Last visit was: 03 Aug 2024, 06:25 It is currently 03 Aug 2024, 06:25
Toolkit
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Request Expert Reply

# In the rectangular coordinate system shown above, does the

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 24 Jun 2009
Posts: 31
Own Kudos [?]: 666 [256]
Given Kudos: 2
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94776
Own Kudos [?]: 646249 [416]
Given Kudos: 86843
Manager
Joined: 22 Dec 2009
Posts: 179
Own Kudos [?]: 957 [28]
Given Kudos: 48
General Discussion
Retired Moderator
Joined: 02 Sep 2010
Posts: 613
Own Kudos [?]: 2973 [0]
Given Kudos: 25
Location: London
Q51  V41
Re: In the rectangular coordinate system shown above, does the [#permalink]
(1) Slope is -1/6.
So line is y = -x/6 + c.
Let x=-6+6c-6|c|. Notice this value of x is negative for all choices of c. If c<0, then x becomes -6+12c, if c=0, then x becomes -6, if c>0, then x becomes -6.
At this point, the value of y is 1+|c| which is always positive.
Showing that the line will always pass thru the 2nd quadrant (As pointed out earlier this is true for all lines with negative slope)
So (1) is sufficient

(2) Y-Int is -6
Consider the line x=-6 (does not pass thru quadrant II)
But we know if the line had negative slope it wud pass thru second qudrant, Eg. y=-x-6
Not sufficient

A alone is enough
Hence, y-int is not enough to say anything
VP
Joined: 02 Jul 2012
Posts: 1001
Own Kudos [?]: 3166 [6]
Given Kudos: 116
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE:Engineering (Energy and Utilities)
Re: In the rectangular coordinate system shown above, does the [#permalink]
4
Kudos
2
Bookmarks
SreeViji wrote:
Does line k intersect quadrant II?
a. Slope of k is -1/6
b. Y intercept of k is -6

We are asked if the line passes through the top left quadrant.

1)Slope is negative. A line with a negative slope will definitely pass through the 2nd and 4th quadrants. You can think about it graphically. Unless the line is perfectly vertical, perfectly horizontal or slanting upwards to the right, it will definitely pass through the 2nd and 4th quadrants. Sufficient.

2)As shown below, the line could be one like the green or one like the red. We cant deduce anything from this. Insufficient.

Answer is A
Attachments

Untitled.png [ 5.78 KiB | Viewed 138812 times ]

Manager
Joined: 23 Jan 2013
Posts: 99
Own Kudos [?]: 172 [0]
Given Kudos: 41
Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
WE:Information Technology (Computer Software)
Re: In the rectangular coordinate system shown above, does the [#permalink]
I am a little confused on this one ...
Here the slope will be negative and line will not pass through Y axis
Attachments

File comment: Screenshot

Screenshot-2.png [ 6.16 KiB | Viewed 125386 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 94776
Own Kudos [?]: 646249 [1]
Given Kudos: 86843
Re: In the rectangular coordinate system shown above, does the [#permalink]
1
Kudos
Expert Reply
shelrod007 wrote:
I am a little confused on this one ...
Here the slope will be negative and line will not pass through Y axis

Line extends in both directions without end (infinitely). What you've drawn there is a line segment.
Director
Joined: 26 Oct 2016
Posts: 506
Own Kudos [?]: 3412 [2]
Given Kudos: 877
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE:Education (Education)
Re: In the rectangular coordinate system shown above, does the [#permalink]
2
Kudos
Knowing below rules first and attacking problem will save lot of time.

1) If a line has a positive slope, it definitely goes through sectors 1 and 3.

2) If a line has a negative slope, it definitely goes through sectors 2 and 4.

As an aside:

If a line is parallel to the x or y axis, it will go through exactly 2 different sectors.

(Except, of course, for the lines x=0 and y=0, which are the axes.)

If a line is not parallel to the x or y axis it will:

a) go through exactly 2 sectors if it passes through the origin; or

b) go through exactly 3 sectors if it does not pass through the origin.

Now, coming back to statements :-

1) The slope of the line is -(1/6)

You could use trial and error to see that a line with this slope will, eventually, go through sector 2.
Sufficient.

(2) the y-int is -6

This tells us that the line passes through (0,-6). We could draw a horizontal line through that point which never touches quadrant 2. We can also draw a diagonal line that does go through quadrant 2. Since the answer is "maybe", (2) is insufficient.
Hence A.
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30924 [8]
Given Kudos: 799
Location: Canada
Re: In the rectangular coordinate system shown above, does the [#permalink]
5
Kudos
3
Bookmarks
Expert Reply
Top Contributor
shanewyatt wrote:

In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II?

(1) The slope of k is -1/6
(2) The y-intercept of k is -6

Attachment:
GMAT_DS_PREP_100.png

Target question: Does line k intersect quadrant II?

Statement 1: The slope of k is -1/6
Here are a few lines with slope -1/6

KEY CONCEPT: As we travel from right to left along a line with slope -1/6, we keep moving up.
So, at some point, the line will surely pass through quadrant II
So, the answer to the target question is YES, line k DOES intersect quadrant II
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The y-intercept of k is -6
There are several possible cases that satisfy statement 2. Here are two:
Case a: The line is horizontal (i.e., has slope zero)

In this case, the answer to the target question is NO, line k does NOT intersect quadrant II

Case b: The line looks like this

In this case, the answer to the target question is YES, line k DOES intersect quadrant II

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Senior Manager
Joined: 05 Feb 2018
Posts: 308
Own Kudos [?]: 831 [1]
Given Kudos: 325
Re: In the rectangular coordinate system shown above, does the [#permalink]
1
Bookmarks
To visualize:

Bunuel wrote:
1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positives, line intersects the quadrant I too, if negative quadrant III.

y=-1x, x int =0, y int =0
y=-1x+3, x int =3, y int =3
y=-1x-3, x int =-3, y int =-3

Bunuel wrote:
2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefor if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

y=1x, x int =0, y int =0
y=1x+2, x int =-2, y int =2
y=1x-2, x int =2, y int =-2

Bunuel wrote:
3. Every line (but the one crosses origin or parallel to X or Y axis) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants.

4. The line with slope 0 is parallel to X-axis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative.

y=0x+2, x int =none, y int =2
y=0x-2, x int =none, y int =-2
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4914
Own Kudos [?]: 7830 [0]
Given Kudos: 221
Location: India
Re: In the rectangular coordinate system shown above, does the [#permalink]
Top Contributor
In the rectangular coordinate system shown above, does the line k (not shown) intersect quadrant II?

(1) The slope of k is -1/6
When a slope of a line is negative that means the line is decreasing, and goes downwards from left to right.
So when we extend the line, it will definitely pass through quadrant II and IV.
Hence Statement 1 alone is sufficient.

(2) The y-intercept of k is -6

The y-intercept is the point where the line intersects the y-axis. Here the y intercept of the line is (0,-6).

Case 1:
At (0,-6), we can draw a line parallel to X axis (Slope is 0) and passing through quadrant III and IV. In this case, line doesn't intersect quadrant II

Case 2 :Also we can draw a line passing through (0,-6) with a negative slope passing through the quadrants II,III and IV.
Here, the line will pass through quadrant II

Case 3:
Similarly a line with positive slope can be drawn at the same point passing through the quadrants I,III and IV. Here the line will not intersect quadrant II

Hence we cannot confirm whether the line k intersect quadrant II or not as both cases are possible .

Statement 2 alone is insufficient.

Option A is the answer

Hope this helps,
Clifin J Francis,
GMAT SME
Non-Human User
Joined: 09 Sep 2013
Posts: 34222
Own Kudos [?]: 857 [0]
Given Kudos: 0
Re: In the rectangular coordinate system shown above, does the [#permalink]
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: In the rectangular coordinate system shown above, does the [#permalink]
Moderator:
Math Expert
94776 posts