Question:
If p, q, x, y, and z are different positive integers, which of the five integers is the median?

(1) p + x < q
(2) y < z

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.

Solutions and Explanation
Approach Solution : 1

Statement - 1 : p + x < q
We understand that q is greater than both p and x because p and x are both positive. Q will be the median if it is less than both y and z. The median will be one of the quantities other than q, though, if it is not.
Therefore this statement is not sufficient.
Statement - 2 : y < z
With this, we have no idea about p, q, and x.
Therefore this statement is not sufficient
We still lack enough details to calculate the median, even when the two statements are taken together. For instance, q is the median if p + x < q < y < z. The median will, however, be a different quantity than q if y < z < q.
Therefore combining them will also not be sufficient.

Correct Answer: (E)

Approach Solution : 2

Statement - 1 : p + x < q
It can either be p x q or x p q if we arrange in increasing order. Since we are unsure of the y and z values, we are unable to arrange them and, as a result, cannot calculate the median of the data points.
Therefore this statement is not sufficient.
Statement - 2 : y < z
In this case, other values are unknown.
Therefore this statement is not sufficient
By putting the two sentences together, the following four combinations can be obtained by arranging the positive integers in ascending order.
p x q y z
x p q y z
y z x p q
y z p x q

Therefore this is also not sufficient as the middle term changes.

Correct Answer: (E)

“If p, q, x, y and z are different positive integers, which of the five” - 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>y^2>z^4, Which of The Following Statements Could Be True? GMAT Data Sufficiency
• A Clothing Manufacturer Makes Jackets That Are Wool or Cotton or a Combination of Wool and Cotton GMAT Data Sufficiency
• Is |x-1| < 1 ? 1. (x-1)^2 >1 2. x < 0 GMAT Data Sufficiency
• Is 2x - 3y < x^2 ? GMAT Data Sufficiency
• In Triangle PQR, if PQ = x, QR = x + 2, and PR = y GMAT Data Sufficiency
• In the Below Figure, O is The Centre of The Circle GMAT Data Sufficiency
• If p is the Perimeter of Rectangle Q, What is the Value of p? GMAT Data Sufficiency
• What is x? (1) x = 4y - 4 (2) xy = 8 GMAT Data Sufficiency
• Is x = y ? (1) 2x/3 - y/3 = 1/3 (2) x/4 - y/4 = 0 GMAT Data Sufficiency
• What Is The Area Of Triangle ABC ? GMAT Data Sufficiency
• If n Is a Positive Integer And r Is The Remainder When n^2 - 1 is Divided By 8 GMAT Data Sufficiency
• If 0 < x < y, what is the value of (x+y)^2/(x−y)^2? GMAT Data Sufficiency
• If The Perimeter of Quadrilateral ABCD is 4, What Is Its Area? GMAT Data Sufficiency
• If Triangle ABC Is Isosceles, What Is The Length Of Side BC? GMAT Data Sufficiency
• Did Insurance Company K have More than $300 Million in Total Net Profits Last Year? GMAT Data Sufficiency
• Is x<5 ? (1)x^2 > 5 (2)x^2 + x < 5 GMAT Data Sufficiency
• Is x < y ? (1) 2x < 3y (2) xy > 0 GMAT Data Sufficiency
• Is c^(abcd) = 1? (1) |a|>|b|>|c|>|d| (2) c^d>3 GMAT Data Sufficiency
• If r and s are The Roots of The Equation x^2 + bx + c = 0 GMAT Data Sufficiency
• Equilateral triangle BDF Is Inscribed in Equilateral Triangle ACE GMAT Data Sufficiency
• What is the value of x if x^3 < x^2? GMAT Data Sufficiency
• If x ≠0, then what is the value of (|x|)x? 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
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• In the xy-Plane, Line k Passes Through The Point (1, 1) And Line m 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
• In the Figure Above, What is the Area of Semicircle DPA? GMAT Data Sufficiency
• Is |x-10| > |x-30|GMAT Data Sufficiency
• What is The Value of (a!+b!)(c!+d!)? 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
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency