Challenge: If line k passes through the points (48, 33) and

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 09, 2018 6:17 am

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If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

Answer: B
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Source: Beat The GMAT — Problem Solving | Mon Jul 09, 2018 6:17 am

Shahrukh@mbabreakspace: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Thu Jul 05, 2018 2:28 am

by Shahrukh@mbabreakspace » Tue Jul 10, 2018 9:28 pm

Slope of the line= (33-22)/(48-31)= 11/17

Equation of the line= (y-22)/(x-31)= 11/17
=>11x-17y=-33
For x intercept, put y=0
So, x=-3

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Jul 11, 2018 6:57 am

Brent@GMATPrepNow wrote:If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

If we sketch the two given points, we can quickly see that the slope (aka rise/run) of the line = 11/17

So, we can use this information to plot another point on the line...

And another point...

..at which point, we can see that the x-intercept is -3

Answer: B

Cheers,
Brent

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jul 11, 2018 7:32 am

Brent@GMATPrepNow wrote:If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

Slope = ∆y/∆x = (33-22)/(48-31) = 11/17.

Since (x, 0) and (31, 22) must yield the same slope, we get:
(0-22)/(x-31) = 11/17
(x-31)(11) = (17)(-22)
x - 31 = (17)(-2)
x - 31 = -34
x = -3.

The correct answer is B.

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by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:24 pm

Brent@GMATPrepNow wrote:If line k passes through the points (48, 33) and (31, 22), what is the x-intercept of line k?

A) -25 10/11
B) -3
C) -1 16/17
D) 1 16/17
E) 25 10/11

We can let the x-intercept be a. Thus the coordinates of the x-intercept will be (a, 0). Since the x-intercept is on line k, the slope measured between the x-intercept and one of the two given points equals the slope measured between the two given points. Using the slope formula, we have:

(0 - 33)/(a - 48) = (22 - 33)/(31 - 48)

-33/(a - 48) = -11/(-17)

3/(a - 48) = 1/(-17)

a - 48 = -51

a = -3

Answer: B

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