ughhh help

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Sun Sep 22, 2013 1:34 am

i have this question from kaplan. the statement one tells all about the slope of two lines. i believe knowing the slope is enough to show either these intersect or not. however the OA is B
please help me to understand this question

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 22, 2013 1:34 am

vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Sun Sep 22, 2013 3:02 am

Statement 1

Slope is -1, but the values of x and y can be anything to arrive at this value. We don't any inofrmation about the co-ordinates x and y

Statement 2

I reasoned it this way, I might be wrong

y = -x+4, y-intercept is 4, that is the line intersects y at 4 (positive)

so x+y=4, then from above x has to 0, so line does not intersect QR, sufficient

Also I did this make x and y equal to zero to obtain values of x and y, it will be (4,4) again it will not intersect, So sufficient.

I don't know whether my steps are logical or not(Co-ordinate Geometry is my nemesis)Neither do I know if this is correct process.

Please please correct me if I am wrong!

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Sun Sep 22, 2013 3:06 am

Lets see what the slope of QR is first

m = (2-3) / (2-1) = -1

That means both lines have the same slope. This would be a trap to believe that Line P is indeed parallel and would never intersect QR.

However, Line P could touching Q or R. Check the attached image. 2 cases where slope = -1 and intersects.

Hence INSUFFICIENT.

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mevicks: Master | Next Rank: 500 Posts; Posts: 269; Joined: Thu Sep 19, 2013 12:46 amFollowed by: 7 members; Thanked: 94 times

by mevicks » Sun Sep 22, 2013 4:15 am

Step 1 (Simplify):
Find the equation of the line segment QR (and thus the slope) using the "two point form"

The two points in consideration : (1, 3) & (2, 2)

(y-3)/(x-1) = (y-2)/(x-2)
y = -x+4
when compared to the standard equation of a line : y = mx + c
Slope of line segment QR = (-1)

Step 2 (Statements 1 & 2):

St1: States that the line p has a slope (-1) which also happens to be the equation of the given line segment QR. However, there are many lines having the slope (-1) and thus they may or may not intersect (or in this case overlap) with line segment QR. Consider the following diagram which has the two lines XY and AB having the same slope, but one overlaps and other doesn't

INSUFFICIENT : As we cannot definitely answer a Yes or a no.

St2: This says the line is the same as the segment QR. i.e The line XY in the above diagram contains the line segment QR. So it does intersect, and we can answer the question definitely.
SUFFICIENT
[spoiler]
Answer = B[/spoiler]

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Sep 22, 2013 6:08 am

Statement 1:
Slope of Line p =-1 .. this point doesn't show any reference of X & y
the line could pass through any point with -1 as slope.
INSUFFICIENT

Statement 2:
y = -x + 4

Try values of Q (1,3)
3 = -1 + 4
3 = 3

Try values of R (2,2)
2 = -2 + 4
2 = 2
Hence, Line coincide..
SUFFICIENT.

ANSWER [spoiler] [/spoiler]

The mistake which you must have done is
Slope of QR is -1 and slope of P is -1.. So they both are parallel.. So you assumed that they don't coincide. BUT, you forgot the case .. what if they overlap....

R A H U L

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Sep 24, 2013 1:36 am

thanks everyone, i guess "overlapping" and "intersecting" are two different terms. Kaplan must use Overlapping in the question.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Tue Sep 24, 2013 3:42 am

sana.noor wrote:

i have this question from kaplan. the statement one tells all about the slope of two lines. i believe knowing the slope is enough to show either these intersect or not. however the OA is B
please help me to understand this question

Two lines in the same plane do intersect if and only if their slopes are different or the two lines are coinciding. The slope of the line segment QR as shown here is -1, and its equation is y = -x + 4. We've to be careful here, because intersection of a line with other line cannot be extended to the intersection of the same line with a segment of the other line.

I. Slope of line p is also -1. Here, no intersection if the line p is distinct from the line segment QR, and there are myriad intersections if otherwise. Insufficient, get rid of A and D

II. This tells us that the line p and the line segment QR are coinciding, hence, [spoiler]YES, they intersect a myriad number of times. Sufficient

Hence, pick B[/spoiler]

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