GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 24 Jan 2020, 03:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A line passes through A(1,1) and B(100,1000). How many other points wi

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60644
A line passes through A(1,1) and B(100,1000). How many other points wi  [#permalink]

### Show Tags

22 Mar 2019, 01:20
21
00:00

Difficulty:

85% (hard)

Question Stats:

33% (01:56) correct 67% (02:41) wrong based on 60 sessions

### HideShow timer Statistics

A line passes through A(1,1) and B(100,1000). How many other points with integer coordinates are on the line and strictly between A and B?

(A) 0
(B) 2
(C) 3
(D) 8
(E) 9

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 8336
Re: A line passes through A(1,1) and B(100,1000). How many other points wi  [#permalink]

### Show Tags

22 Mar 2019, 20:20
2
3
Bunuel wrote:
A line passes through A(1,1) and B(100,1000). How many other points with integer coordinates are on the line and strictly between A and B?

(A) 0
(B) 2
(C) 3
(D) 8
(E) 9

The line is (1,1) to (100,1000), so the slope of line m is $$\frac{1000-1}{100-1}=\frac{999}{99}=\frac{111}{11}$$
Thus the slope form of the equation can be written as .. y=mx....y=$$\frac{111}{11}$$x
Thus, for all points on line, the slope should be same, so if we take a point (x,y), the slope from (x,y) to (1,1) should be $$\frac{111}{11}$$
So, $$\frac{y-1}{x-1}=\frac{111}{11}.....11y-11=111x-111......11y=111x-100.....11y=11x+100x-100......11(y-x)=100(x-1)$$
Since x and y are integers and 11 and 100 are co-prime, x-1 should be a multiple of 11...
Thus x-1 can be 0,11,22,33,44,55,66,77,88,99. The corresponding x values will be 1,12,23,34,45,56,67,78,89,100, so total 10 values.
But 1 and 100 are already the end points of the line, and we are looking at the points in between, so 10-2=8 values

D
_________________
##### General Discussion
VP
Joined: 18 Dec 2017
Posts: 1019
Location: United States (KS)
GMAT 1: 600 Q46 V27
Re: A line passes through A(1,1) and B(100,1000). How many other points wi  [#permalink]

### Show Tags

23 Nov 2019, 10:39
2
Quote:

The line is (1,1) to (100,1000), so the slope of line m is $$\frac{1000-1}{100-1}=\frac{999}{99}=\frac{111}{11}$$
Thus the slope form of the equation can be written as .. y=mx....y=$$\frac{111}{11}$$x
Thus, for all points on line, the slope should be same, so if we take a point (x,y), the slope from (x,y) to (1,1) should be $$\frac{111}{11}$$
So, $$\frac{y-1}{x-1}=\frac{111}{11}.....11y-11=111x-111......11y=111x-100.....11y=11x+100x-100......11(y-x)=100(x-1)$$
Since x and y are integers and 11 and 100 are co-prime, x-1 should be a multiple of 11...
Thus x-1 can be 0,11,22,33,44,55,66,77,88,99. The corresponding x values will be 1,12,23,34,45,56,67,78,89,100, so total 10 values.
But 1 and 100 are already the end points of the line, and we are looking at the points in between, so 10-2=8 values

D

chetan2u

"Jahapana tussi great ho!! Tofa kabul karo" - Bollywood Movie "3 Idiots"

Sir, you're great. I don't know how you solve all these questions flawlessly.

Nicely done. Thank you!
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long

Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topic
You are missing on great learning if you don't know what this is: Project SC Butler
Re: A line passes through A(1,1) and B(100,1000). How many other points wi   [#permalink] 23 Nov 2019, 10:39
Display posts from previous: Sort by