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

It is currently 19 Mar 2019, 14:28

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

Question of the Week - 39 (In the x-y plane, PQ is a straight line)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2709
Question of the Week - 39 (In the x-y plane, PQ is a straight line)  [#permalink]

Show Tags

New post 07 Mar 2019, 23:04
1
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

26% (02:01) correct 74% (01:44) wrong based on 43 sessions

HideShow timer Statistics

e-GMAT Question of the Week #39

In the x-y plane, PQ is a straight line. The coordinate of point P is (a, b), where a > 0. Does point Q lie in the third quadrant?

    Statement 1: The origin bisects PQ in 1: 1 ratio.
    Statement 2: The slope m of the line PQ is non-negative.


Image

_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
B
Joined: 15 Dec 2018
Posts: 30
CAT Tests
Re: Question of the Week - 39 (In the x-y plane, PQ is a straight line)  [#permalink]

Show Tags

New post 07 Mar 2019, 23:18
IMO E

Both statements do not indicate anything. It could also be that the line can be just the X axis

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 11 Dec 2018
Posts: 10
Re: Question of the Week - 39 (In the x-y plane, PQ is a straight line)  [#permalink]

Show Tags

New post 08 Mar 2019, 03:46
IMO C

We know that P has a>0, so point P lie or in the first quadrant or in the fourth quadrant.

1) statment 1 not sufficient, because it tells us that the origin bisects the segment PQ in two equal segments. But Point Q can lie either in the second or in the third quadrant;

2) statment 2 not sufficent. We can only say that point Q cannot be in the second quadrant.

1+2) sufficient.

from 1: origin bisects PQ with ratio 1:1
from 2: the slope isn't negative, so Q can't be in the second quadrant.

IMO P lie in the first quadrant and Q in the third.

Hope my answer is correct.
Intern
Intern
avatar
B
Joined: 22 Oct 2017
Posts: 19
Re: Question of the Week - 39 (In the x-y plane, PQ is a straight line)  [#permalink]

Show Tags

New post 10 Mar 2019, 07:11
EgmatQuantExpert wrote:
e-GMAT Question of the Week #39

In the x-y plane, PQ is a straight line. The coordinate of point P is (a, b), where a > 0. Does point Q lie in the third quadrant?

    Statement 1: The origin bisects PQ in 1: 1 ratio.
    Statement 2: The slope m of the line PQ is non-negative.


Image


1) Only tells us that x-axis will cut the line in 2, but still don't know anything about P and Q positions
2) Only tells us that the line is either horizontal or increasing

1)+2) still ambiguous about which one between P or Q is at the bottom or top of x-axis
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2709
Re: Question of the Week - 39 (In the x-y plane, PQ is a straight line)  [#permalink]

Show Tags

New post 13 Mar 2019, 01:19

Solution



Given:


    • PQ is a straight line.
    • Coordinate of point P is (a, b).
    • a > 0.

To find:

    • In which quadrant Q lies.

Let us assume the coordinate of point Q is (x, y)
To find the quadrant of point Q, we need to find the exact value of the coordinate of point Q.

Analysing statement 1:

The origin bisects PQ in 1: 1 ratio.
Hence, 0 = \(\frac{a + x}{2}\)and 0= \(\frac{b + y}{2}\)
• Therefore. x= -a and y= -b
• However, we still don’t know the exact value of x and y.

Hence, statement 1 is not sufficient to answer the question.

Analysing statement 2:

The slope m of the line PQ is non-negative.
Slope m of a line is \(\frac{y2 – y1}{x2-x1}\).
Hence, m= \(\frac{y-b}{x-a}\)
However, we still don’t have any information about the values of x and y.
Hence, statement 2 is not sufficient to answer the question.

Combining both the statements together:

From statement 1:
• x= -a and y= -b
From statement 2:
• m= \(\frac{y-b}{x-a}\)
We cannot find the value of x and y even after combining both the statements together.
Hence, option E is the correct answer.

Correct answer: option E.
_________________








Register for free sessions
Number Properties:- Get 5 free video lessons, 50 practice questions | Algebra:-Get 4 free video lessons, 40 practice questions
Quant Workshop:- Get 100 practice questions | Free Strategy Session:- Key strategy to score 760

Success Stories
Q38 to Q50- Interview call form Wharton | Q35 to Q50 | More Success Stories

Ace GMAT
Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
B
Joined: 21 Apr 2018
Posts: 8
CAT Tests
Re: Question of the Week - 39 (In the x-y plane, PQ is a straight line)  [#permalink]

Show Tags

New post 15 Mar 2019, 04:37
EgmatQuantExpert Bunuel
EgmatQuantExpert wrote:

Solution



Given:


    • PQ is a straight line.
    • Coordinate of point P is (a, b).
    • a > 0.

To find:

    • In which quadrant Q lies.

Let us assume the coordinate of point Q is (x, y)
To find the quadrant of point Q, we need to find the exact value of the coordinate of point Q.

Analysing statement 1:

The origin bisects PQ in 1: 1 ratio.
Hence, 0 = \(\frac{a + x}{2}\)and 0= \(\frac{b + y}{2}\)
• Therefore. x= -a and y= -b
• However, we still don’t know the exact value of x and y.

Hence, statement 1 is not sufficient to answer the question.

Analysing statement 2:

The slope m of the line PQ is non-negative.
Slope m of a line is \(\frac{y2 – y1}{x2-x1}\).
Hence, m= \(\frac{y-b}{x-a}\)
However, we still don’t have any information about the values of x and y.
Hence, statement 2 is not sufficient to answer the question.

Combining both the statements together:

From statement 1:
• x= -a and y= -b
From statement 2:
• m= \(\frac{y-b}{x-a}\)
We cannot find the value of x and y even after combining both the statements together.
Hence, option E is the correct answer.


Correct answer: option E.




Can you let me know where I have gone wrong in my reasoning.

I thought C is the answer and my reasoning is given below.

Given a straight line PQ, with co-ordinates of P as (a,b) where a > 0

=> P is either on the 1st quadrant or on x axis or on the 4rth quadrant. Any pattern of line with positive, negative, infinite or zero slope can be drawn using points in these quadrants.

STATEMENT 1 : Origin bisects the line in the ratio 1 : 1

From the set of lines that could possibly be the answer we can eliminate all lines that doesnt pass through the origin.

As line passes through origin and a >0, line y axis and all lines with slope infinity (|| to y axis) can be eliminated.

If point P is in quadrant 1 it has to pass though quadrant 3 to satisfy this condition. This implies that the line will have a positive slope

If b is 0, then PQ is part of the x axis itself, and the point Q will be (-a,0) => Slope is 0 here

If the point P lies in 4rth quadrant, then Q must lie in the 2nd quadrant so that the origin bisects PQ. Here PQ will have negative slope.

HENCE STATEMENT 1 is not enough to answer the question

STATEMENT 2 : slope is non negative.

0 is neither positive nor negative. So I believe this statement essentially means slope is positive. We cannot narrow down the options here. The point Q could be in first quadrant itself

However, combining the 2 we can conclude that Q should pass through origin and should be in third quadrant. Hence both together can answer the question
GMAT Club Bot
Re: Question of the Week - 39 (In the x-y plane, PQ is a straight line)   [#permalink] 15 Mar 2019, 04:37
Display posts from previous: Sort by

Question of the Week - 39 (In the x-y plane, PQ is a straight line)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.