Wipro Sample Algebraic Problems

Below are three model problems dealing with the formulae (x+y)2 = x2 + y2 + 2xy and (x-y)2 = x2 + y2 - 2xy
Question 1
Find X when X - Y = 3 and X2 + Y2 = 89 where X and Y are integers.
a)10 b)-5 c)-10 d)-3
Answer : b)-5.
Solution :
We know that (x - y)2 = x2 + y2 - 2xy
Sub. the given values,
32 = 89 - 2XY
9 - 89 = -2XY
80 = 2XY
XY = 40
Since X and Y are integers and XY = 40,the possibilities of X and Y are as follows:
(1,40), (2,20), (4,10), (5,8), (-1,-40), (-2,-20), (-4,-10) and (-5,-8)
X - Y is a positive integer(3), so X will be greater than Y.
By checking the given condition X - Y = 3, we have X = 8, Y = 5 or X = -5, Y = -8.
i.e., X is either 8 or -5.
From the given options we can conclude that X = -5.
Question 2
If the summation and multiplication of two integer is 24 and 143 respectively then the difference of them is:
a)2 b)1 c)12 d)4
Answer : a)2
Solution :
Let A and B be two integers.
Then A + B = 24 and AB = 143.
We know that (x+y)2 = x2 + y2 + 2xy
Here, 242 = A2 + B2 + 2(143)
576 - 286 = A2 + B2
A2 + B2 = 290.
i.e., Summation of the square of two integers is 290.
i.e., A2 or B2 is < or = 290.
Since A and B are integers, the possibilities are {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289}.
From the above set of square numbers, the values may be
A2 + B2 = 1 + 289 or 121 + 169 = 290
A2 + B2 = 12 + 172 or 112 + 132 = 290
The condition A + B = 24 and AB = 143, is satisfied by A = 11, B = 13 or A = 13, B = 11
We have to find the difference of A and B.
Hence the difference is 2.
Question 3
If X - Y = 9, X2 + Y2 = 257 and X,Y are integers then what will be the value of X and Y ?
a)21,12 b)15,6 c)none of these d)cannot be determined
Answer : d)cannot be determined
Solution :
Here we use the formula, (x-y)2 = x2 + y2 - 2xy
92 = 257 - 2XY
XY = (257-81)/2 = 176/2 = 88
XY = 88
Since X and Y are integers and XY = 88 then the possibilities of X and Y are (1,88), (2,44), (4,22), (8,11), (-1,-88), (-2,-44), (-4,-22) and (-8,-11).
By observing, none of the above possibility of X and Y satisfies X - Y = 9.
Hence, the values of X and Y cannot be determined by given conditions.

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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