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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
Joined: 16 Aug 2015
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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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29 Jun 2018, 00:16
1
5
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Difficulty:

45% (medium)

Question Stats:

56% (01:22) correct 44% (01:17) wrong based on 55 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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1217 Location: India GPA: 3.82 In the xy-plane, the line K passes through a point (a,b), where a>0 an [#permalink] ### Show Tags 29 Jun 2018, 08:04 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6661 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the xy-plane, the line K passes through a point (a,b), where a>0 an [#permalink] ### Show Tags 01 Jul 2018, 17:09 => 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. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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, 17:09
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