GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Aug 2019, 13:53

### 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

# Line M has x-intercept as -40 and y-intercept as 70. If the line M

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Nov 2016
Posts: 4
Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

### Show Tags

04 Mar 2017, 02:47
1
12
00:00

Difficulty:

85% (hard)

Question Stats:

51% (02:28) correct 49% (02:30) wrong based on 81 sessions

### HideShow timer Statistics

Line M has x intercept as -40 and y intercept as 70. If the line M cuts x-axis at point P and y-axis at point Q,then how many points on line segment PQ have both x coordinate and y coordinate as integers?

a)40
b)70
c)10
d)11
e)30
Math Expert
Joined: 02 Sep 2009
Posts: 57025
Re: Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

### Show Tags

04 Mar 2017, 04:00
4
4
Bhalla wrote:
Line M has x intercept as -40 and y intercept as 70. If the line M cuts x-axis at point P and y-axis at point Q,then how many points on line segment PQ have both x coordinate and y coordinate as integers?

a)40
b)70
c)10
d)11
e)30

The equation of a straight line whose x and y intercepts are a and b, respectively, is: $$\frac{x}{a}+\frac{y}{b}=1$$ (check for more here: https://gmatclub.com/forum/math-coordin ... 87652.html)

Thus, the equation of line M is -x/40 + y/70 = 1.

y = 7x/4 + 70. For y to be an integer 7x/4 must be an integer, thus x must be a multiple of 4, from 0 to -40 inclusive. There are 11 multiples of 4 in this range: 0, -4, -8, -12, -16, -20, -24, -28, -32, -36, and -40.

Attachment:

Untitled.png [ 11.36 KiB | Viewed 4411 times ]

_________________
##### General Discussion
Manager
Joined: 02 Aug 2015
Posts: 153
Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

### Show Tags

Updated on: 05 Mar 2017, 07:34
1
Bhalla wrote:
Line M has x intercept as -40 and y intercept as 70. If the line M cuts x-axis at point P and y-axis at point Q,then how many points on line segment PQ have both x coordinate and y coordinate as integers?

a)40
b)70
c)10
d)11
e)30

We know two points through which the line PQ passes through: (-40,0) and (0,70).

Equation of a line passing through two points can be found using the formula (y-y1)/(y2-y1) = (x-x1)/(x2-x1).

Equation of the line PQ is 4y-7x=280.

y=7(40+x)/4.

For y to be an integer (40+x)/4 should be an integer. So 40+x should be divisible by 4. Here x can vary from -40 to 0. All multiples of 4 between 0 and -40 will satisfy the condition. So there are 11 such numbers, including 0.

Hence D.

Cheers!

Originally posted by Diwakar003 on 04 Mar 2017, 09:07.
Last edited by Diwakar003 on 05 Mar 2017, 07:34, edited 1 time in total.
Non-Human User
Joined: 09 Sep 2013
Posts: 12005
Re: Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

### Show Tags

04 Aug 2019, 13:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Line M has x-intercept as -40 and y-intercept as 70. If the line M   [#permalink] 04 Aug 2019, 13:35
Display posts from previous: Sort by