TCS Sample Problems On Odd & Even Integers

Questions on numbers on concepts dealing with odd and even and a new class called "even-odd" numbers.

Below are three questions on numbers on concepts dealing with odd and even and a new class called "even-odd" numbers.
Question 1
If n is an even-odd number then which of the following must be false?
(A number is called "even-odd" if it is halfway between an even integer and an odd integer.)
a) n/2 is not an integer
b)(2n)2 is an integer
c)4n is an odd integer
d)none of these
Answer : c)4n is an odd integer
Solution:
A number is called "even-odd" if it is halfway between an even integer and an odd integer. For example, consider an even integer 10 and an odd integer -5. Number halfway between them will be (10 - (-5)) / 2 = 7.5. Here 7.5 is an "even-odd" number.
i.e., an even-odd number will be in the form x + 1/2 = x.5 where x is any integer.
Let us see with each option:
Consider option a :
Since n is a fraction number then n/2 is also a fraction.
i.e., n/2 is not an integer.
Hence option a is true.
Consider option b :
(2n)2 = 4n2
since n is an even-odd number then n^2 is not an integer.
Also n2 will have 1/4 = .25 in its decimal place. (For example, consider n = 7/2. Then n2 will be 7/2 x 7/2 = 49/4. 49/4 can be written as 49 + 1/4. Here 1/4 will contribute to the decimal part.)
When we multiply n2 by 4 we have an integer, since .25 x 4 = 1.
Hence option b is true
Consider option c:
We can express 4n as 2 x 2n.
Since n is X.5 then 2n must be an integer and any multiple of 2 gives an even integer.
But the statement says that 4n is an odd integer.
Hence option c is false.
Question 2
If p is an odd number and q is an even number, which of the following must be an even?
I. 2p+3q
II. p2 - q2
III.(pq)2
IV. (1+pq)2
Options:
a) I only b)II&IV only c)I&III only d)I,II&III only
Answer : c)I&III only
Solution:
We know that any multiple of 2 is even and 3 times of an even number is also even.
Then 2p and 3q both are even.
Since the addition of two even numbers is again an even, then 2p+3q is even.
i.e., I is even.
Now, the square of any even number is even and the square of an odd is odd. Then p2 is odd and q2 is even
And difference between even number and odd number is an odd number.
Then p2 - q2 is an odd.
Hence II is odd.
The multiplication of an odd and even number will be an even number, then pq is even,
And the square of an even is even, so (pq)2 is also even.
Hence III is even.
since pq is even, then 1 + pq will be odd.
And the square of odd is odd. Therefore (1 + pq)2 is odd.
Hence IV is odd.
Therefore only I and III are even. Thus the answer is I & III only.
Question 3
If n is an odd integer, then which of the options will be even.
a)(n2)/2 + n b)nn + n + 1 c)(n2 + 3)2 d)none of these
Answer : c)(n2 + 3)2
Solution :
Consider option a,
since n is an odd number then n2 is also an odd
We can express (n2)/2 + n as ( n2 + 2n)/ 2.
And n2 is odd and 2n is even, then n2 + 2n will be odd
Then ( n2 + 2n)/ 2 is not an even integer.
Consider option b,
since n is odd, then n power anything is odd and nn is odd.
The addition of 3 odd numbers is odd, then nn + n + 1 is an odd integer.
Consider option c,
Here n2 is odd and then n2 + 3 is also odd.
Now, the square of an odd integer is odd, then (n2 + 3)2 is an even integer.
Hence the option c)(n2 + 3)2 is the answer.

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10th 3i InfoTech Academic Books Accenture ACIO ActiveX ADT Agricultural AIEEE Air Force Algebraic Amdocs Android Answers Application Development Aptitude Aptitude Questions Architectures ASP ATOS B.Sc B.Tech.B.E. Bank Exam BCA BE Board Exam Books break-continue Business Plan C C Programming C# C++ Campus campus interview Candidate profile Capgemini Career CDS Certification CET Challenge Circle Cisco class code Cognizant communication Company Company Profile Competitive Exams computer Computer Networks concentric circles constructor Course Credit Suisse CSS CTS Data Structure DBMS DC Deloitte difficult interview questions dimensions Distributed Computing do while dotNet Download ds Dynamic Web Development e-Admit card Educational engineering entertainment Even Odd Events exam schedule exception for loop fresher GATE general Discussion general knowledge Get Placed Government Job Hall Ticket HCL how to answer How to Prepare HR HR Interview HSC hypertext preprocessor IB IBM IBPS IIT Indian Army Information infosys Intelligence Bureau Internship interview Experience interview questions Interview Tips IntroC IntroC# IntroJava IntroPHP IT J2EE J2ME Java JavaScript jobs Language Books Language Tutorial Languages limit number of objectsJava Limit the number of objects being created in JAVA Linux Linux Administrator Linux Developer Logical Questions loops M Tech M.E. M.Tech M.Tech AND B.Tech Management Management Skills Matrices MBA mca ME microsoft mistakes Mixture Mobile Computing mock questions mock test MySql naukri NDA OOP opening Operating System Oracle paper Persistent PHP php programming php string variables PL/SQL Placement placement guide Placement Paper Placement Process preparing for placement presentation probability Problems Professional program Programming Project Engineer project idea Projects Puzzle qualities Question of the day Questions Quiz Question Recruitment Recruitment Pattern Requirement Result Resume Reviews Screen Sizes Scripting Session Skills Software Software Engineering solved papers Source Code Speed time and distance SQL SSC story Stress Interview Study Material study tips submit resume Synonym TCS Tech Mahindra tech news Technical Books Technical Interview Testing thank you letter Thought Time Table TutC++ Unix questions asked in aptitude and inteviews for MCA UPSC verbal Web Designing Web Developer Website Development What to read while loop Wipro Writing Resume