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

 It is currently 24 Sep 2018, 04:37

### 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

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

# How to tell when an equation with two variables has only one solution?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Aug 2017
Posts: 7
How to tell when an equation with two variables has only one solution?  [#permalink]

### Show Tags

05 Nov 2017, 18:45
I have notice that it is often the case on DS case questions that the test writers will give you an equation with two variables as one condition. The other condition will give you one of the variables and you end up falling into the "C trap". Does anyone know if there is a way to tell that an equation with two variables has only one unique solution? If so, is there to quickly generate the solution besides simple guess and test? Thanks in advance.
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 931
Location: India
GPA: 3.64
Re: How to tell when an equation with two variables has only one solution?  [#permalink]

### Show Tags

06 Nov 2017, 08:27
candyandy wrote:
I have notice that it is often the case on DS case questions that the test writers will give you an equation with two variables as one condition. The other condition will give you one of the variables and you end up falling into the "C trap". Does anyone know if there is a way to tell that an equation with two variables has only one unique solution? If so, is there to quickly generate the solution besides simple guess and test? Thanks in advance.

Incase of equation with two variables two equations are required. However, incase only 1 equation is given in DS, check if any other condition is given such as number will be integer or positive or it is within some range, so that it can be easily tested with trial and error. In such cases there is no other method rather than trial and error.
_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Intern
Joined: 17 Jun 2017
Posts: 18
Re: How to tell when an equation with two variables has only one solution?  [#permalink]

### Show Tags

08 Nov 2017, 20:12
candyandy wrote:
I have notice that it is often the case on DS case questions that the test writers will give you an equation with two variables as one condition. The other condition will give you one of the variables and you end up falling into the "C trap". Does anyone know if there is a way to tell that an equation with two variables has only one unique solution? If so, is there to quickly generate the solution besides simple guess and test? Thanks in advance.

If you have two linearly independent equations for two variables, you will be able to solve for both variables.

Linearly independent:

What is the value of $$x$$?
$$1) x+y=2$$
$$2) x+2y=3$$

The two equations are linearly independent because they are not equivalent. In other words, you are unable to transform either of the equations into another. Since we need 1) and 2) to get two linearly independent equations, we need both statements to be sufficient. Pick C.

Not linearly independent:

What is the value of $$x$$?
$$1) x+y=2$$
$$2) 2x+2y+3=7$$

You can subtract 3 from both sides in 2) to get $$2x+2y = 4$$, and then divide both sides by 2 to get $$x+y=2$$. This means that 2) is equivalent to 1), so we actually do not have two separate equations. Statements 1) and 2) combined are insufficient. Pick E.
_________________

Source: We are an NYC based, in-person and online GMAT tutoring company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to ask us a question!

Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 596
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: How to tell when an equation with two variables has only one solution?  [#permalink]

### Show Tags

13 Nov 2017, 12:59
1
candyandy wrote:
I have notice that it is often the case on DS case questions that the test writers will give you an equation with two variables as one condition. The other condition will give you one of the variables and you end up falling into the "C trap". Does anyone know if there is a way to tell that an equation with two variables has only one unique solution? If so, is there to quickly generate the solution besides simple guess and test? Thanks in advance.

Are you talking about questions that look like this?

Quote:
What is the value of 2x + 2y?

(1) x + y = 15
(2) x = 6

If so, this is called a 'combo' problem - 'combo' refers to the fact that you're solving for a combination of two variables, rather than just one variable. (In this case, it's a combo because the question asks you to solve for 2x + 2y, rather than just x by itself or just y by itself.) You can sometimes answer combo questions without actually solving for the variables separately. There isn't a quick and easy way to tell whether this is possible - you just have to take each statement and see if you can use it to figure out the value of the combo 2x + 2y. In the example problem I gave, you'd take statement 1 and multiply both sides by 2, which would give you the value of 2x + 2y.
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

Intern
Joined: 26 Sep 2017
Posts: 6
Re: How to tell when an equation with two variables has only one solution?  [#permalink]

### Show Tags

30 Nov 2017, 00:57
1
If there is only one linear equation with 2 unknown variables and without any condition, it will have infinite solutions.
In case there is a trap in a question, there would be some other information mentioned such as number will be integer or positive or it is within some range. So we need to follow the condition mentioned and solve the question.

Lets say there are 2 linear equations with 2 unknown variables:
ax+by+c=0 &
dx+ey+f=0
If a/d ≠ b/e, there is only one solution

Ex: 2x+3y=6 & 4x+5y=15
These 2 equations have only one solution, as 2/4 ≠ 3/5
Re: How to tell when an equation with two variables has only one solution? &nbs [#permalink] 30 Nov 2017, 00:57
Display posts from previous: Sort by

# How to tell when an equation with two variables has only one solution?

## Events & Promotions

 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®.