It is currently 21 Nov 2017, 22:46

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

Events & Promotions in June
Open Detailed Calendar

If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42281

Kudos [?]: 132991 [0], given: 12402

If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]

Show Tags

New post 18 Mar 2016, 00:13
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:11) correct 20% (01:35) wrong based on 159 sessions

HideShow timer Statistics

Kudos [?]: 132991 [0], given: 12402

SC Moderator
User avatar
P
Joined: 13 Apr 2015
Posts: 1505

Kudos [?]: 1183 [0], given: 890

Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
GMAT ToolKit User Premium Member CAT Tests
If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]

Show Tags

New post 18 Mar 2016, 01:50
St1: z = \(16x^2 + 25y^2\) --> 10(x + y) = 10 --> x + y = 1. Sufficient

St2: Clearly insufficient as we do not know the value of y and z

Answer: A

Kudos [?]: 1183 [0], given: 890

Expert Post
Math Revolution GMAT Instructor
User avatar
P
Joined: 16 Aug 2015
Posts: 4341

Kudos [?]: 3050 [0], given: 0

GPA: 3.82
Premium Member CAT Tests
Re: If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]

Show Tags

New post 19 Mar 2016, 23:19
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 10x+10y+16x^2+25y^2=10+z , what is the value of x + y?

(1) z=(4x)^2+(5y)^2
(2) x=1


When you modify the original condition and the question, x+y=(10+z-16x^2-25y^2)/10 is derived. For 1), x+y=1 is derived from z=16x^2+25y^2, which is sufficient. The answer is A.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3050 [0], given: 0

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1850

Kudos [?]: 2620 [1], given: 362

Location: Canada
Re: If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]

Show Tags

New post 07 Aug 2016, 14:19
1
This post received
KUDOS
Expert's post
Top Contributor
Bunuel wrote:
If \(10x + 10y + 16x^2 + 25y^2 = 10 + z\), what is the value of x + y?

(1) z = (4x)² + (5y)²
(2) x = 1


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

Given: 10x + 10y + 16x² + 25y² = 10 + z

Statement 1: z = (4x)² + (5y)²
In other words, z = 16x² + 25y²
Take the given info (10x + 10y + 16x² + 25y² = 10 + z) and replace z with 16x² + 25y²
We get: 10x + 10y + 16x² + 25y² = 10 + 16x² + 25y²
Subtract 16x² from both sides to get: 10x + 10y + 25y² = 10 + 25y²
Subtract 25y² from both sides to get: 10x + 10y = 10
Factor the left side: 10(x + y) = 10
Divide both sides by 10 to get: x + y = 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x = 1
Take the given info (10x + 10y + 16x² + 25y² = 10 + z) and replace x with 1
We get: 10(1) + 10y + 16(1²) + 25y² = 10 + z
As you can see, two variables remain, which means y and z can have any number of values.
This means the sum x + y can have any number of values.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:
[Reveal] Spoiler:
A


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2620 [1], given: 362

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15562

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y? [#permalink]

Show Tags

New post 30 Oct 2017, 06:35
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

Kudos [?]: 283 [0], given: 0

Re: If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y?   [#permalink] 30 Oct 2017, 06:35
Display posts from previous: Sort by

If 10x + 10y + 16x^2 + 25y^2 = 10 + Z, what is the value of x + y?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.