Does line L pass through point (-2/3, 1/2)?

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Bens4vcobra: Senior | Next Rank: 100 Posts; Posts: 76; Joined: Thu Feb 19, 2009 12:10 pmFollowed by: 2 members; Thanked: 3 times

by Bens4vcobra » Thu Jun 16, 2011 5:49 am

On the xy cord. plane, line L has a slope of 3/4. Does line L pass through the point (-2/3, 1/2)?

1) Line L passes through point (4, 4)

2) Line L passes through point (-4, -2)

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Source: Beat The GMAT — Problem Solving | Thu Jun 16, 2011 5:49 am

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Thu Jun 16, 2011 6:09 am

Bens4vcobra wrote:On the xy cord. plane, line L has a slope of 3/4. Does line L pass through the point (-2/3, 1/2)?

1) Line L passes through point (4, 4)

2) Line L passes through point (-4, -2)

Slope equation between two points is slope = y2-y1/x2-x1

We know that our line has a slope of 3/4. Each of the statements also gives us a point on the line. All we really need to do is find whether the slope bwtween the point given and (-2/3,1/2) is dequal to 3/4 or not.

stat. (1) 4-1/2 / 4-(-2/3) = 3.5 / 4+2/3 = 7/2 / 14/3 = 7/2 * 3/14 = 1/2 * 3/2 = 3/4. the answer is yes. Sufficient

Stat. (2) -2-1/2 / -4-(-2/3) = -2.5 / -4+2/3 = -5/2 / -10/3 = -5/2 * 3/-10 = 1/2 * 3/2 = 3/4. the answer is yes. Sufficient

the answer is D.

Last edited by Geva@EconomistGMAT on Thu Jun 16, 2011 6:33 am, edited 1 time in total.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Jun 16, 2011 6:11 am

Bens4vcobra wrote:On the xy cord. plane, line L has a slope of 3/4. Does line L pass through the point (-2/3, 1/2)?

1) Line L passes through point (4, 4)

2) Line L passes through point (-4, -2)

To determine whether a line passes through a particular point, we need to know the equation of the line. Now the slope of the line is given.

Say, the equation of the line is y = mx + c, then we know m but we don't know c. We can easily determine c if we know the coordinates of a point on the line.

Hence, if we know the coordinate of a point that lies on the line, we can determine equation of the line and hence we can determine whether the line passes through the given point or not.

As both statements gives us the coordinate of a point lying on the line. Both of them are sufficient to answer the question.

The correct answer is D.

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Thu Jun 16, 2011 6:11 am

Bens4vcobra wrote:On the xy cord. plane, line L has a slope of 3/4. Does line L pass through the point (-2/3, 1/2)?

1) Line L passes through point (4, 4)

2) Line L passes through point (-4, -2)

Incidentally, it is not even required to calculate the actual slope. Once you have a point on the line, and the required point, you know that you CAN calculate the slope of the line between the two points, and see whether it is equal to 3/4 or not. The answer is going to be a "yes", or the answer is going to be a "no", but either way you will have a definite answer, and the statements will be sufficient.

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by Anurag@Gurome » Thu Jun 16, 2011 6:22 am

Geva@MasterGMAT wrote:Stat. (2) -4-1/2 / -2-(-2/3) = -4.5 / -2+2/3 = -9/2 / -4/3 = 9/2 * 3/4 = 27/8. This is not equal to 3/4, and the answer is a definite "no" - but that is also sufficient, since yo9u CAN answer the question.

Hi Geva, please check the red part.
It should be (-2 - (1/2))/(-4 - (-2/3)) = ... = 3/4

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Thu Jun 16, 2011 6:30 am

Thanks, I'll edit my post.

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