If Equation |x| + |y| = 5 Encloses a Certain Region on the Graph, What is the Area of that Region?

Question: If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?

1. 5
2. 10
3. 25
4. 50
5. 100

“If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?”- 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.

Answer

Approach Solution 1

There is only one approach to solving this problem.

X and Y intercepts are (0,5), (0,-5), (5,0), and (-5,0) (just make x = 0 and find y and then make y equal to zero and find x). Now if we join these points we will get the following region:

The diagonals of the quadrilateral are equal (10,10), and also perpendicular bisectors of each other (as they are on X and Y axis), so the figure must be a square.

Area of a square equals to \(\frac{Diagonal^2}{2}=\frac{10^2}{2}\) =50

Correct option: D

Suggested GMAT Quant Questions

• GMAT Problem Solving - How Many Litres of a 90% Solution of Concentrated Acid Needs to be Mixed with a 75% Solution
• GMAT Problem Solving - What is the Largest Power of 3 Contained in 200!
• GMAT Problem Solving- What is the units digit of the product (32^28) (33^47) (37^19)?
• GMAT Problem Solving- Is Zero Even Integer or Odd Integer?
• GMAT Problem Solving- How many even divisors of 1600 are not multiples of 16?
• GMAT Problem Solving- How many 5 digit (digit = 0 - 9) zip codes can exist in which at least one digit is repeated ?
• GMAT Problem Solving- How Much is the Greatest of Five Consecutive Even Integers Greater than the Smallest?
• GMAT Problem Solving- The least number of digits (including repetitions) needed to express 10^100 in decimal notation
• GMAT Problem Solving- largest 3 digit number to have an odd number of factors
• GMAT Problem Solving- Bag A Contains Red, White and Blue Marbles such that
• GMAT Problem Solving- Greg Assembles Units of a Certain Product at a Factory.
• GMAT Problem Solving- A Scientific Research Study Examined a Large Number of Young Foxes
• GMAT Problem Solving- The Smallest of Six Consecutive Odd Integers Whose Average (arithmetic mean) is x + 2
• GMAT Problem Solving- The Greatest 6-Digit Number When Divided by 6, 7 ,8 , 9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8
• GMAT Problem Solving- If 20 Men or 24 Women or 40 Boys can do a Job in 12 Days
• GMAT Problem Solving- If 10 millimeters equal 1 centimeter, how many square centimeters does 1 square millimeter equal?
• GMAT Problem Solving- How many Terminating Zeroes does 200 Have?
• GMAT Problem Solving- Properties of Circle
• GMAT Problem Solving- If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible?
• GMAT Problem Solving- For How Many Values of k is 12^12 the Least Common Multiple