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In the xy-plane, the line K passes through a point (a,b), where a>0 an

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Math Revolution GMAT Instructor
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In the xy-plane, the line K passes through a point (a,b), where a>0 an  [#permalink]

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New post 29 Jun 2018, 01:16
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A
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D
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Difficulty:

  45% (medium)

Question Stats:

60% (01:00) correct 40% (01:00) wrong based on 50 sessions

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[GMAT math practice question]

In the xy-plane, the line K passes through a point \((a,b)\), where \(a>0\) and \(b>0\). Is the slope of line \(K\) greater than \(0\)?

1) Line \(K\) passes through the point \((-a,-b).\)
2) Line \(K\) passes through the point \((c,d)\), where \(a>c\) and \(b>d\)

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In the xy-plane, the line K passes through a point (a,b), where a>0 an  [#permalink]

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New post 29 Jun 2018, 09:04
MathRevolution wrote:
[GMAT math practice question]

In the xy-plane, the line K passes through a point \((a,b)\), where \(a>0\) and \(b>0\). Is the slope of line \(K\) greater than \(0\)?

1) Line \(K\) passes through the point \((-a,-b).\)
2) Line \(K\) passes through the point \((c,d)\), where \(a>c\) and \(b>d\)


Slope of any line \(= \frac{y_1-y_2}{x_1-x_2}\). we are given one point \((a,b)\) where \(a\) & \(b\) are positive

Statement 1: gives \((x_2,y_2)=(-a,-b)\)

Hence slope \(= \frac{b-(-b)}{a-(-a)}=\frac{2b}{2a}=\frac{a}{b}>0\). Sufficient

Statement 2: gives \((x_2,y_2)=(c,d)\)

Hence slope \(= \frac{b-d}{a-c}>0\), because \(a>c\) & \(b>d\). Sufficient

Option D
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Re: In the xy-plane, the line K passes through a point (a,b), where a>0 an  [#permalink]

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New post 01 Jul 2018, 18:09
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Condition 1):
The slope of line \(K\) is \(\frac{( b – ( -b ) )}{( a – ( -a ) )}\) = \(\frac{2b}{2a} = \frac{b}{a}\). Moreover, \(\frac{b}{a} > 0\) since \(a>0\) and \(b>0\).
Thus, condition 1) is sufficient.

Condition 2)
The slope of line \(K\) is \(\frac{( b – d )}{( a – c )}\). This is greater than zero since \(b > d\) and \(a > c\).
Thus, condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: In the xy-plane, the line K passes through a point (a,b), where a>0 an &nbs [#permalink] 01 Jul 2018, 18:09
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