Question: If r > 0 and s > 0, is r/s < s/r?
(1) r/(3s) = ¼
(2) s = r + 4
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- 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: (1) 4r = 3s (2) Since r= s−4, r Approach Solution 3: 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: “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
Since r and s are both positive, we can simplify the inequality to r^2
r= 3/4s
So r < s. Sufficient.
Statement One Alone:
r/(3s) = ¼
4r = 3s
r = 3s/4
Since s = r + 4, r < s. Therefore, r/s < s/r. Statement two alone is sufficient.
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