Question: Which of the following equations has a root in common with\(x^2-6x+5=0\)?

A. \(x^2+1=0\)
B. \(x^2-x-2=0\)
C. \(2x^2-2=0\)
D. \(x^2-2x-3=0\)
E. \(x^2-10x-5=0\)

Answer:
Approach Solution (1):

First, let’s solve\(x^2-6x+5=0\)by factoring:
(x – 5) (x – 1) = 0
Therefore, x = 5 or x = 1
We can solve the equations in the given choices by factoring also. However, we see that the equation in choice A is not factorable (the equation is a sum of square), so we can start with choice B
B. (x – 2) (x + 1) = 0
X = 2 or x = -1
We see that the equation in choice B does not have a root in common with\(x^2-6x+5=0\)
\(2(x^2-1)=0\)
\(2(x-1)(x+1)=0\)
C. \(x=1orx=-1\)
We can see that the equation in choices C does have a root in common with (namely x = 1)
Correct option: C

Approach Solution (2):
It given that:
\(x^2-6x+5=0\)
\((x-1)(x-5)=0\)
Hence, roots are 1 and 5
Substitute these roots in all the given equations:
\(x^2+1=0\)
x=1;
1. \(1^2+1=1+1=2!=0\)
Not a root
x=5;
\(5^2+1=25+1=26!=0\)
Not a root
\(x^2-x-2=0\)
x=1;
2. \(1^2-1-2=2!=0\)
Not a root
x=5;
\(5^2-5-2=25-7=18!=0\)
Not a root
\(x^2-10x-5=0\)
x=1;
3. \(1^2-10*1-5=-14!=0=-2!=0\)
Not a root
x=5;
\(5^2-10*5-5=25-55=-30!=0\)
Not a root
\(2x^2-2=0\)
x=1;
4. \(2*1^2-2=2-2=0=0\)
1 is a root
We can stop here
x=5;
\(2*5^2-2=50-2=48!=0\)
Not a root
\(x^2-2x-3=0\)
x=1;
5. \(1^2-2*1-3=-3!=0\)
Not a root
x=5;
\(5^2-2*5-3=12!=0\)
Not a root
Correct option: C

Approach Solution (3):
\(x^2-6x+5=0\)
x = 5 or 1
3.\(2x^2-2=0\)
x = 1 or -1
Root x = 1 common
Correct option: C

“Which of the following equations has a root in common with\(x^2-6x+5=0\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Suggested GMAT Problem Solving Questions:

• if 80 lamps can be lighted, 5 hours per day for 10 days for $21.25, then the number of lamps, GMAT Problem Solving
• Few of the corporate contributions to the earthquake relief fund, aside from Pterocom GMAT Problem Solving
• X is Older Than Y, Z Is Younger Than W And V Is Older Than Y GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• Find the Greatest Number That Will Divide 43,91 and 183 So as to Leave GMAT Problem Solving
• A Right Angled Triangle has its Sides in Arithmetic Progression and Being Integers GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 seconds Respectively GMAT Problem Solving
• A Man can Hit a Target Once with 4 Shots. If He Fires 4 Shots in Success GMAT Problem Solving
• A is twice as good a workman as B and together they finish a piece of GMAT Problem Solving
• Frances can complete a job in 12 hours, and Joan can complete the same GMAT Problem Solving
• The Average Age of Chief Executive Officers (CEO’s) in a Large Sample of Companies is 57 GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines can GMAT Problem Solving
• If a and b are positive integers such that a – b and a/b are both even GMAT Problem Solving
• If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
• What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
• What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students GMAT Problem Solving
• If 4 People are Selected from a Group of 6 Married Couples, What is the Probability That none of Them would be Married to Each Other? GMAT Problem Solving
• If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph, What is the Area of that Region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
• A Chord of a Circle is Equal to its Radius. GMAT Problem Solving
• A Clock loses a Minute Every Three Hours for 4 Days and Gains 1% in the Subsequent 6 Days. GMAT Problem Solving
• The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
• If tu=xytu=xyand ty=uxty=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving
• A Farm has Chickens, Cows and Sheep. The Number of Chickens and Cows Combined is 3 Times the Number of Sheep. GMAT Problem Solving
• In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• The product of the first 10 prime numbers is closest to which of the following? GMAT Problem Solving
• There is a 120 liter mixture of alcohol and water. The ratio of alcohol to water is 7 : 5 GMAT Problem Solving
• An equilateral triangle ABC is inscribed in square ADEF, forming three right triangles GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B. The Selling Price of Model A is $120 GMAT Problem Solving
• A contractor combined x tons of a gravel mixture that contained 10 percent gravel G GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• How many litres of a 90% solution of concentrated acid needs to be mixed with a 75% solution GMAT Problem Solving
• Jug Contains Water And Orange Juice In The Ratio 5:7 . Another Jug Contains Water And Orange J GMAT Problem Solving
• The number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated GMAT Problem Solving
• A train travels from Albany to Syracuse, a distance of 120 miles, at an average rate of 50 miles per hour GMAT Problem Solving
• The hexagon ABCDEF is regular. That means all its sides are the same length and all its interior angles are the same size. GMAT Problem Solving
• y varies directly as x and when x = 6, y = 24. What is the value of y, when x = 5? GMAT Problem Solving
• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT Problem Solving
• How many factors does 36^2 have? GMAT Problem Solving
• A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively GMAT Problem Solving
• Walking at 6/7 th of his usual speed, a man is 25 min too late GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes Whereas a leak in the Bottom of the Cistern can Empty a Filled Tank in 40 minutes GMAT Problem Solving
• A milkman cheats his customers by adding water to the milk he sells GMAT Problem Solving