Last visit was: 03 Nov 2024, 16:40 It is currently 03 Nov 2024, 16:40
Close
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
gmatt1476
Joined: 04 Sep 2017
Last visit: 15 Oct 2024
Posts: 334
Own Kudos:
Given Kudos: 61
Posts: 334
Kudos: 21,957
 [122]
6
Kudos
Add Kudos
115
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
shridhar786
Joined: 31 May 2018
Last visit: 08 Feb 2022
Posts: 325
Own Kudos:
1,628
 [19]
Given Kudos: 132
Location: United States
Concentration: Finance, Marketing
Posts: 325
Kudos: 1,628
 [19]
16
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 02 Nov 2024
Posts: 19,684
Own Kudos:
23,720
 [16]
Given Kudos: 287
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 19,684
Kudos: 23,720
 [16]
13
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
General Discussion
User avatar
Jsound996
User avatar
Current Student
Joined: 19 Jan 2018
Last visit: 11 Sep 2023
Posts: 105
Own Kudos:
118
 [6]
Given Kudos: 3,158
Products:
Posts: 105
Kudos: 118
 [6]
6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
In the rectangular coordinate system, line k passes through the point (n, −1). Is the slope of line k greater than zero?

(1) Line k passes through the origin.
(2) Line k passes through the point (1, n + 2).


DS35210.01

We know that line k passes through (n, -1) so if we graph that, we should get this: (figure 1)
We are trying to figure out if the Slope is positive.

1.) This means line K goes through (0,0).
We have 2 scenarios (Figure 2)
If K>0
If K<0
Insufficient

2.) Refer to Figure 3:
This means we could have a point anywhere on line X = 1 (Pink Line)
Once again, we have 2 scenarios that could happen, where K can be both negative and positive.
Insufficient

1+2 Refer to Figure 4.
K has to be greater than 0 in order to intersect the origin and cross both y = -1 and x= 1.
From statement 2, because (1, n+2), you can't have a negative slope that also intersects the origin.
That means both 1 and 2 are enough.

C is the Answer!
Attachments

File comment: Figure 4. Both 1 + 2
gmat coordinate.png
gmat coordinate.png [ 19.58 KiB | Viewed 18885 times ]

File comment: Figure 3: From Statement 2
gmat coordinate.png
gmat coordinate.png [ 24.94 KiB | Viewed 18839 times ]

File comment: Figure 2: From Statement 1
gmat coordinate.png
gmat coordinate.png [ 23.96 KiB | Viewed 18800 times ]

File comment: Figure 1: Beginning Info
gmat coordinate.png
gmat coordinate.png [ 14.84 KiB | Viewed 18694 times ]

avatar
Akp880
Joined: 24 Mar 2019
Last visit: 08 Nov 2021
Posts: 193
Own Kudos:
134
 [3]
Given Kudos: 196
Location: India
Concentration: Marketing, Operations
Schools: IIMA PGPX'23 IIM
WE:Operations (Aerospace and Defense)
Schools: IIMA PGPX'23 IIM
Posts: 193
Kudos: 134
 [3]
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In the rectangular coordinate system, line k passes through the point (n, −1). Is the slope of line k greater than zero?

(1) Line k passes through the origin.
(2) Line k passes through the point (1, n + 2).


Easiest Explanation:

As per S1-

line k passes through (0,0) and (n,-1)
Hence equation of line will be
y=-nx (with slope=-n)

We can't comment whether slope is positive or negative as value of 'n'is still unknown.Hence insufficient.

As per S2-

line k passes through (1,n+2) and (n,-1)


Similar to S1 ,here again We can't comment whether slope is positive or negative as value of 'n'is still unknown.Hence insufficient.

Now combining both S1& S2

You have points (0,0) (n,-1) from which line k passes

y=-nx is the equation
(slope=-n)

In S2 already given that line passes through (1,n+2)

Put this in above derived line equation y= -nx,you will get-

n+2=-n*1
n=-1

Hence slope(-n) of line k= 1 (slope>0)

C is the correct answer.

Award kudos if you like the explanation.?

Regards,
Atul Pandey

Posted from my mobile device
avatar
AK1307
avatar
Current Student
Joined: 02 Jan 2019
Last visit: 10 May 2021
Posts: 17
Own Kudos:
Given Kudos: 272
Schools: LBS '23 (A)
Schools: LBS '23 (A)
Posts: 17
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel can you please help with a solution? I can't understand how to combine statement 1 and 2. Thanks.
User avatar
BrentGMATPrepNow
User avatar
GMAT Club Legend
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,790
Own Kudos:
31,803
 [2]
Given Kudos: 799
Location: Canada
Expert reply
Posts: 6,790
Kudos: 31,803
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476
In the rectangular coordinate system, line k passes through the point (n, −1). Is the slope of line k greater than zero?

(1) Line k passes through the origin.
(2) Line k passes through the point (1, n + 2).

DS35210.01
Given: Line k passes through the point (n, −1)

Target question: Is the slope of line k greater than zero?

Key concept: If points \((a, b)\) and \((c, d)\) both lie on a line, then the slope of that line \(= \frac{d-b}{c-a}\)

Statement 1: Line k passes through the origin.
In other words, line k passes through the point \((0,0)\)
Since we also know line k passes through the point \((n, −1)\), the slope of line k \(= \frac{(-1)-0}{n-0}=\frac{-1}{n}\)
So, if \(n = 1\), the slope of line k \(= \frac{-1}{1} = -1\), which means the answer to the target question is NO.
Conversely, if \(n = -1\), the slope of line k \(= \frac{-1}{-1} = 1\), which means the answer to the target question is YES.
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line k passes through the point (1, n + 2).
Since we also know line k passes through the point \((n, −1)\), the slope of line k \(= \frac{(n+2)-(-1)}{1-n}=\frac{n+3}{1-n}\)
So, if \(n = 2\), the slope of line k \(= \frac{2+3}{1-2} = -5\), which means the answer to the target question is NO.
Conversely, if \(n = 0\), the slope of line k \(= \frac{0+3}{1-0} = 3\), which means the answer to the target question is YES.
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Key concept: The slope between any two points on a line will always be the same.
The following three points all lie on line k: (n, −1), (0, 0) and (1, n + 2)
This means that slope between (n, −1) and (0, 0) = the slope between (0, 0) and (1, n + 2)

In other words: \(\frac{n - 0}{(-1) - 0} = \frac{(n+2)-0}{1-0}\)

Simplify: \(\frac{n}{-1} = \frac{n+2}{1}\)

Cross multiply: (-1)(n+2) = (n)(1)
Expand: -n - 2 = n
Solve: n = -1
Now that we know the value of n, we COULD perform all of the calculations necessary to determine the slope of line k (and thus answer the target question).
Since we could answer the target question with certainty, the combined statements are sufficient.

Answer: C
User avatar
CrackverbalGMAT
User avatar
GMAT Club Legend
Joined: 03 Oct 2013
Last visit: 03 Nov 2024
Posts: 4,887
Own Kudos:
8,029
 [1]
Given Kudos: 223
Affiliations: CrackVerbal
Location: India
Posts: 4,887
Kudos: 8,029
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In the rectangular coordinate system, line k passes through the point (n, −1). Is the slope of line k greater than zero?

(1) Line k passes through the origin.
(2) Line k passes through the point (1, n + 2).

This question clearly tests the understanding of the slope of the line.

If a line passes through the points (x1,y1) and (x2,y2) , then the slope of the line is \(\frac{(y2-y1)}{(x2-x1)}\).

Also, a few traps are hidden in the question. Here it's given that line k passes through the point (n,-1). Remember, 'n' could be any real number i.e positive, negative, or zero. We cannot assume that n is a positive value.

We are asked to find if the slope of line K is positive or not.

(1) Line k passes through the origin.

It's already given in the question that the line passes through (n,-1). From St1, it is given the line passes through origin i.e (0,0).

Since the line passes through (0,0)and (n,-1), the slope of line k =\( \frac{(y2-y1)}{(x2-x1)}\) = \(\frac{(-1-0)}{(n-0)}\) = \(\frac{-1}{n}\)

Is the slope of line k is positive? It depends on the value of n.

If n is a negative value, the slope of the line is positive and if n is a positive value, the slope will be negative. Since we don't have a definite YES/ NO to the Question stem, Statement 1 alone is not sufficient.

(2) Line k passes through the point (1, n + 2).

We know about the 2 points the line k passes through i.e (n,-1) and (1, n + 2)

Slope of the line k = \(\frac{(n+2 --1)}{(1-n)}\)= \(\frac{(n+3)}{(1-n)}\).
Here 'n' will determine the sign of the slope in this case.

For example: n= -1, Slope = -1+3/1--1 = 2/2 = 1 ==> Slope is positive
n=2, slope = 2+3/1-2 = 5/-1 = -5 ==> Slope is negative

Based on the value of n, the slope of the line k could be positive or negative. Hence Statement 2 alone is not sufficient.

The next step is to combine both statements.

We figured out that the slope of line k from St 1 is \(\frac{ -1}{n} \). From statement 2, we found that the slope of the same line is \( \frac{(n+3)}{(1-n)}\)

Since both the slopes represent the same line k, we can equate both.

\(\frac{ -1}{n} \) = \( \frac{(n+3)}{(1-n)}\)

n-1 = \(n^2\) + 3n

\(n^2\) + 2n + 1 = 0

\((n+1)^2\) = 0

n+1 =0 ===> n =-1
On solving, we found the value of n as -1.

Therefore , the slope of line k = \(\frac{ -1}{n} \) = -1/-1 = 1 (positive)

Is the slope of line k greater than zero? YES

We are getting a definite answer to the Question stem by combining both statements. Hence,Option C is the correct answer.

Thanks,
Clifin J Francis,
GMAT Mentor
User avatar
Iamcomingarv
Joined: 03 Dec 2020
Last visit: 14 Feb 2024
Posts: 2
Given Kudos: 205
GMAT 1: 620 Q43 V34
GMAT 2: 690 Q42 V41
GMAT 1: 620 Q43 V34
GMAT 2: 690 Q42 V41
Posts: 2
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi How is (n+1)^2 = 0 , becoming N+1=0. Should we not take squareroot and make them absolute value? CrackverbalGMAT
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,346
Own Kudos:
Posts: 35,346
Kudos: 902
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Math Expert
96505 posts