PS -co-ordinates

Question

sheetal.GIF

alpha_plus_gamma · Answer

Is it D. 11?

y = -3/5*x + c

both x and y will be integers when x is divisible by 5,

so x can 0, 5...50

11 values

abhijit_sen · Answer

PQ is a straight line passing through (50,0) and (0,30).
Slope of line = (30-0)/(0-50) = -3/5
Y intercept = 30
Equation of line = y = mx + c, y = -3/5x + 30
=> 3x+5y = 150

Now you need only value for x and y those are integer values and those that will satisfy this equation. Moreover you cannot have -ve values and for x max value is 50 and and for y it is 30.

For x = 0, 5, 10, 15, ..., 50 you can have integer Y ranging from 30 to 0.

So total possible integer value = 11

IMO D.

x97agarwal · Answer

First create your equation of your line

y = mx + c
slope of PQ is -3/5 and intercept is 30

Hence y = -(3/5)x + 30
 5y + 3x = 150
Find the calue of y and x such that 5y + 3x adds up to 150
So if x is 0 then 5(30) = 150
 x is 5 then 5(27) = 135
 
so divide 50/5 and add one for zero = 10 + 1 = 11

greenoak · Answer

Alternative approach: 
Number of integer points can be calculated as GCD(30,50)+1=11.

hi0parag · Answer

this seems to be a promising solution.
pl confirm if it can be applied to other similar problems?

greenoak · Answer

It seems that yes, it can be. Here is my reasoning:

Let x/A+y/B=1 be the equation of the line (A, B are non-zero integers). Let’s take an integer n: 1 y=B(n-1)/n.

So, we need to find n not greater than A such that both A/n and B(n-1)/n are integers. B(n-1)/n is an integer B – B/n is integer B/n is integer.

It means we need to find the greatest possible n such that both A/n and B/n are integers (for such an n, A/n will correspond to the smallest coordinate x such that the point (x,y) on the line will be integer. x-coordinates of other integer points will be 2/n*A, 3/n*A, ..., (n-1)/n*A, A). And, by definition, the greatest possible n such that A/n, B/n are integers is GCD(A,B).

We need to add 1 because the case (0,B) also gives us an integer, but we did not count that point.

Therefore, in general case, the formula for the number of integer points on the line segment is N = GCD(A,B)+1.

***
I'd be grateful for other people's comments on the reliability of this reasoning.

PS -co-ordinates

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards