Question Bank  Number Theory

Number of Questions : 15
Topic : Number Theory
Answer key available ? : Yes (Last Post)
Source :

Q1) From a set of first 20 consecutive positive integers, 3 are picked randomly and their sum is found as S. How many different values of S are possible?
A. 18
B. 52
C. 57
D. 1140

Q2) TGₐ is a two digit number in basea such that T > 0 and T, G < a. For which value of TG, can TGₐ be a perfect square in some basea?
A. 32
B. 43
C. both of these
D. none of these

Q3) Find the remainder when 484848 is divided by 728.
A. 0
B. 28
C. 48
D. none of these

Q4) How many distinct integers are there in the sequence [1²/100], [2²/100], [3²/100], [4²/100]... [100²/100] where [x] is greatest integer less than or equal to x?
A. 75
B. 76
C. 100
D. 101

Q5) Sum of ten consecutive integers is N. What is the sum of next ten consecutive integers?
A. 2N
B. N + 45
C. N + 55
D. N + 100

Q6) How many 21 digit numbers are there whose first 10 digits are 1 each and last 10 digits are 2 each and also the complete 21 digit number is divisible by 7?
A. 0
B. 1
C. 2
D. 3

Q7) What is the highest possible common factor of two consecutive terms of a sequence whose nth term is given by n² + 10?
A. 1
B. 2
C. 41
D. 59

Q8) On planet LOGIKA, an alien digit φ is being used between 3 and 4 along with all the usual digit we use on earth. What will be the age of a 94 years old inhabitant of LOGIKA on earth?
A. 103
B. 104
C. 114
D. 115

Q9) Nimai wrote all natural numbers, none of whose digits is a prime number, in order. First ten numbers which Nimai wrote are as follows: 1, 4, 6, 8, 9, 10, 11, 14, 16, 18. What is the 123rd number, Nimai might be writing?
A. 646
B. 666
C. 816
D. 840

Q10) What is the highest power of 2 which divides [10²ºººº/(10¹ºº + 2)] completely where [x] is greatest integer less than or equal to x?
A. 99
B. 100
C. 199
D. 200

Q11) Number of factors of 12100 which are less than 110 but not factors of 110 is
A. 6
B. 7
C. 8
D. 9

Q12) For how many positive integers, N there are odd number of factors of N² + 3N + 13?
A. 0
B. 1
C. 2
D. 3

Q13) Find the remainder when 6{(p  4)!} is divided by p where p is a prime number greater than 2013.
A. 0
B. 1
C. p  1
D. none of these

Q14) Number of factors of P is Q. Number of factors of Q is R. Number of factors of R is S and number of factors of S is 3. If P is smallest such number then what is the sum of digits of P?
A. 3
B. 6
C. 9
D. 12

Q 15) In how many ways can 100 be written as sum of two or more consecutive odd integers?
A. 2
B. 3
C. 4
D. 5

Answer Key:
#1. B 52
#2. D none of these
#3. A 0
#4. B 76
#5. D (N + 100)
#6. C 2
#7. C 41
#8. D 115
#9. A 646
#10. C 199
#11. A 6
#12. B 1
#13. B 1
#14. B 6
#15. D 5

@kamal_lohia 20C3..how come 52 is the ans?

@kamal_lohia Option A 0 is the answer

@kamal_lohia (N+100)