Question: If r > 0 and s > 0, is r/s < s/r?

(1) r/(3s) = ¼
(2) s = r + 4

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: D
Solution and Explanation:
Approach Solution 1:
(1) r/3s = 1/4:
Rewrite as: r/s = 34;
The above, on the other hand, can also be written as: s/r = 4/3;
So, we have that (r/s = 3/4)<(4/3 = s/r). Thus the answer to the question is sufficient.

(2) s=r+4;

This implies that s>r. Since given that r>0, then s>r>0. And finally, s>r>0 means that s/r>1>r/s. Thus the answer to the question is sufficient.

Approach Solution 2:
Since r and s are both positive, we can simplify the inequality to r^2<s^2, and by taking the square root of both sides, r<s.

(1) 4r = 3s
r= 3/4s
So r < s. Sufficient.

(2) Since r= s−4, r<s. Sufficient.
Therefore, each statement alone is sufficient.

Approach Solution 3:
Statement One Alone:
r/(3s) = ¼
4r = 3s
r = 3s/4

We see that r is ¾ of s. Given that both r and s are positive, we see that r < s. Therefore, r/s < s/r. Statement one alone is sufficient.

Statement Two Alone:
Since s = r + 4, r < s. Therefore, r/s < s/r. Statement two alone is sufficient.

“If r > 0 and s > 0, is r/s < s/r?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide". 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 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
• 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
• 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
• In the Below Figure, O is The Centre of The Circle 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
• 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
• What Is The Value Of N GMAT Data Sufficiency
• What is the value of x^2 + 1/x^2 ? 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
• 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
• 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 Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle 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
• What is The Volume of the Right Circular Cylinder X ? GMAT Data Sufficiency
• 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