If |x – 6| = 5, What is the Value of x? GMAT Data Sufficiency

Question: If |x – 6| = 5, what is the value of x?

(1) x > 0
(2) x^2 = 121

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.

Correct Answer: B

Solution and Explanation:
Approach Solution 1:
The problem statement suggests that:
Given:

• |x – 6| = 5

 Find out:

• The value of x

Since |x – 6| = 5
Therefore, we can say,
|x - 6 | = x - 6 if x >= 6
|x - 6 | = -(x-6) if x < 6

From statement 1 we have x > 0.
This implies that x can be 1, 2, or greater than 6.
Therefore, after opening the modulus, we will obtain
|x-6| = 5
x-6 = 5
x = 11
or -(x-6) = 5
-x+6 = 5
x = 1
Therefore, we get 2 values of x that is 11 and 1
Since, both values are greater than zero.
Option 1 is insufficient.
From statement 2. we have x^2 = 121.
Therefore, x will have one of two values: 11 or -11.
Option 2 is Sufficient.
Therefore, Statement 1 is insufficient , but statement 2 is sufficient.

Approach Solution 2:

The problem statement informs that:
Given:

• |x – 6| = 5

 Find out:

• The value of x

Another approach to this question is given which is fairly simple and uses variable approach. 
The Variable Approach method begins with modifying the original condition and question. The question is then rechecked.
|x−6|=5|
x−6=±5
x=6±5
x=11 or x=1
In condition 1- There is no unique solution because we have x=11 or x=1 from x>0.
As a result, condition 1 is insufficient.
In condition 2- x=±11, Because we only have solution 11, condition 2 is sufficient
Therefore, statement 1 is insufficient, but statement 2 is sufficient.

Approach Solution 3:

The problem statement informs that:
Given:

• |x – 6| = 5

 Find out:

• The value of x

|x – 6| = 5 means x-6 = 5 or x-6= -5

Therefore, the value of x maybe 11 or 1----(a).

1. The statement states x > 0. Since x=11 or 1, the statement is insufficent
2. The statement states x^2 = 121, therefore, x=11 or -11. however from (a), x=11 or 1.
   Therefore, x= 11. Hence sufficient.

​Therefore, statement 1 is insufficient, but statement 2 is sufficient.

“If |x – 6| = 5, what is the value of x?”- is.a topic of GMAT Quantitative reasoning section of GMAT. This GMAT Data Sufficiency question tests the potentiality and skill level of the candidates to solve the quantitative problems. GMAT Quant practice papers represent various quantitative problems that will enhance the calculative skills of the candidates.  

Suggested GMAT Data Sufficiency Questions:

• If x Is A Positive Integer, What Is The Value Of (x+24)^(½) − x^(½) GMAT Data Sufficiency
• Points x And y Lie On A Line Segment. How Many Units Long Is The Line GMAT Data Sufficiency
• Which Sport Utility Vehicle has a Higher List Price, the Touristo or GMAT Data Sufficiency
• What is The Average (arithmetic mean) Annual Salary of the 6 Employees GMAT Data Sufficiency
• If S is a Set of Ten Consecutive Integers, is the Integer 5 GMAT Data Sufficiency
• What is the Perimeter of a Square Chessboard, If a Chessboard is made GMAT Data Sufficiency
• A Company has Two Models of Computers, Model M and Model N GMAT Problem Solving
• Is the sum of four different positive prime integers an odd integer? GMAT Data Sufficiency
• Is Positive Integer x Divisible By 24? GMAT Data Sufficiency
• 10 Students took a Chemistry Exam that was Graded on a Dcale of 0 to 100 GMAT Data Sufficiency
• If m and n are positive integers, is the remainder of GMAT Data Sufficiency
• In quadrilateral ABCD, is AC longer than BD GMAT Data Sufficiency
• N is a positive integer. Is n the square of an integer? GMAT Data Sufficiency
• If z Is An Integer Smaller Than Integer n But Greater Than Zero GMAT Data Sufficiency
• If y Is An Odd Number And x^3 ∗ y^4 = 648, y=? 1) y Is Positive 2) x Is Gmat Data Sufficiency
• A Pyramid-Shaped Box To Protect A Plant Is Constructed With 4 Lateral Faces GMAT Data Sufficiency
• Is abc/d an Integer if a, b, c, and d are Positive integers? GMAT Data Sufficiency
• If n is a positive integer, is (1/10)^n < 0.01? GMAT Data Sufficiency
• If m and n are nonzero integers, is m^n an integer? GMAT Data Sufficiency
• In A Certain Office, 50 Percent Of The Employees Are College GMAT Data Sufficiency
• As Shown Above, A Rectangle Is Divided Into Smaller Rectangles Of The GMAT Data Sufficiency
• The Revenue of a Company is Directly Proportional to the Number of Customers GMAT Data Sufficiency
• Starting from the same point, a sparrow and a hawk flew in opposite directions GMAT Data Sufficiency
• Even/Odd: Are Negative Numbers and Decimals Even or Odd? GMAT Data Sufficiency
• If x,y and z are positive numbers, is z between x and y? GMAT Data Sufficiency
• What Is The Value Of 2^X + 2^(-X)? GMAT Data Sufficiency
• Is Quadrilateral ABCD a Square? GMAT Data Sufficiency
• Is |x - y| > |x| - |y|? (1) y < x (2) xy < 0 GMAT Data Sufficiency
• On a Trolley Ride Around an Amusement Park, a Child GMAT Data Sufficiency
• If x Is The Sum Of Factorials Of The First n Positive Integers GMAT Data Sufficiency
• Is Quadrilateral ABCD A Rhombus? GMAT Data Sufficiency
• What Is The Volume Of Rectangular Box R? GMAT Data Sufficiency
• On Sunday Morning, a Printing Press Printed its Newspapers at a GMAT Data Sufficiency
• Is n<0? GMAT Data Sufficiency
• Is n an even number GMAT Data Sufficiency
• If x ≠ 0, what is the value of x? GMAT Data Sufficiency
• If x is an integer, is 9^x + 9^(-x) = b ? (1) 3^x + 3^(-x) = (b + 2) GMAT Data Sufficiency
• If x is an integer, can the number (5/28)(3.02)(90%)(x) be GMAT Data Sufficiency
• Is quadrilateral ABCD a parallelogram? GMAT Data Sufficiency
• If Vertices of a Triangle have Coordinates (-2,2) (3,2) GMAT Data Sufficiency
• If Set S Consists of Even Number of Integer, Is the Median GMAT Data Sufficiency
• What Is The Value Of N GMAT Data Sufficiency
• What is the value of x^2 + 1/x^2 ? GMAT Data Sufficiency
• Is the range of a combined set (S,T) bigger than the sum of the ranges of sets S and T? GMAT Data Sufficiency
• How many integers in a group of 5 consecutive positive integers are divisible by 4? GMAT Data Sufficiency
• Is the standard deviation of set S greater than the standard deviation of set T? GMAT Data Sufficiency
• Is a^7∗b^2∗c^3>0? (1) bc < 0 (2)ac > 0 GMAT Data Sufficiency
• If n is a non-negative integer, is 10^n+8 divisible by 18? GMAT Data Sufficiency
• Is the Range of Set S Greater than its Mean? GMAT Data Sufficiency
• Does the curve (x−a)^2+(y−b)^2=16 intersect the Y axis? GMAT Data Sufficiency