Question Bank  Number Theory  Hemant Malhotra

Number of Questions: 100
Topic: Number Theory
Answer key available? : No
Source: Elite's Grid forum

Q1) If a! + (a+1)! has 19 zeroes at the end , what is the value of a
a) 77
b) 78
c) 79
d) 80
e) CBD

Q2) How many sets of two or more consecutive positive integers have a sum of 15?

Q 3) How many fourdigit positive integers have at least one digit that is a 2 or a 3?
a) 2439
b) 4096
c) 5416
d) 4896

Q 4) For prime numbers a and b , a + b = 102 and a > b. What is the least possible value of a  b

Q 5) A randomly selects two distinct numbers from the set { 1, 2, 3, 4, 5 }, and B randomly selects a number from the set { 1, 2, ..., 10 } . What is the probability that B's number is larger than the sum of the two numbers chosen by A?

Q 6) How many fourdigit numbers, which are divisible by 15, are there such that the number 15 occurs in them?

Q 7) Sarah intended to multiply a twodigit number and a threedigit number, but she left out the multiplication sign and simply placed the twodigit number to the left of the threedigit number, thereby forming a fivedigit number. This number is exactly nine times the product Sarah should have obtained. What is the sum of the twodigit number and the threedigit number?

Q8) x = 1/10 + 1/40 + 1/88 + ... + 1/(90298)
a) 50/151
b) 25/151
c) 100/151
d) 1/11

Q9) How many integers can be expressed as a sum of three distinct numbers if chosen from the set {4, 7,10,13, ..., 46}?

Q 10) ABC is a 3 digit natural number such that ABC=5 * (AB + BC + CA). Find total number of possible values for ABC

Q 11) What is the largest possible number of elements in a subset P of S = {1, 2, 3, ... , 9} such that the sum of every pair of distinct elements in P is different

Q12) A = 5^56,
B = 10^51,
C =17^35,
D = 31^28.
which is largest number ?
(1) A
(2) B
(3) C
(4) D
(5) 2 numbers are equal

Q13) Let P be the prime number greater than 3.Find the remainder when P^2 + 17 is divided by 12 ?

Q14) If a and b are two real numbers which satisfy a + b − ab = 1 and a is not an integer, then b
(a) is never an integer
(b) must be some positive integer
(c) must be some negative integer
(d) must be equal to 0
(e) may either be an integer or a noninteger

Q15) Find eight digit numbers which is formed by doubling the first four digits (for example, 12341234) divisible by 137.

Q16) Find the sum of all 8 digit number that can be formed with the digits 1, 1, 1, 5, 5, 7, 8 and 9

Q17) Find the number of two digit numbers where the product of the digits is greater than the sum of the digits.

Q18) Find the maximum possible remainder if (104)^n is divided by 51, given that n is a natural number greater than 8

Q19) Find the smallest positive number with 21 divisors.