If x = - |x|, Then Which One of the Following Statements GMAT Problem Solving

Question: If x = - |x|, then which one of the following statements could be true?

1. x = 0
2. x < 0
3. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

Correct Answer: (D)

Solution and Explanation:

Approach Solution 1:

The problem statement implies that

Given:

• x = - |x|

Asked:

• To find out which of the following statements could be true that is

1. x = 0
2. x < 0
3. x > 0

The equation x = - |x| indicates that:

1. x can be zero.
2. x can be any negative integer.

Now, let’s verify each of the options

1. x = 0 => True since it depends on point (1)
2. x < 0 => True since it depends on point (2)
3. x > 0 => False, since the value of x should be either zero or less than 0.

Approach Solution 2:

The problem statement cites an equation x = - |x|

Find Out:

• Which of the following statements could be true

1. x = 0
2. x < 0
3. x > 0

The equation as stated in the question is x = - |x|
We can rewrite the equation as |x| is greater than or equal to 0
Hence, -|x| is less than or equal to 0
Therefore, x must be 0 or less than 0.

Approach Solution 3:

The problem statement informs that:

Given: x = - |x|

Find Out: Which of the following statements could be true:

1. x = 0
2. x < 0
3. x > 0

We can solve the problem by using the trial and error process.

1. x = 0, therefore, we can say,
   0= -|0| = 0 — YES.
2. x < 0, therefore by substituting we get,
   -1= -|1|
   -1= -1 — YES.

3.  x > 0, therefore by substituting we get,
   2= -|2|
   2 = -2 — NO.

“If x = - |x|, then which one of the following statements”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This question has been taken from GMAT Official Guide Quantitative Review 2021. GMAT Problem Solving questions test the logical thinking capacity of candidates in order to solve quantitative problems. GMAT Quant practice papers comprise miscellaneous kinds of questions that enable candidates to boost their mathematical knowledge.

Suggested GMAT Problem Solving Questions

• The Earth Travels Around The Sun At A Speed Of Approximately 18.5 miles GMAT Problem Solving
• There are 8 ounces in a 1/2 pound. How many ounces are in 7 3/4 lbs? GMAT Problem Solving
• In isosceles triangle EFG above, angle FEG measures 60 degrees GMAT Problem Solving
• In the Figure, O is the Center of the Circle. Which One of the Following GMAT Problem Solving
• If a and b are Positive Integers and (2a)^b= 2^3, What is the Value GMAT Problem Solving
• What is the Remainder When 3^243 is Divided by 5? GMAT Problem Solving
• A Fashion Designer Sold a Pair of Jeans to a Retail Store for 40 Percent GMAT Problem Solving
• A Rectangular-Shaped Carpet Remnant That Measures x Feet GMAT Problem Solving
• In The Figure Above, If The Square Inscribed In The Circle Has An Area GMAT Problem Solving
• A Right Triangle Is Inscribed In A Circle. The Legs Of The Triangle GMAT Problem Solving
• Tom and Jerry are running on the same road towards each other. If Tom GMAT Problem Solving
• A number is said to be prime saturated if the product of all the different GMAT Problem Solving
• What is the sum of first 10 non-negative even integers GMAT Problem Solving
• A certain computer program randomly generates equation of line is form GMAT Problem Solving
• A perfect number is one which is equal to the sum of all its positive GMAT Problem Solving
• At A Prestigious Dog Show, Six Dogs Of Different Breeds Are To Be GMAT Problem Solving
• The Average Wages of a Worker During a Fortnight Comprising 15 GMAT Problem Solving
• Which of the Following Fractions is the Largest? GMAT Problem Solving
• Alice and Bob Traveled in the Same Direction Along the Same Route at GMAT Problem Solving
• Paul, Quallis and Robert Divide a Sum of Money Among Themselves in the GMAT Problem Solving
• If A Sphere With Radius r Is Inscribed In A Cube With Edges Of Length GMAT Problem Solving
• A Globe Of Radius 8 Inches Is To Be Placed Into A Square Box For Shipment GMAT Problem Solving
• What is the sum of digits in decimal notation of number (10^20) - 16? GMAT Problem Solving
• Which of the following is equivalent to the pair of GMAT Problem Solving
• A password to a certain database consists of digits that can GMAT Problem Solving
• A Can do 1/3 of the Work in 5 Days and B Can do 2/5 of the Work in 10 Days GMAT Problem Solving
• The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
• Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
• For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
• The quantities S and T are positive and are related by the equation GMAT Problem Solving
• A child paints the six faces of a cube with six different GMAT Problem Solving
• In an opera theater. there are 300 seats available GMAT Problem Solving
• At the Rate of m Meters Per s Seconds, How Many Meters Does a Cyclist GMAT Problem Solving
• NASA Received Three Messages in a Strange Language From a Distant Planet GMAT Problem Solving
• Two Cyclists Start From the Same Place to Ride in the Same Direction GMAT Problem Solving
• A Sphere is Inscribed in a Cube with an Edge of 10. What is GMAT Problem Solving
• If AC = BC and CD = DE Then, in Terms of x, the Value of y is GMAT Problem Solving
• What Is The Units Digit Of The Product Of Any Five Consecutive Positive Integers GMAT Problem Solving
• A Large Cube Consists Of 125 Identical Small Cubes GMAT Problem Solving
• A Pizzeria Makes Pizzas That Are Shaped As Perfect Circles GMAT Problem Solving
• The Number Of Diagonals Of A Polygon Of n Sides Is Given By The Formula GMAT Problem Solving
• The Work Done By A Woman In 8 Hours Is Equal To The Work Done By A Man GMAT Problem Solving
• A Circle Is Inscribed Inside Right Triangle Abc Shown Above GMAT Problem Solving
• The Temperatures In Degrees Celsius Recorded At 6 In The Morning In GMAT Problem Solving
• A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
• If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
• The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
• A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
• The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
• When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving