[email protected] wrote:How many points (x, y) lie on the line segment between (22, 12 2/3) and (7, 17 2/3) such that x and y are both integers?
[spoiler]Ans:5[/spoiler]
The equation of a line is as follows:
y = mx + b, where m is the slope, and b is the y-intercept.
Step 1: Determine the slope
m = (y₂ - y�)/(x₂ - x�) = (17 2/3 - 12 2/3)/(7 - 22) = 5/-15 = -1/3.
Thus far, the equation of the line is as follows:
y = (-1/3)x + b.
Step 2: To determine the y-intercept, plug in one of the two given points
Substituting (7, 17 2/3) into y = (-1/3)x + b, we get:
17 2/3 = (-1/3)(7) + b
53/3 = -7/3 + b
60/3 = b
b = 20.
Thus, the final equation of the line is as follows:
y = (-1/3)x + 20
For y to be an integer, x must be a multiple of 3.
List the multiples of 3 between the two given x-values (7 and 22):
9, 12, 15, 18, 21.
Total options =
5.
Last edited by
GMATGuruNY on Sat Apr 19, 2014 6:52 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
