Line L1 has a slope A and Line L2 has the slope B.Is AB?

Question

Line L1 has a slope A and Line L2 has the slope B.Is A>B?

(1) The y intercept of L1 is greater than the y intercept of line L2
(2) L1 and L2 intersect at point Q(5,9)

fantaisie · Accepted Answer

Algebraic approach:

Slope L1 = A
Slope L2 = B
Question: Is A>B?

L1: y1 = AX1 + b1
L2: y2 = BX2 + b2

1) y-intercept is when x = 0, thus
If b1 > b2, and given those two formulas above, we still know nothing about A & B.
NOT SUFFICIENT

2) Both lines go through point (5,9) and intercept at that point:
y1 = 9 = 5A + b1
y2 = 9 = 5B + b2
5A + b1 = 5B + b2
NOT SUFFICIENT

1,2) We know that:
b1 > b2
5A + b1 = 5B + b2

Hence, if b1 > b2 and then 5B has to be larger than 5A to compensate for the difference in b-values and maintain the equation equal.
We can conclude that A < B.

Answer:  C

Hope it helps someone! Cheers!

Bunuel · Answer

Almost the same question: lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-line-n-127999.html Similar questions to practice: if-the-slopes-of-the-line-l1-and-l2-are-of-the-same-sign-is-126759.html lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-line-n-127999.html in-the-xy-plane-is-the-slope-of-line-l-greater-than-the-126941.html if-the-slopes-of-the-line-l1-and-l2-are-of-the-same-sign-is-126759.html slopes-of-m-and-n-124025.html in-the-xy-plane-both-line-k-and-l-intersect-with-axis-y-is-94508.html point-r-s-lies-on-the-line-l-is-the-line-s-intercept-with-94505.html lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-the-line-30553.html lines-n-and-p-lie-in-the-xy-plane-is-the-slope-of-line-n-97007.html Hope it helps.

shivanigs · Answer

Thank you very much Bunuel!

1022lapog · Answer

The Answer is 'C'. 
The y intercept of L1 > The y intercept of L2 can be either way with A>B or B>A. 
L1 and L2 intersect at point Q(5,9), doesn't itself give much info on the slopes.
These two taken together, the Line L2 got to be rapidly rising than line L1 (as L1 is above L2). Also L1 got to be of lesser slope to meet L2 somewhere (here at 5,9). If L1 is rising at higher rate than L2 then they can't possibly meet. That was my reason.
Have a nice day.

tbo89 · Answer

First post and it seems to be the right time after 3months of prac!

so :

1) Stat. 1 is telling us nothing about the slope of Line A and Line B. If both lines are horizontal the slope will be 0 and therefore A>/B
2) Stat. 2 Both lines are intercepting at (5,9) therefore both lines have a slope greater or less than 0 and thus not horizontal. However, it is possible that the slope of Line B could be positive and thus the Line A negative as both lines have an intercept point

C) Combine both and try to graph it and you will see that is necessary that B must be larger than A. As a result the data provided are sufficient to tell that A is not greater than B!

Good night, and good luck.

Nick90 · Answer

https://uploads.tapatalk-cdn.com/20160720/449b10fd25292e0b61a640e0b5d52a6a.jpg

Sent from my Le X507 using  GMAT Club Forum mobile app

mvictor · Answer

this question can easily be solved if you can visualize it.
1. we can have infinite options for both slopes.
2. gives only 1 point for both lines - again, we can have an infinite options.

1+2. lines intersect at point (5;9) and we know that L2 has a lower y intercept - therefore L2 has steeper slope than the other one
eventually, we can try few options and see which one is which.

C

profileusername · Answer

What's the mistake I'm making in my imagination?

The y-intercepts for lines L1 and L2 tell us that for L1 it's higher than for L2. But if both lines intersect at (5,9) and both the lines have their y-intercepts > 9 then shouldn't that make slope for L2 less steeper than slope for L1?

I hope I have put it clearly. Would really appreciate some help here.

Fdambro294 · Answer

Way too late to be of any help since it's been years, but I made a similar mistake when I took a quiz that had this question....

In the situation you described (both Y-Intercepts are greater than > 9), both of the Slopes would then necessarily be Negative.

L1, having the Y-Intercept "Higher" on the Y-Axis, will have a Steeper (-)Negative Slope than L2 will have.

ex: L1's slope = -4 ---- and----- L2's slope = -1

The trap of the (-)Negative!

-4 < -1

so even in this case L1's Slope is Less than L2's Slope.

However, L1's Slope is STEEPER than L2's Slope.....but that is not what the question is asking. It wants to know whether A > B?

so we are comparing the numbers from a Value perspective.....

bumpbot · Answer

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Line L1 has a slope A and Line L2 has the slope B.Is A>B?

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Line L1 has a slope A and Line L2 has the slope B.Is A>B?

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