129 + Interview Questions in Number Theory And Cryptography in Discrete Mathematics Page 3 InterviewSolution

101.	LCM(a, b) is equals to _________(a) ab/(GCD(a, b))(b) (a+b)/(GCD(a, b))(c) (GCD(a, b))/ab(d) none of the mentionedThis question was addressed to me by my school teacher while I was bunking the class.My enquiry is from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» The correct option is (a) ab/(GCD(a, b)) EXPLANATION: ab = LCM(a, b)*gcd(a, b), which IMPLIES LCM(a,b) = ab/(GCD(a,b)).

Discussion

102.	State whether the given statement is True or False.(a) = LCM(a,(LCM(b,(LCM(c, d)))).(b) True(c) FalseI have been asked this question in an online interview.This interesting question is from Number Theory topic in section Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT CHOICE is (a) = LCM(a,(LCM(B,(LCM(C, d)))). For explanation: LCM function can be reursively defined.

Discussion

103.	If a number is 2^2 x 3^1 x 5^0 and b is 2^1 x 3^1 x 5^1 then lcmof a, b is?(a) 2^2 x 3^1 x 5^1(b) 2^2 x 3^2 x 5^2(c) 2^3 x 3^1 x 5^0(d) 2^2 x 3^2 x 5^0The question was asked during an interview.This question is from Number Theory topic in division Number Theory and Cryptography of Discrete Mathematics
Answer» The correct OPTION is (a) 2^2 X 3^1 x 5^1 Explanation: LCM is the product of sets having highest exponent value among a and B.

Discussion

104.	If LCM of two number is 14 and GCD is 1 then the product of two numbers is?(a) 14(b) 15(c) 7(d) 49The question was posed to me in exam.I'm obligated to ask this question of Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» RIGHT choice is (a) 14 The explanation: The lcm of TWO NUMBER a and b is given by lcm(a, b) = ab/(GCD(a, b)), this IMPLIES ab = lcm(a, b) * gcd(a, b).

Discussion

105.	The product of two numbers are 12 and their Greatest common divisor is 2 then LCM is?(a) 12(b) 2(c) 6(d) None of the mentionedI had been asked this question in an internship interview.This question is from Number Theory topic in portion Number Theory and Cryptography of Discrete Mathematics
Answer» The correct option is (c) 6 Explanation: The lcm of TWO number a and B is GIVEN by lcm(a, b) = AB/(GCD(a, b)).

Discussion

106.	LCM of 6, 10 is?(a) 60(b) 30(c) 10(d) 6This question was posed to me by my college director while I was bunking the class.The origin of the question is Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» Correct option is (b) 30 To EXPLAIN I would SAY: Since 30 is the smallest INTEGER divisible by 6 and 10.

Discussion

107.	If a, b are integers such that a > b then lcm(a, b) lies in _________(a) a>lcm(a, b)>b(b) a>b>lcm(a, b)(c) lcm(a, b)>=a>b(d) none of the mentionedThe question was posed to me by my college professor while I was bunking the class.My question comes from Number Theory in division Number Theory and Cryptography of Discrete Mathematics
Answer» Correct answer is (c) lcm(a, B)>=a>b For explanation I WOULD say: LCM of number is either equal to the BIGGEST number or GREATER than all.

Discussion

108.	The LCM of two number 1, b(integer) are _________(a) b + 2(b) 1(c) b(d) None of the mentionedThis question was posed to me in class test.My doubt is from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» The CORRECT OPTION is (c) b The EXPLANATION: Since b is the SMALLEST integer DIVISIBLE by 1 and b.

Discussion

109.	A Least Common Multiple of a, b is defined as __________(a) It is the smallest integer divisible by both a and b(b) It is the greatest integer divisible by both a and b(c) It is the sum of the number a and b(d) None of the mentionedI had been asked this question in final exam.Asked question is from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» Correct option is (a) It is the smallest integer divisible by both a and B Explanation: DEFINITION of LCM(a, b)-smallest multiple of a and b.

Discussion

110.	Pseudo prime are classified based on property which they satisfy, which of the following are classes of pseudoprimes?(a) Fermat pseudoprime(b) Fibonacci pseudoprime(c) Euler pseudoprime(d) All of the mentionedI have been asked this question during an interview for a job.My question is taken from Number Theory topic in section Number Theory and Cryptography of Discrete Mathematics
Answer»

Discussion

111.	What is pseudo prime number?(a) is a probable prime and is not a prime number(b) is a prime number(c) does not share any property with prime number(d) none of the mentionedThis question was posed to me during an online exam.Origin of the question is Number Theory in portion Number Theory and Cryptography of Discrete Mathematics
Answer» Correct CHOICE is (a) is a probable prime and is not a prime number To explain I would say: A pseudo prime number is an INTEGER that SHARES a property COMMON to all prime number and is not a prime number.

Discussion

112.	Which of the following is a quardratic residue of 11?(a) 4(b) 5(c) 9(d) All of the mentionedThe question was posed to me in a national level competition.My doubt is from Number Theory in section Number Theory and Cryptography of Discrete Mathematics
Answer» The CORRECT choice is (d) All of the mentioned Easiest EXPLANATION: Since 4, 16, 32 satisfies the criteria, all are quardratic residue of 11.

Discussion

113.	8 is quardratic residue of 11.(a) True(b) FalseThis question was posed to me during an internship interview.My enquiry is from Number Theory in division Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT ANSWER is (B) False Best explanation: SINCE x^2 ≡ 8(mod)17 has no SOLUTIONS.

Discussion

114.	4 is quardratic residue of 7.(a) True(b) FalseI had been asked this question during an internship interview.This intriguing question originated from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT OPTION is (a) True Best explanation: SINCE 25 ≡ 4(mod)7, 4 is quardratic residue of 7.

Discussion

115.	8 is quardratic residue of 17.(a) True(b) FalseI got this question in a national level competition.The question is from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» The CORRECT OPTION is (a) True Easy explanation: Since 25 ≡ 8(mod)17.

Discussion

116.	5 is quardratic non-residue of 7.(a) True(b) FalseThis question was addressed to me by my college professor while I was bunking the class.This key question is from Number Theory in division Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT OPTION is (a) True The explanation: Since there EXISTS no NUMBER which gives 5 modulo 7 when squared.

Discussion

117.	The Fermat’s little theorem for odd prime p and coprime number a is?(a) a^p-1 ≡ 1 (mod p)(b) a^p-1 ≡ 7 (mod p)(c) a^p(2)-1 ≡ 1 (mod p)(d) none of the mentionedI got this question by my college director while I was bunking the class.The query is from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT choice is (a) a^p-1 ≡ 1 (MOD p) The best I can EXPLAIN: According to Fermat’s little theorem a^p-1 ≡ 1 (mod p).

Discussion

118.	If there exist no integer x such that x^2 ≡ q (mod n). then q is called __________(a) Quadratic Residue(b) Quadratic Nonresidue(c) Pseudoprime(d) None of the mentionedI had been asked this question during a job interview.The question is from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» Correct CHOICE is (B) Quadratic Nonresidue To EXPLAIN I WOULD say: q is called quadratic nonresidue if it is not congurent to a perfect square modulo n.

Discussion

119.	If there exist an integer x such that x^2 ≡ q (mod n). then q is called ______________(a) Quadratic Residue(b) Linear Residue(c) Pseudoprime(d) None of the mentionedThis question was posed to me during an online exam.This intriguing question comes from Number Theory in section Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT option is (a) QUADRATIC RESIDUE To elaborate: q is called quadratic residue if it is congruent to a PERFECT square MODULO n.

Discussion

120.	If a, b are two distinct prime number than a highest common factor of a, b is ___________(a) 2(b) 0(c) 1(d) abThe question was asked during an online interview.Question is from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» The CORRECT ANSWER is (c) 1 The EXPLANATION: HCF of two PRIME numbers is 1.

Discussion

121.	If a, b, c, d are distinct prime numbers with an as smallest prime then a * b * c * d is a ___________(a) Odd number(b) Even number(c) Prime number(d) None of the mentionedI had been asked this question in a job interview.My question is from Number Theory topic in division Number Theory and Cryptography of Discrete Mathematics
Answer» Correct ANSWER is (B) Even number To explain: SINCE a is 2, 2 * b * c * d = Even number.

Discussion

122.	How many prime numbers are there between 1 to 20?(a) 5(b) 6(c) 7(d) None of the mentionedThis question was addressed to me in an interview for internship.Question is from Number Theory in division Number Theory and Cryptography of Discrete Mathematics
Answer» RIGHT CHOICE is (d) None of the mentioned Easiest explanation: The prime numbers between 1 to 20 are 2, 3, 5, 7, 11, 13, 17, 19.

Discussion

123.	Sum of two different prime number is a ____________(a) Prime number(b) Composite number(c) Either Prime or Composite(d) None of the mentionedThe question was asked during an interview for a job.This intriguing question comes from Number Theory in division Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT answer is (c) Either PRIME or Composite Explanation: Eg:- 2 + 3 = 5 a prime, 3 + 7 = 10 a composite.

Discussion

124.	There are finite number of prime numbers.(a) True(b) FalseI had been asked this question by my school teacher while I was bunking the class.I'd like to ask this question from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» The CORRECT choice is (B) False The EXPLANATION is: There are infinite NUMBERS of primes.

Discussion

125.	Difference of two distinct prime numbers is?(a) Odd and prime(b) Even and composite(c) None of the mentioned(d) All of the mentionedThe question was posed to me in quiz.I want to ask this question from Number Theory topic in division Number Theory and Cryptography of Discrete Mathematics
Answer» RIGHT choice is (c) None of the mentioned Easiest EXPLANATION: 3 – 2 = 1 is NEITHER prime nor composite.

Discussion

126.	3 is the smallest prime number possible.(a) True(b) FalseThis question was addressed to me at a job interview.I would like to ask this question from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics
Answer» Right ANSWER is (B) False To explain: 2 is also a prime NUMBER.

Discussion

127.	What is the number ‘ 1’?(a) Prime number(b) Composite number(c) Neither Prime nor Composite(d) None of the mentionedThis question was addressed to me during an interview.I would like to ask this question from Number Theory topic in section Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT OPTION is (c) NEITHER Prime nor COMPOSITE The explanation is: 1 is neither prime NUMBER nor composite.

Discussion

128.	All prime numbers are odd.(a) True(b) FalseThe question was posed to me during an online interview.This interesting question is from Number Theory in section Number Theory and Cryptography of Discrete Mathematics
Answer» CORRECT choice is (b) False To ELABORATE: 2 is even as well as PRIME.

Discussion

129.	The number of factors of prime numbers are ___________(a) 2(b) 3(c) Depends on the prime number(d) None of the mentionedThe question was posed to me during a job interview.I need to ask this question from Number Theory topic in division Number Theory and Cryptography of Discrete Mathematics
Answer» The CORRECT option is (a) 2 The EXPLANATION is: A prime number is only DIVISIBLE by 1 and itself.

Discussion

Explore topic-wise InterviewSolutions in .

State whether the given statement is True or False.(a) = LCM(a,(LCM(b,(LCM(c, d)))).(b) True(c) FalseI have been asked this question in an online interview.This interesting question is from Number Theory topic in section Number Theory and Cryptography of Discrete Mathematics

If LCM of two number is 14 and GCD is 1 then the product of two numbers is?(a) 14(b) 15(c) 7(d) 49The question was posed to me in exam.I'm obligated to ask this question of Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

The product of two numbers are 12 and their Greatest common divisor is 2 then LCM is?(a) 12(b) 2(c) 6(d) None of the mentionedI had been asked this question in an internship interview.This question is from Number Theory topic in portion Number Theory and Cryptography of Discrete Mathematics

LCM of 6, 10 is?(a) 60(b) 30(c) 10(d) 6This question was posed to me by my college director while I was bunking the class.The origin of the question is Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

The LCM of two number 1, b(integer) are _________(a) b + 2(b) 1(c) b(d) None of the mentionedThis question was posed to me in class test.My doubt is from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics

Which of the following is a quardratic residue of 11?(a) 4(b) 5(c) 9(d) All of the mentionedThe question was posed to me in a national level competition.My doubt is from Number Theory in section Number Theory and Cryptography of Discrete Mathematics

8 is quardratic residue of 11.(a) True(b) FalseThis question was posed to me during an internship interview.My enquiry is from Number Theory in division Number Theory and Cryptography of Discrete Mathematics

4 is quardratic residue of 7.(a) True(b) FalseI had been asked this question during an internship interview.This intriguing question originated from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics

8 is quardratic residue of 17.(a) True(b) FalseI got this question in a national level competition.The question is from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

5 is quardratic non-residue of 7.(a) True(b) FalseThis question was addressed to me by my college professor while I was bunking the class.This key question is from Number Theory in division Number Theory and Cryptography of Discrete Mathematics

If a, b are two distinct prime number than a highest common factor of a, b is ___________(a) 2(b) 0(c) 1(d) abThe question was asked during an online interview.Question is from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

How many prime numbers are there between 1 to 20?(a) 5(b) 6(c) 7(d) None of the mentionedThis question was addressed to me in an interview for internship.Question is from Number Theory in division Number Theory and Cryptography of Discrete Mathematics

There are finite number of prime numbers.(a) True(b) FalseI had been asked this question by my school teacher while I was bunking the class.I'd like to ask this question from Number Theory topic in chapter Number Theory and Cryptography of Discrete Mathematics

Difference of two distinct prime numbers is?(a) Odd and prime(b) Even and composite(c) None of the mentioned(d) All of the mentionedThe question was posed to me in quiz.I want to ask this question from Number Theory topic in division Number Theory and Cryptography of Discrete Mathematics

3 is the smallest prime number possible.(a) True(b) FalseThis question was addressed to me at a job interview.I would like to ask this question from Number Theory in chapter Number Theory and Cryptography of Discrete Mathematics

What is the number ‘ 1’?(a) Prime number(b) Composite number(c) Neither Prime nor Composite(d) None of the mentionedThis question was addressed to me during an interview.I would like to ask this question from Number Theory topic in section Number Theory and Cryptography of Discrete Mathematics

All prime numbers are odd.(a) True(b) FalseThe question was posed to me during an online interview.This interesting question is from Number Theory in section Number Theory and Cryptography of Discrete Mathematics

The number of factors of prime numbers are ___________(a) 2(b) 3(c) Depends on the prime number(d) None of the mentionedThe question was posed to me during a job interview.I need to ask this question from Number Theory topic in division Number Theory and Cryptography of Discrete Mathematics