# 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 base-a such that T > 0 and T, G < a. For which value of TG, can TGₐ be a perfect square in some base-a?
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

#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)

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