What Is The Value Of X + Y In The Figure Above? GMAT Data Sufficiency

Question:

What is the value of x + y in the figure above?

(1) w= 95
(2) z = 125

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: (C)

Approach Solution : 1

We must ascertain what x + y will be. We can see that the quadrilateral's x and y are two of its exterior angles, and its w and z are the other two. The sum of the measures of the exterior angles of a polygon is always 360 degrees, so take note that x + y + w + z = 360. Therefore, we can determine the value of x + y if we know the values of both w and z or if we know the value of w + z.
Statement - 1 : w = 95
This statement alone is insufficient because the value of z is unknown.
Statement - 2 : z = 125
This statement alone is insufficient because the value of w is unknown.
Let us combine both the statements.
Note that x + y + w + z = 360. As a result, we get
=> x + y + 95 + 125 = 360
=> x + y + 220 = 360
=> x + y = 140
Therefore both the statements together are sufficient.

Approach Solution : 2

180(n-2) is the sum of a polygon's interior angles, where n is its number of sides (so is the number of angles). Therefore, 180*2=360 is the total of a quadrilateral's interior angles.
In accordance with the above diagram, we can write the following.

=> (180-x)+(180-y)+(180-z)+(180-w) = 360
=> x+y = 360-w-z
So all we need to know is the values of w and z.
Statement - 1 : w = 95
This statement alone is insufficient because the value of z is unknown.
Statement - 2 : z = 125
This statement alone is insufficient because the value of w is unknown.
By combining both statements we can get the answer as both of them each has the values for z and w respectively. Therefore both the statements together are sufficient.

“What is the value of x + y in the figure above?” - is a topic of the GMAT Quantitative reasoning section of GMAT. 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

• 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
• 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
• If the average of four distinct positive integers is 60, how many integers of these four are less than 50? GMAT Data Sufficiency
• Is |x−1|<1? 1. (x−1)^2 ≤1 2. x^2−1>0 GMAT Data Sufficiency
• If the Vertices of a Triangle have Coordinates (x,1) (5,1) and (5,y) Where x<5 and y>1, What is the Area of the Triangle? GMAT Data Sufficiency
• Each Term of Set T is Multiple of 5. Is Standard Deviation of T Positive? GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio GMAT Data Sufficiency
• If x and y are positive integers and xy is divisible by prime number. Is p an even number? GMAT Data Sufficiency
• What is the Product of 6 Consecutive Numbers? GMAT Data Sufficiency
• If x is an integer is an x/12 integer? GMAT Data Sufficiency
• Is 7^7 / 7^x an integer? GMAT Data Sufficiency
• The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC? GMAT Data Sufficiency
• Is the area of the triangle ABC greater than the area of the triangle DEF? GMAT Data Sufficiency
• There is atleast one viper and atleast one cobra in Pandora’s Box GMAT data sufficiency
• If L not equals to 0, is 18K/L an Integer? GMAT Data Sufficiency
• If a, b, and c are positive and a^2 + c^2 = 202, what is the value of b – a – c? GMAT Data Sufficiency
• If x and y are positive integers, is x odd? GMAT Data Sufficiency
• If 0 < x < 53, what is the value of integer x? 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 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 probability of getting a jack from a 52-card deck on both the first and second draw if the cards are not replaced? GMAT Data Sufficiency
• Is P – 1 even? 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 a, b, and c are distinct positive integers, is (a/b)/c an integer? GMAT Data Sufficiency