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Two Slope Questions

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Two Slope Questions

by dongkim2 » Tue Jun 15, 2010 10:46 am
Line k passes through point (n, -1). Is slope of K positive?

(1) k passes through the origin point.
(2) k passes through (1, n+2)

OA: C



A line in x-y coordinate system goes through the origin and point (a, b), is a < b?
(1) slope < 0
(2) a < 0

OA: C


Can anyone help me to understand how I can approach these two questions? I basically tried to solve these by plugging in some numbers, but it didn't work out well.
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by Haaress » Tue Jun 15, 2010 3:41 pm
Line k passes through point (n, -1). Is slope of K positive?

(1) k passes through the origin point.
(2) k passes through (1, n+2)

Rephrase: What is the vlaue of n?

Stmt 1 provises an additional point of (0, 0) on top of the (n, -1) ; however, we have an unknown variable in an expression ( not an equation) i.e we would not be able to compute the value of n using the slope formula of Rise/ Run. .. (-1 - 0)/(n-0). Thus Insufficient.

Stmt 2. Same as 1 above, we have 2 points (n, -1) and (1, n+2) , yet this info does not help in calculating the value of n.

Combining the 2 stmts. We now have three points (n,-1) (0, 0) and (1, n+2),

So, the slope btw any 2 points of a line are equal, thus (-1 - 0) / (n-0) = ( n+2 - 0)/(1-0)
-1/n = (n+2)/1
-1 = n(n+2), which becomes n^2 +2n +1 = 0 or (n+1)(n+1)=0 or n = -1. meaning that the lines goes through (-1, -1) , (0,0) and (1,1) and therefore the slope is not a negative slope. Hope that helps!
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by Rich@VeritasPrep » Tue Jun 15, 2010 7:51 pm
Hey Haaress,

Be careful, because you keep referring to the fact that we can't find the value of n.

That would be the most pertinent thing if the question asked for the value of n. But the question asks if the slope of the line is positive. This is a YES/NO question as opposed to a VALUE question.

It turns out that you got the correct answer in this case, but in another question, you might potentially be able to find whether or not the slope is positive or negative without knowing the exact value of n.

Since slope is the most pertinent thing here, much better to think about the statements in terms of slope:

(1) tells us that the line passes through (0,0) and (n, -1). Slope is (y1 - y2) / (x1 - x2) = (-1 - 0) / (n - 0) = -1/n

We don't need to know the exact value of n, but we DO need to know whether it is positive or negative. Because we don't, this is INSUFFICIENT.

(2) tells us that the line passes through (1, n+2) and (n, -1). Slope is (n+2 - -1) / (1 - n) = (n+3) / (1-n).

If you plug in n = -3, the slope becomes 0, which isn't positive. Plug in n=0, and you get a slope of 3, which is positive. INSUFFICIENT. Again, the issue of positive vs. negative slope is more important than the value of n itself.

Then, you did a good job outlining why the statements in combination are sufficient! Nice work!
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by Rich@VeritasPrep » Tue Jun 15, 2010 7:58 pm
A line in x-y coordinate system goes through the origin and point (a, b), is a < b?
(1) slope < 0
(2) a < 0


(1) tells us nothing about the coordinates of (a,b), thus there's no way to compare their values. INSUFFICIENT

(2) tells us nothing about b. INSUFFICIENT

(1) and (2) together:

If the line goes through (0,0) and has a negative slope, then it could only go into Quadrant IV (in which x is positive and y is negative), and Quadrant II (in which x is negative and y is positive).

We're told in (2) that a < 0, which means that the point (a,b) has to be in Quadrant II. That means b > 0, and since a < 0, a will always be less than b. SUFFICIENT
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by nikhilkatira » Wed Jun 16, 2010 5:16 am
raz1024 wrote:A line in x-y coordinate system goes through the origin and point (a, b), is a < b?
(1) slope < 0
(2) a < 0


(1) tells us nothing about the coordinates of (a,b), thus there's no way to compare their values. INSUFFICIENT

(2) tells us nothing about b. INSUFFICIENT

(1) and (2) together:

If the line goes through (0,0) and has a negative slope, then it could only go into Quadrant IV (in which x is positive and y is negative), and Quadrant II (in which x is negative and y is positive).

We're told in (2) that a < 0, which means that the point (a,b) has to be in Quadrant II. That means b > 0, and since a < 0, a will always be less than b. SUFFICIENT
Raz1024 gr8 explanation.
Can you please tell me the level of these two questions ?
Best,
Nikhil H. Katira
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by Rich@VeritasPrep » Thu Jun 17, 2010 3:32 pm
Hey Nikhil!

If you want, you could take a guess as to what the difficulty level of any GMAT question is. But in the end, you'd just be guessing. The GMAT is protective of its content, and all questions are patented. There's no public information on the difficulty level of any given question.

If you see a super-difficult problem, you could probably say with reasonable certainty that it's a 700+ level problem. But in the end, you'd still just be estimating. And anyway, it doesn't help to think about problems this way. Much better to figure out what concepts individual questions test and make sure you've mastered those concepts.

Good luck with your studies!
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by Testluv » Thu Jun 17, 2010 5:53 pm
Can you please tell me the level of these two questions ?
About low 600s.
Kaplan Teacher in Toronto
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