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

It is currently 22 Oct 2018, 18:03

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

What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

Show Tags

New post 10 Feb 2017, 09:50
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:26) correct 30% (01:18) wrong based on 159 sessions

HideShow timer Statistics

VP
VP
User avatar
P
Joined: 05 Mar 2015
Posts: 1000
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

Show Tags

New post 10 Feb 2017, 10:21
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5



(1) no info on z
insuff.
(2) similar reason as (1)
insuff

combining
substituting the value of z from (1) as 3z=8-3.5x-1.5y+5 to equation (2)
we get x+y=2
suff

Ans C
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3031
Location: Canada
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

Show Tags

New post 10 Feb 2017, 11:28
1
Top Contributor
1
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5


Great question!

Target question: What is the value of x + y?

Statement 1: 7x + 3y + 6z = 16
Notice that, since we have the 3rd variable, z, we can assign ANY values to x and y and then simply make the z-value such that the equation holds true.
For example, if we let x = 0 and y = 0, then we get 0 + 0 + 6z = 16. So, z = 16/6. In this case, x + y = 0 + 0 = 0
Similarly, if we let x = 1 and y = 1, then we get 7 + 3 + 6z = 16. So, z = 6/6. In this case, x + y = 1 + 1 = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3x + 5y = 3z + 5
We can apply the same logic that we used for statement 1 to show that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 7x + 3y + 6z = 16
Statement 2 tells us that 3x + 5y = 3z + 5

IMPORTANT: Many students will assume that, since we have a system of 3 equations with 2 variables, then we cannot answer the target question.
This would be a correct assumption IF the target question asked for the individual values of x and y.
HOWEVER, notice that the target question only asks for the sum of x and y.
This we might be able to find.

First, take 3x + 5y = 3z + 5 and subtract 3z from from both sides to get: 3x + 5y - 3z = 5
Then multiply both sides by 2 to get: 6x + 10y - 6z = 10

We now have:
7x + 3y + 6z = 16
6x + 10y - 6z = 10

ADD the equations to get: 13x + 13y = 26
Divide both sides by 13 to get: x + y = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
_________________

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

Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 948
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

Show Tags

New post 22 May 2017, 13:13
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5


x+y = ?

(1) We don't know Z, So - Not Sufficient
(2) We don't know Z, So - Not Sufficient

Combine

When we see the equation we see that 3Z & 6Z can be cancelled if we multiply equation (2) by 2

Adding we get:

13x + 13y = 26

x+y = 2

Answer is - C
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Intern
Intern
avatar
B
Joined: 28 Mar 2018
Posts: 46
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5  [#permalink]

Show Tags

New post 12 Apr 2018, 12:23
GMATPrepNow wrote:
Bunuel wrote:
What is the value of x + y?

(1) 7x + 3y + 6z = 16

(2) 3x + 5y = 3z + 5


Great question!

Target question: What is the value of x + y?

Statement 1: 7x + 3y + 6z = 16
Notice that, since we have the 3rd variable, z, we can assign ANY values to x and y and then simply make the z-value such that the equation holds true.
For example, if we let x = 0 and y = 0, then we get 0 + 0 + 6z = 16. So, z = 16/6. In this case, x + y = 0 + 0 = 0
Similarly, if we let x = 1 and y = 1, then we get 7 + 3 + 6z = 16. So, z = 6/6. In this case, x + y = 1 + 1 = 2
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3x + 5y = 3z + 5
We can apply the same logic that we used for statement 1 to show that statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 7x + 3y + 6z = 16
Statement 2 tells us that 3x + 5y = 3z + 5

IMPORTANT: Many students will assume that, since we have a system of 3 equations with 2 variables, then we cannot answer the target question.
This would be a correct assumption IF the target question asked for the individual values of x and y.
HOWEVER, notice that the target question only asks for the sum of x and y.
This we might be able to find.


First, take 3x + 5y = 3z + 5 and subtract 3z from from both sides to get: 3x + 5y - 3z = 5
Then multiply both sides by 2 to get: 6x + 10y - 6z = 10

We now have:
7x + 3y + 6z = 16
6x + 10y - 6z = 10

ADD the equations to get: 13x + 13y = 26
Divide both sides by 13 to get: x + y = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent


I made the highlighted mistake. Is it universally true that in this type of scenario, we can solve for X+Y with two equations, or does it need to be mathematically determined in each case?
GMAT Club Bot
Re: What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5 &nbs [#permalink] 12 Apr 2018, 12:23
Display posts from previous: Sort by

What is the value of x + y? (1) 7x + 3y + 6z = 16 (2) 3x + 5y = 3z + 5

  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®.