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

It is currently 23 Sep 2018, 22:51

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

The system of equations above has how many solutions?

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

Hide Tags

Manager
Manager
avatar
Joined: 11 May 2007
Posts: 103
The system of equations above has how many solutions?  [#permalink]

Show Tags

New post Updated on: 06 Jan 2014, 03:07
3
11
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

56% (00:28) correct 44% (00:26) wrong based on 469 sessions

HideShow timer Statistics

x - y = 3
2x = 2y + 6

The system of equations above has how many solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many

Originally posted by yogachgolf on 15 Nov 2007, 14:21.
Last edited by Bunuel on 06 Jan 2014, 03:07, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: algebra  [#permalink]

Show Tags

New post 07 Jul 2011, 21:41
1
6
ssarkar wrote:
x-y=3
2x=2y+6

The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


Say, the given equations are:

ax + by = c
dx + ey = f

If \(\frac{a}{d} \neq \frac{b}{e}\), then the system of equations has a unique solution.

If \(\frac{a}{d} = \frac{b}{e} \neq \frac{c}{f}\), then the system of equations has no solution.

\(\frac{a}{d} = \frac{b}{e} = \frac{c}{f}\), then the system of equations has infinitely many solutions.

Here, \(\frac{1}{2} = \frac{-1}{-2} = \frac{3}{6}\) so there are infinitely many solutions.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Most Helpful Community Reply
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: System of Equations  [#permalink]

Show Tags

New post 04 Apr 2011, 04:57
4
1
petrifiedbutstanding wrote:
Attachment:
1.JPG

The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


Sol:

\(x-y=3\) is same as \(2x=2y+6\)

\(2x=2y+6\)
Dividing both sides by 2;
\(x=y+3\)
Subtracting y from both sides;
\(x-y=3\)

Thus, we have only one equation:
\(x-y=3\)
This has infinitely many solutions such as:
x=3,y=0
x=100,y=97
x=-100,y=-103
x=0.001, y=-2.999
x=1, y=-2
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

General Discussion
Manager
Manager
avatar
Joined: 08 Nov 2007
Posts: 93
Re: Equations & Solutions  [#permalink]

Show Tags

New post 15 Nov 2007, 14:52
yogachgolf wrote:
yogachgolf wrote:
x-y = 3
2x= 2y+6

The system of equations above has how many
solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


I thought it's A as well. But OA is E?


I see your point ... A + B can be an infinite number of things... I suppose we answered it on the basis that the two solutions given gave us no CERTAIN solutions...

I think the question is a touch ambiguous, but I suppose we could have read it more closely.
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2410
Re: Equations & Solutions  [#permalink]

Show Tags

New post 15 Nov 2007, 15:19
alrussell wrote:
yogachgolf wrote:
yogachgolf wrote:
x-y = 3
2x= 2y+6

The system of equations above has how many solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


I thought it's A as well. But OA is E?


I see your point ... A + B can be an infinite number of things... I suppose we answered it on the basis that the two solutions given gave us no CERTAIN solutions...

I think the question is a touch ambiguous, but I suppose we could have read it more closely.


seems ok but we cannot solve the equations do not provide any value for x and y.
Intern
Intern
avatar
Joined: 06 Sep 2007
Posts: 8
OA is E  [#permalink]

Show Tags

New post Updated on: 16 Nov 2007, 22:42
to satisfy x-y=3

(1,-2)
(2,-1)
......
infinitely

two equation are same.

If we think these based on function, these are same linear.

therefore answer is E

Originally posted by LEE SANG IL on 15 Nov 2007, 23:12.
Last edited by LEE SANG IL on 16 Nov 2007, 22:42, edited 1 time in total.
Manager
Manager
avatar
Joined: 25 Jul 2007
Posts: 107
  [#permalink]

Show Tags

New post 16 Nov 2007, 02:50
Any single linear equation with more than 1 variable in it has infinite solutions (provided no constraints are given).

Edit: I do not see any ambiguity in the question.

The number of solutions for a linear equation is the number of possible values the variables can have so as to satisfy the equation. There are infinite possible values for the variables x & y in the given equation and therefore there are infinite solutions.
Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1451
Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: System of Equations  [#permalink]

Show Tags

New post 04 Apr 2011, 05:50
1
Both the equations are same, so it will have infinitely many solutions.

Answer - E.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 670
Re: algebra  [#permalink]

Show Tags

New post 06 Jul 2011, 19:53
1
given two equations are exactly same.

so different values of x , will yield different values of y.

=> infinite solutions

Answer is E.
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1868
Re: algebra  [#permalink]

Show Tags

New post 07 Jul 2011, 10:47
ssarkar wrote:
x-y=3
2x=2y+6

The system of equations above has how many solutions?
(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


x-y=3 ---------------1
2x=2y+6 ---------------2

Divide equation 2 by 2:
2x/2=(2y+6)/2
x=y+3
x-y=3----------------3

Equation 1 and 3 are equal and thus have infinitely many solutions:


x-y=3
x=5, y=2
x=6, y=3
x=7, y=4

Ans: "E"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 31 May 2011
Posts: 81
Location: India
Concentration: Finance, International Business
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Re: Pls help me to solve this problem.  [#permalink]

Show Tags

New post 31 Jul 2011, 05:19
tracyyahoo wrote:
x-y=3
2x=2y+6

The system of equations above has how many solutions?

a) None
b) Exactly one
c) Exactly two
d) Exactly three
e) Infinitely many

I calculate that x will substracted by the equation, and I think it is b.


Actually both the equations represent the same i.e.

2x = 2y+6
=> x=y+3
=> x-y = 3 same as eq 1

Hence there are Infinitely many solutions to the equations as there are no restrictions

Hence E
Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 123
Re: x-y = 3 2x= 2y+6 The system of equations above has how many  [#permalink]

Show Tags

New post 05 Jan 2014, 23:53
yogachgolf wrote:
x-y = 3
2x= 2y+6

The system of equations above has how many
solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


Equation 1 = x = y + 3
Equation 2 = x = y + 3

Since both the equations represent a single line hence there will be infinitely many solutions for this.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 118
Re: The system of equations above has how many solutions?  [#permalink]

Show Tags

New post 22 Aug 2015, 06:35
yogachgolf wrote:
x - y = 3
2x = 2y + 6

The system of equations above has how many solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


Note that they are not parallel but one and the same. Therefore, x and y take infinitely many values.
Manager
Manager
User avatar
S
Joined: 09 Dec 2015
Posts: 118
Location: India
Concentration: General Management, Operations
Schools: IIMC (A)
GMAT 1: 700 Q49 V36
GPA: 3.5
WE: Engineering (Consumer Products)
Reviews Badge
Re: The system of equations above has how many solutions?  [#permalink]

Show Tags

New post 19 Sep 2016, 09:46
ax + by = c
dx + ey = f

If ad≠bead≠be, then the system of equations has a unique solution.

If ad=be≠cfad=be≠cf, then the system of equations has no solution.

ad=be=cfad=be=cf, then the system of equations has infinitely many solutions.

Very useful for line problems. This question was too easy. E is the right choice.
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 590
Schools: Cambridge'16
Re: The system of equations above has how many solutions?  [#permalink]

Show Tags

New post 21 Sep 2016, 00:30
20 sec approach

x=y+3
2x=2y+6

the second equation is the first one doubled, so it is the same equation

E
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2889
Location: Canada
Re: The system of equations above has how many solutions?  [#permalink]

Show Tags

New post 10 May 2018, 09:19
Top Contributor
yogachgolf wrote:
x - y = 3
2x = 2y + 6

The system of equations above has how many solutions?

(A) None
(B) Exactly one
(C) Exactly two
(D) Exactly three
(E) Infinitely many


One approach is to begin solving the system (using the elimination method) and see what happens.

Given:
x - y = 3
2x = 2y + 6

Take bottom equation and divide both sides by 2 to get:
x - y = 3
x = y + 3

Take bottom equation and subtract y from both sides to get:
x - y = 3
x - y = 3

Now subtract the bottom equation from the top equation to get:
0x + 0y = 0
As we can see, this equation has infinitely many solutions.

Answer: E

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

GMAT Club Bot
Re: The system of equations above has how many solutions? &nbs [#permalink] 10 May 2018, 09:19
Display posts from previous: Sort by

The system of equations above has how many solutions?

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

Events & Promotions

PREV
NEXT


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®.