4gmat diagnostic test q9 - data sufficiency - coordinate geometry
TRANSCRIPT
GMAT QUANTITATIVE REASONING
COORDINATE GEOMETRY
DATA SUFFICIENCY
Diagnostic Test
Question
Does line L pass through the IV quadrant?
Statement 1: The slope of the line is 2
Statement 2: The line passes through the point (3, 6)
Step 1
Get clarity on when the data is sufficient
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient?
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient?
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient?
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Yes – If the line definitely passes throughthe IV quadrant. Data SUFFICIENT.
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient?
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Yes – If the line definitely passes throughthe IV quadrant. Data SUFFICIENT.
No – If the line will NOT pass through theIV quadrant. Data SUFFICIENT.
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient? What is the approach to take?
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Yes – If the line definitely passes throughthe IV quadrant. Data SUFFICIENT.
No – If the line will NOT pass through theIV quadrant. Data SUFFICIENT.
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient? What is the approach to take?
With the information given in eachstatement, try and find a counter example
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Yes – If the line definitely passes throughthe IV quadrant. Data SUFFICIENT.
No – If the line will NOT pass through theIV quadrant. Data SUFFICIENT.
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient? What is the approach to take?
With the information given in eachstatement, try and find a counter example
i.e., one case where the line passesthrough the IV quadrant and one whereit does not.
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Yes – If the line definitely passes throughthe IV quadrant. Data SUFFICIENT.
No – If the line will NOT pass through theIV quadrant. Data SUFFICIENT.
Does line L pass through the IV quadrant?We will not even look at the statements while answering the following questions
When is the data sufficient? What is the approach to take?
With the information given in eachstatement, try and find a counter example
i.e., one case where the line passesthrough the IV quadrant and one whereit does not.
If you succeed data Not sufficient. Else sufficient.
For a “does” question the data issufficient if we get a conclusive “yes” or a“no” as an answer from the statements
Yes – If the line definitely passes throughthe IV quadrant. Data SUFFICIENT.
No – If the line will NOT pass through theIV quadrant. Data SUFFICIENT.
Step 2
Let’s evaluate statement 1 alone
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV Does NOT pass through IV
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Statement 1 alone is NOT sufficient
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV Does NOT pass through IV
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Eliminate choices A and DStatement 1 alone is NOT sufficient
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV Does NOT pass through IV
Does line L pass through the IV quadrant?Statement 1: The slope of the line is 2
Choices narrow down to B, C or E.
Eliminate choices A and DStatement 1 alone is NOT sufficient
Approach: With slope 2 draw two lines – one passing through IV quadrant and another that does not
pass through the IV quadrant
III
III IV
III
III IV
Line with slope 2
Is a positive sloping line. An upward sloping line. Goes from bottom left to top right
Passes through IV Does NOT pass through IV
Step 3
Let’s evaluate statement 2 alone.
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
(3, 6)
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
(3, 6)
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
(3, 6)
Passes through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
III
III IV
(3, 6)
Passes through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
(3, 6)
III
III IV
(3, 6)
Passes through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
(3, 6)
III
III IV
(3, 6)
Passes through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
III
III IV
(3, 6)
III
III IV
(3, 6)
Passes through IV Does NOT pass through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
Statement 2 alone is NOT sufficient
III
III IV
(3, 6)
III
III IV
(3, 6)
Passes through IV Does NOT pass through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Eliminate choice B
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
Statement 2 alone is NOT sufficient
III
III IV
(3, 6)
III
III IV
(3, 6)
Passes through IV Does NOT pass through IV
Does line L pass through the IV quadrant?Statement 2 : The line passes through the point (3, 6)
Choices narrow down to C or E.
Eliminate choice B
Approach: Passing through (3, 6) draw two lines – one passing through IV quadrant and another that does
not pass through the IV quadrant. (3, 6) is a point in the I quadrant – both x and y coordinates positive
Statement 2 alone is NOT sufficient
III
III IV
(3, 6)
III
III IV
(3, 6)
Passes through IV Does NOT pass through IV
Step 4
Let’s combine data from both the
statements.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
A line of the form y = mx passes through the origin. Note: There is no y-intercept ‘c’ in this equation. Lines passing through origin do not have ‘c’.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
A line of the form y = mx passes through the origin. Note: There is no y-intercept ‘c’ in this equation. Lines passing through origin do not have ‘c’.
If a line passes through the origin, it will NOT pass through the IV quadrant.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
A line of the form y = mx passes through the origin. Note: There is no y-intercept ‘c’ in this equation. Lines passing through origin do not have ‘c’.
If a line passes through the origin, it will NOT pass through the IV quadrant.
Conclusive NO is the answer.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Statements together are SUFFICIENT
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
A line of the form y = mx passes through the origin. Note: There is no y-intercept ‘c’ in this equation. Lines passing through origin do not have ‘c’.
If a line passes through the origin, it will NOT pass through the IV quadrant.
Conclusive NO is the answer.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Eliminate choice EStatements together are SUFFICIENT
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
A line of the form y = mx passes through the origin. Note: There is no y-intercept ‘c’ in this equation. Lines passing through origin do not have ‘c’.
If a line passes through the origin, it will NOT pass through the IV quadrant.
Conclusive NO is the answer.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Answer is choice C
Eliminate choice EStatements together are SUFFICIENT
Given slope ‘m’ and point (x1, y1) through which a line passes, equation of line: (y – y1) = m(x – x1)
Approach: Frame the equation and verify whether the line passes through the IV quadrant
Slope 2, point (3, 6). equation of the line is (y – 6) = 2(x – 3) or y = 2x
A line of the form y = mx passes through the origin. Note: There is no y-intercept ‘c’ in this equation. Lines passing through origin do not have ‘c’.
If a line passes through the origin, it will NOT pass through the IV quadrant.
Conclusive NO is the answer.
Alternative Reasoning
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Statement 1 alone: Slope of line 2
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Statement 1 alone: Slope of line 2
Infinite possibilities. Some passing through IV and some not.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Statement 1 alone: Slope of line 2
Statement 2 alone: Passes through (3, 6)
Infinite possibilities. Some passing through IV and some not.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Statement 1 alone: Slope of line 2
Statement 2 alone: Passes through (3, 6)
Infinite possibilities. Some passing through IV and some not.
Infinite possibilities. Some passing through IV and some not.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Statement 1 alone: Slope of line 2
Statement 2 alone: Passes through (3, 6)
Combining the two statements
Infinite possibilities. Some passing through IV and some not.
Infinite possibilities. Some passing through IV and some not.
Does line L pass through the IV quadrant?Statements Together : The slope of the line is 2 and the line passes through the point (3, 6)
Is there only one line possible with the data given?
If YES, data is sufficient. Answer
will be definite
If NO, unless all possibilities give
same answer data NOT sufficient
Statement 1 alone: Slope of line 2
Statement 2 alone: Passes through (3, 6)
Combining the two statements
Infinite possibilities. Some passing through IV and some not.
Infinite possibilities. Some passing through IV and some not.
Only ONE line possible. Can provide a definite YES or a definite NO.
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