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# In the xy-plane line k passes through the origin. Is the slope of line

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In the xy-plane line k passes through the origin. Is the slope of line  [#permalink]

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23 May 2019, 03:28
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Difficulty:

95% (hard)

Question Stats:

12% (01:22) correct 88% (02:07) wrong based on 25 sessions

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FRESH GMAT CLUB TESTS QUESTION

In the xy-plane line k passes through the origin. Is the slope of line k is greater than 1 ?

(1) Line k does not pass through any point (a, b) where a and b are positive and a > b.
(2) Line k passes through the point (c, d +1) where c and d are consecutive integers and c > d.

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Re: In the xy-plane line k passes through the origin. Is the slope of line  [#permalink]

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23 May 2019, 08:41
The line y=x, which has a slope exactly equal to 1, does not pass through any point (a, b) where a > b (since a=b for every point on the line), so using Statement 1, the line could have a slope of 1 exactly. Then the answer to the question is 'no'. But the line could also be, say y = 2x or any other line through the origin with a slope greater than 1, so the answer can also be 'yes'.

Using Statement 2, we know c and d are consecutive integers, and c > d, so c = d + 1. So the point the Statement is talking about is (c, c). Now if c were any nonzero number at all, this would tell us we have the points (0, 0) and (c, c) on our line, and our line would need to be y=x. So it would have a slope of 1. But nothing in the wording rules out the possibility that c=0, so Statement 2 could just be telling us that "the origin is on the line", which we already know. So since it's possible Statement 2 is not giving us any new information whatsoever, Statement 2 can't even be useful when combined with other information, and the answer must be A or E, and since Statement 1 was not sufficient, the answer is E.
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Re: In the xy-plane line k passes through the origin. Is the slope of line   [#permalink] 23 May 2019, 08:41
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