What is the value of x^2 + 1/x^2 ? (1) x + 1/x = 2 (2) x^2 - 1 = 0 GMAT Data Sufficiency

Question: What is the value of x^2 + 1/x^2 ?

(1) x + 1/x = 2
(2) x^2 - 1 = 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is the value of x^2 + 1/x^2?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review 2022". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:
Approach Solution 1:

(1) x+1/x=2

Square both sides
(x+1/x)^2 = 2^2
x^2+1/x^2+2*x*1/x= 4
x^2+1/x^2+2= 4
x^2+1/x^2= 2

(2) x^2= 1

Substitute in the equation x^2+1/x^2
1+1/1= 1+1= 2

Correct Answer: D

Approach Solution 2:

What is the value of x^2 + 1/ x^2?

1. x + 1/ x= 2 Sufficient

x+1/x= 2
x^2+1= 2x
x^2-2x+1= 0
(x-1)(x-1)= 0
x=1

2. x^2-1= 0 Sufficient

(x+1)(x-1)= 0
x=1=x^2=1/x^2=(1)x^2+1/(1)^2= 2
x=-1=x^2+1/x^2=(-1)^2+1/(-1)^2= 2

Correct Answer: D

Approach Solution 3:

(1) x+1/x=2

Square both sides
(x+1/x)^2 = 2^2
x square +1/x square+2*x*1/x= 4
x square+1/x square+2= 4
X square+1/x square= 2

2. x^2-1= 0 Sufficient

(x+1)(x-1)= 0
x=1=x^2=1/x^2=(1)x^2+1/(1)^2= 2
x=-1=x^2+1/x^2=(-1)^2+1/(-1)^2= 2

Correct Answer: D

Suggested GMAT Data Sufficiency Questions

• A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively GMAT Data Sufficiency
• What is the circumference of circle C ? (1) The radius of circle C is 2π GMAT Data Sufficiency
• Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units GMAT Data Sufficiency
• If each side of parallelogram P has length 1, what is the area of P? GMAT Data Sufficiency
• Is the positive integer n a multiple of 24? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• Is |x-10| > |x-30| GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at RandomGMAT Data Sufficiency-
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT Data Sufficiency
• P and Q are prime numbers less than 70. What is the units digit of P*Q? GMAT Data Sufficiency