S, which contains all the numbers from 1 to 50. What is the minimum number of numbers you need to choose from S such that there are at least two numbers with a common divisor greater than 1 in those numbers always ?
[OA: 17]

Q93) A, B, C, D, E and F are six singledigit nonnegative integers such that A < B < C < D < E < F. Threedigit number CFC is a perfect square, BE is a twodigit prime number and A + D + F = B + C + E.
1  What is the value of D?
a. 4
b. 5
c. 6
d. Cannot be determined2  The fourdigit natural number BEFC is definitely not divisible by which of the following twodigit numbers?
a. CB
b. AA
c. CC
d. CE[OA: Option d, Option d]

Q95) There are 5 distinct real numbers out of which all possible triplets are selected and for each triplet the three numbers are added. The different sums that are generated are:
(– 8, 1, 3, 5, 7, 8, 10, 16, 19 and 23).1  The smallest among the 5 numbers is
a. – 6
b. – 9
c. – 8
d. – 72  The third largest number is
a. – 1
b. 1
c. 0
d. 7[OA: Option a, Option b]

Q12)
[OA: Option 4]

Q13) N is an eight digit number and S(N) is the sum of the digits of N. If N + S(N) = 100,000,000 what would be N?
[OA: 99999941]

Q21)
[OA: 1277]

Q22) N represents a series in which all the terms are consecutive integers and the sum of all the terms of N is 100. If the number of terms of N is greater than one, find the difference between the maximum and the minimum possible number of terms.
a. 20
b. 30
c. 45
d. 195[OA: 195]

Q25)
[OA: 8]

Q26) The sequence 3, 15, 24, 48, contains numbers that are multiples of 3 and one less than a perfect square. Find the remainder when the 1,994th term of the series is divided by 1,000.
[OA: 63]

Q34) 1010101… is a 94digit number. What will be the remainder obtained when this number is divided by 375?
[OA: 260]

Q40) If n = 999 ... 99 is an integer consisting of a string of 2009 nines, then find the sum of digits of n^2.
[OA: 18081]

Q44) (11/3) + (11/8) + (11/15) + (11/24) + (11/35) + ... (11/99) = ?
[OA: 36/5]

Q45) Which of the following can be the number of zeroes at the end of the factorial of a natural number?
a) 156
b) 29
c) 30
d) 155[OA: Option a]

Q46)
[OA: 1]

Q49) What is the largest integer x for which 85! is completely divisible by 42^x?
[OA: 13]

Q51) Find the sum of all positive integers from 1 to 100 which will give a remainder of 2 when divided by 3.
[OA: 1650]