Question: Does point (10,10) lie on line m?

1. Lines m passes through point (10,11)
2. Line m passes through point (11,10)

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.

“Does point (10,10) lie on line m GMAT Data Sufficiency?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from 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.

Answer:
Approach Solution (1):

Statement 1: Line m passes through point (10,11)
There may be infinite lines passing through (10,11) and x = 10 is one of such line which passes through both at the same time there are infinite lines which pass through only one of those points; Hence, not sufficient.
Statement 2: Line m passes through point (11,10)
There may be infinite lines passing through (11,10) and y=10 is one of such lines which passes through both at the same time there are infinite lines which pass through only one of those points; Hence, not sufficient.
Combined:
There is a unique line which passes through two points, hence sufficient

Correct option: C
Approach Solution (2):

S1: passes through (10,11)
Insufficient since the line could be parallel to the y-axis, in that case it will pass through (10,10). But if it is downward or upward sloping it will not pass. Insufficient
S2: same reason. If it is parallel to the x-axis it will pass through the point (10,10) but it could be otherwise as well.
On combining both statements we got to know it is a downward sloping line. Therefore, it will not pass through (10,10)

Correct option: C

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