Question: If x is a non-zero integer, what is the value of x?
- \(x^{4x}=x^{16}\)
- \((x^x) (x^2)=x^6\)
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
Solution with Explanation:
Approach Solution (1):
(1) \(x^{4x}=x^{16}\)
Clearly, when base is 1, the power could be anything. Thus x = 1 is a possibility.
Equation the power as the base is x: 4x = 14 or x = 4
Insufficient
(2) \((x^x) (x^2)=x^6\)
Clearly, when base is 1, the power could be anything. Thus x = 1 is a possibility.
Also, \(x^{x+2}=x^6\). Equating the power as the base is x: x + 2 = 6 or x = 4
Insufficient
Combined
x can still be 1 or 4
Insufficient
Correct Option: E
Approach Solution (2):
(1) \(x^{4x}=x^{16}\)
Let’s begin by assuming \(x\neq0,x\neq1, and x\neq-1\)
Since the bases are equal, the exponents are equal, which means we can write: 4x = 16
So, x = 4 is one solution (so far)
We must now test the provisos (other than x = 0, since we are told x is a non-zero integer)
First let’s test x = 1 by plugging it into the equation to get: \(1^{4(1)}=1^{16}\)
Evaluate to get 1 = 1. WORKS!
So, x = 1 is another possible solution.
Now let’s test x = -1 by plugging it into the equation to get: \((-1)^{4(-1)}=(-1)^{16}\)
Evaluate to get 1 = 1. WORKS!
So, x = -1 is another possible solution
Since, x can equal 4, 1, or -1, statement 1 is NOT SUFFICIENT
(2) \((x^x) (x^2)=x^6\)
First apply the product law to get: \(x^{x+2}=x^6\)
Once again let’s assume \(x\neq0,x\neq1, and x\neq-1\)
Since the bases are equal, the exponents are equal, which means we can write: x + 2 = 6
So, x = 4 is one solution (so far)
Now let’s test x = 1 by plugging it into the equation to get: \(1^{1+2}=1^6\)
Evaluate to get 1 = 1. WORKS!
So, x = 1 is another possible solution.
Now, let’s test x = -1 by plugging it into the equation to get: \(1^{(-1)+2}=1^6\)
Evaluate to get -1 = 1. Doesn’t work
Since, x can equal 4 or 1, statement 2 is not sufficient
(1) + (2)
S1 tells us that x can equal 4, 1, or -1
S2 tells us that x can equal 4 or 1
So when we combine the statements, we know that x can equal 4 or 1
Since we can’t answer the target question with certainty, the combined statements are not sufficient.
Correct Option: E
“If x is a non-zero integer, what is the value of x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". 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.
Suggested GMAT Data Sufficiency Samples
- The Cardinality of a Finite Set is the Number of Elements in the Set., GMAT Data Sufficiency
- What is the Radius of the Circle above with Center O?, GMAT Data Sufficiency
- Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median?, GMAT Data Sufficiency
- If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?, GMAT Data Sufficiency
- If There are 78 People Working at an Office, How Many of Them are Women Older than 40?, GMAT Data Sufficiency
- From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
- If L \(\neq\) 0, is \(\frac{18K}{L}\) an Integer?
- If 0 < x < 53, What is the Value of Integer x? GMAT Data Sufficiency
- Is quadrilateral ABCD a parallelogram? GMAT Data Sufficiency
- Is P – 1 Even?, GMAT Data Sufficiency
- Buster Leaves the Trailer at Noon and Walks Towards the Studio at a Constant Rate of B Miles Per Hour., GMAT Data Sufficiency
- If ab = ac is b = 2?, GMAT Data Sufficiency
- The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency, GMAT Data Sufficiency
- Is Quadrilateral ABCD a Rectangle?, GMAT Data Sufficiency
- If \(x^2\)=\(2^x\), What is the Value of x ?, GMAT Data Sufficiency
- A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle, GMAT Data Sufficiency
- If m is a positive integer, is \(\sqrt{m}>25\) ? , GMAT Data Sufficiency
- What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
- In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle GMAT Data Sufficiency
- What is the Remainder when 333^222 is Divided by 7? GMAT Data Sufficiency
- Is 1/(a - b) > b - a ? GMAT Data Sufficiency
- If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True? GMAT Data Sufficiency
- What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency
- If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency
- If m is a positive integer, is √m>25? GMAT Data Sufficiency
- If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency
- If ab = ac is b = 2? GMAT Data Sufficiency
- If x is a positive integer, what is the value of x? GMAT Data Sufficiency
- If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) And M101 GMAT Data Sufficiency
- Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour GMAT Data Sufficiency
- If sq rt{3+sq rt(x-1)} = 4, what is the value of x? GMAT Data Sufficiency
- What is the sum of a, b, and c? GMAT Data Sufficiency
- What is the value of \(6x^2+9y^2\)?, GMAT Data Sufficiency
- If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even?, GMAT Data Sufficiency
- If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency
- A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
- The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
- Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
- If J≠0, What Is The Value Of J? GMAT Data Sufficiency
- Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon 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
- What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
- Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
- S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency
- P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q?, GMAT Data Sufficiency