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# How many solution set exist for the following set of equatio

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Intern
Joined: 05 Nov 2013
Posts: 12

Kudos [?]: 28 [0], given: 4

Schools: Cambridge, HEC '15
How many solution set exist for the following set of equatio [#permalink]

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11 Jan 2014, 20:42
Hi,

I am pasting two similar looking questions in this post however the answers seem to be very different for both

Please explain the solution for both and is there an easy technique to handle such questions? How are both questions different from each other?

Question 1:

How many solution set exist for the following set of equations ?

(1) 4x + 6y = 20
(2) 6x + 9y = 30

Ans provided in the book is: C

Question 2:

What is the value of x ?
(1) 4x + 6y = 20
(2) 6x + 9y = 50

Ans provided in the book is E

Many thanks,

Amita

Kudos [?]: 28 [0], given: 4

Intern
Joined: 22 Jan 2013
Posts: 7

Kudos [?]: 1 [0], given: 25

Re: How many solution set exist for the following set of equatio [#permalink]

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12 Jan 2014, 12:33
May be these questions are not complete

1) 4x + 6y = 20
2) 6x + 9y = 30 == 3/2(4x + 6y = 20)

In Question(1)
the only possible answers can be
1) infinite many solutions
2) no solution
3) one solution
combining two equations we get only one answer as infinite many solutions
Therefore C

(1) 4x + 6y = 20
(2) 6x + 9y = 50 ;; 3/2(4x + 6y) =6x+ 9y
In question(2) we need to solve for x and after solving the equations
statement 1 gives infinite values
statement 2 gives infinite values
combined : we get no values of x as lines are parallel

Therefore E

Kudos [?]: 1 [0], given: 25

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17359 [0], given: 232

Location: Pune, India
Re: How many solution set exist for the following set of equatio [#permalink]

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13 Jan 2014, 22:53
amitasagar23 wrote:
Hi,

I am pasting two similar looking questions in this post however the answers seem to be very different for both

Please explain the solution for both and is there an easy technique to handle such questions? How are both questions different from each other?

Question 1:

How many solution set exist for the following set of equations ?

(1) 4x + 6y = 20
(2) 6x + 9y = 30

Ans provided in the book is: C

Question 2:

What is the value of x ?
(1) 4x + 6y = 20
(2) 6x + 9y = 50

Ans provided in the book is E

Many thanks,

Amita

These questions are not appropriate GMAT questions.

In question 1, using both statements, we get that x and y can take infinite values (which is what we infer from each statement alone too). Both the statements actually represent the same line.
(1) 2x + 3y = 10
(2) 2x + 3y = 10
When the question asks for number of solution sets, it is looking for a unique defined answer. The answer you get is 'infinite' which is not defined.

In question 2, statements 1 and 2 conflict with each other.
(1) 2x + 3y = 10
(2) 2x + 3y = 50/3
These two equations represent two parallel lines. There is no common x. So what is the value of x is not a valid question.

For details on equations and lines, check here: http://www.veritasprep.com/blog/2011/08 ... nd-points/
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Kudos [?]: 17359 [0], given: 232

Re: How many solution set exist for the following set of equatio   [#permalink] 13 Jan 2014, 22:53
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