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

It is currently 19 Nov 2018, 21:49

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

If a and b are positive numbers, what are the coordinates of

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

Hide Tags

Director
Director
avatar
Joined: 17 Sep 2005
Posts: 837
If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post Updated on: 27 Jul 2014, 14:57
3
13
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

81% (00:32) correct 19% (00:50) wrong based on 385 sessions

HideShow timer Statistics

If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b)
(2) The coordinates of D are (1-a, b)

Originally posted by b14kumar on 09 Sep 2007, 14:56.
Last edited by Bunuel on 27 Jul 2014, 14:57, edited 1 time in total.
Edited the question and added the OA.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50672
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 18 Apr 2010, 04:40
3
5
sandranjeim wrote:
If a and b are positive numbers, what are the coordinates pf the midpoint of line segment CD in the xy plane?


1) C (a, 1 - b)

2) D (1 - a, b)


OA = C


Coordinates of the midpoint \(M (x_m,y_m)\) of the line segment AB, (\(A (x_1,y_1)\) and \(B (x_2,y_2)\)) are \(x_m=\frac{x_1+x_2}{2}\) and \(y_m=\frac{y_1+y_2}{2}\)

(1) C (a, 1 - b). Not sufficient.

(2) D (1 - a, b). Not sufficient.

(1)+(2) \(M (x_m,y_m)=M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=M(\frac{a+1-a}{2},\frac{1-b+b}{2})=M(\frac{1}{2},\frac{1}{2})\). Sufficient.

Answer: C.

sandranjeim wrote:
So we find the coordinates of the midpoint in terms of a and b right?

Thanks


If it were so, then answer would be E. In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1055
Location: London
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 09 Sep 2007, 16:39
1
1
b14kumar wrote:
If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in xy plane?

1. The coordinates of C are (a,1-b)
2. The coordinates of D are (1-a,b)

- Brajesh


to find the mid point u just take the mean of x1 and x2 and mean of y1 and y2, that leaves us with mid point coordinates of x=1/2 y=1/2
to have it we need to use both statements
C
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 4851
Location: Singapore
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 09 Sep 2007, 17:26
St1 and St2 by themselves are insufficient.

Using both, the midpoint is ((a+1-a/2), (1-b+b)/2) -> (1/2, 1/2). Sufficient.

Ans C
Senior Manager
Senior Manager
User avatar
Joined: 27 Aug 2007
Posts: 250
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 10 Sep 2007, 05:55
It is necessary to add values of X and Y than divide by 2

Ans: C
Manager
Manager
avatar
Joined: 29 Aug 2007
Posts: 109
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 10 Sep 2007, 06:07
C indeed

To find the mid point , you need co-ordinates of C and D

The forumulae to calculate Mid POint, given 2 points

(X1, Y1) and ( X2, Y2) = (X1+X2)/2 , (Y1+y2)/2
Intern
Intern
avatar
Joined: 11 Apr 2010
Posts: 16
If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 17 Apr 2010, 02:21
If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b)
(2) The coordinates of D are (1-a, b)
Manager
Manager
avatar
Joined: 07 May 2008
Posts: 72
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post Updated on: 17 Apr 2010, 03:34
It's pretty straightforward, knowing the coordinates of C and D the midpoint of line segment CD can be found out. Option C.

Do you any specific doubt in this question?

PS: Would be good if you can use the spoiler option for the OA :) thanks

Originally posted by sh00nya on 17 Apr 2010, 03:25.
Last edited by sh00nya on 17 Apr 2010, 03:34, edited 1 time in total.
Intern
Intern
avatar
Joined: 11 Apr 2010
Posts: 16
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 17 Apr 2010, 03:28
So we find the coordinates of the midpoint in terms of a and b right?

Thanks
Manager
Manager
avatar
Joined: 07 May 2008
Posts: 72
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 17 Apr 2010, 03:37
1
Yes you find the coordinates of the midpoint but if you look closely your answer will be a definite value and not in terms of a and b.
Manager
Manager
avatar
Joined: 27 Dec 2009
Posts: 139
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 17 Apr 2010, 04:02
coordinates of the midpoint will be (1/2,1/2). both statements will be required to find out the answer.
Intern
Intern
avatar
Joined: 07 Sep 2010
Posts: 16
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 05 Nov 2010, 03:15
Point to be noted

"In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc. "

Thanks Bunuel!
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6527
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 30 Nov 2015, 09:48
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?

(1) The coordinates of C are (a, 1-b)
(2) The coordinates of D are (1-a, b)

There are 2 variables (x,y) and 2 equations are given by the 2 conditions, so there is high chance (C) will be the answer.
Looking at the conditions together,
midpoint=(a+1-a/2, 1-b+b/2)=(1/2,1/2)
This is unique and sufficient,
so the answer becomes (C).

For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
User avatar
Joined: 17 Jun 2015
Posts: 216
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT ToolKit User
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 17 Dec 2015, 09:40
In order to find the midpoint of a line segment, both the end points of a line are needed. What further solves the question is the victory over laziness before one selects E due to presence of variables from the two statements; they get cancelled and the midpoint is (0.5,0.5)

Also, I applied a learning from a previous question. Positive numbers and Positive Integers are different. While we tend to know the difference, remembering the same every time we see integers and numbers pop up on the screen is important. Be careful folks!
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Director
Director
User avatar
G
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 669
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post Updated on: 05 Aug 2016, 06:37
1
Top Contributor
Bunuel wrote:
In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc.


I know what you mean (solving in terms of a variable is rarely sufficient), but we have to be careful--this is not always true. If the question being asked is a yes/no question ("is x positive?" or "is y less than 0?"), then the statements could be sufficient even if we can get multiple values for x or y, so long as they always result in the same answer to the question being asked (either "always yes", or "always no").

There are some cases on DS where both solving in terms of a variable, and getting multiple numerical values, can be sufficient.

For example, if the question asks, "is x > 5?" and statement #1 leads me to the conclusion that x = 10, 15, or 20, then I can conclude "sufficient," even though I found multiple solutions for x, because the answer to the question being asked is always yes.

This can also be true when solving in terms of a variable. If the question asked "is x positive?" and I am able to solve for x as \((y^2+1)\), then I know that regardless of the value of y, x must be positive. Hence it would be sufficient.
_________________

Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club.)

...or find me on Reddit: http://www.reddit.com/r/GMATpreparation


Originally posted by mcelroytutoring on 04 Aug 2016, 15:48.
Last edited by mcelroytutoring on 05 Aug 2016, 06:37, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50672
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 05 Aug 2016, 03:47
mcelroytutoring wrote:
Bunuel wrote:
In DS questions statement(s) is (are) sufficient only if we can get single numerical value of variable, midpoint coordinates, etc.


I know what you mean (solving in terms of a variable is rarely sufficient), but we have to be careful--this is not always true. If the question being asked is a yes/no question ("is x positive?" or "is y less than 0?"), then the statements could be sufficient even if we can get multiple values for x or y, so long as they always result in the same answer to the question being asked (either "always yes", or "always no").

There are some cases on DS where both solving in terms of a variable, and getting multiple numerical values, can be sufficient.

For example, if the question asks, "is x > 5?" and statement #1 leads me to the conclusion that x = 10, 15, or 20, then I can conclude "sufficient," even though I found multiple solutions for x, because the answer to the question being asked is always yes.

This can also be true when solving in terms of a variable. If the question asked "is x positive?" and I am able to solve for x as \((y^2+1)\), then I know that regardless of the value of y, x must be positive. Hence it would be sufficient.


Yes. This is a value question so I think it's clear what I meant: When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8846
Premium Member
Re: If a and b are positive numbers, what are the coordinates of  [#permalink]

Show Tags

New post 27 Oct 2018, 06:31
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If a and b are positive numbers, what are the coordinates of &nbs [#permalink] 27 Oct 2018, 06:31
Display posts from previous: Sort by

If a and b are positive numbers, what are the coordinates of

  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®.