Is the Range of a Combined Set (S,T) Bigger than the Sum of the Ranges of Sets S and T? GMAT Data Sufficiency

Question: Is the range of a combined set (S,T) bigger than the sum of the ranges of sets S and T?

1. The largest element of T is bigger than the largest element of S.
2. The smallest element of T is bigger than the largest element of S.

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.

“Is the range of a combined set (S,T) is bigger than the sum of the ranges of sets S and T?”– is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review". 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.

Solution and Explanation

Approach Solution 1

There is only one solution to this problem.

\(range_t=t_{max}-t_{min}\)

\(range_s=s_{max}-s_{min}\)

Question: \(range_{tan ds}=(t_{max}-t_{min})+s_{max}-s_{min}?\)

1. The largest element of T is bigger than the largest element of S

Given: \(t_{max}>s_{max}\), so the largest element of combined set is \(t_{max}\) but we still don’t know which the smallest element of the combined set is:
If it’s \(t_{min}\) then the question becomes is \(t_{max}-t_{min}>t_{max}-t_{min}+s_{max}-s_{min}\)

OR: is \(0>s_{max}-s_{min}\) and the answer would be NO;
If it’s \(s_{min}\)then the question becomes is \(t_{max}-s_{min}>t_{max}-t_{min}+s_{max}-s_{min}\)

OR:is \(t_{min}>s_{max}\) and the answer would be sometimes NO and sometimes YES.
Hence this statement is NOT SUFFICIENT

2. The smallest element of T is bigger than the largest element of S.

Given: \(t_{min}>s_{max}\) , so the largest element of the combined set is \(t_{max}\)and the smallest element of the combined set is \(s_{min}\) .
So the question becomes is \(t_{max}-s_{min}>t_{max}-t_{min}+s_{max}-s_{min}\)

OR: is\(t_{min}>s_{max}\) ?

And that is true, so the answer is YES.
Hence this statement is SUFFICIENT.

Correct Answer: B
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