Question: Points x and y lie on a line segment. How many units long is the line segment?

(1) Point x is 15 units from one end of the segment and point y is 15 units from the other end.
(2) There are 10 units between points x and y.

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.

“Points x and y lie on a line segment. How many units long is the line” is a topic of the GMAT Quantitative reasoning section of GMAT. This GMAT Data Sufficiency question has been borrowed from the book "GMAT Official Guide 2021". The questions of GMAT Data Sufficiency emerge with a problem statement and two factual statements. The quantitative section of the GMAT exam constitutes two sections- Data Sufficiency and Problem Solving. It tests the efficiency of students in arithmetic, algebra and geometry. The candidates usually ignore the smart accent of words expressed in the question which is regarded as the most complex portion of these questions. GMAT Quant section consists of a set of 31 questions. GMAT data sufficiency includes 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

The problem statement states that

Given:

• Points x and y lie on a line segment.

Find out:

• The length of the line segment.

1. The statement says that Point x is 15 units from one end of the segment and point y is 15 units from the other end.

1. From the claim of the statement, there may arise three conditions such as:
   The point X and Y lie at the same point which signifies that the length of the line segment is 30 units.
2. Point X stands to the right of Y and the reference frame for X is from the far left and for Y from the far right.
   In this condition, the statement is insufficient as we do not know the distance between X and Y.
3. Point X may stand to the left of Y and the reference frame for X is from the far left and for Y from the far right.
   In this condition, the statement is insufficient as we do not know the distance between X and Y.

Therefore, statement (1) alone is not sufficient.

2. The statement explains that there are 10 units between points x and y.
   ​Two conditions can be derived from this statement. They are as follows:

1. Point X stands to the right of Y and the reference frame for X is from the far left and for Y far right. Therefore, the length of the line segment will be 5+10+5 = 20.
2. Point X stands to the left of Y and the reference frame for X is from the far left and for Y far right. Therefore, the length of the line segment will be 15+10+15= 40.

Therefore, statement (2) alone is not sufficient since we are not getting any specific value.

By combining both statements, we are yet left with the two conditions of statement B. Therefore, we cannot be able to find the value of the length of the line segment.
Thus both statements together are not sufficient to find the answer.

Correct Answer: (E)

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