Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Sep 2014, 06:28

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 09 Nov 2012
Posts: 170
GMAT 1: 700 Q43 V42
Followers: 4

Kudos [?]: 43 [0], given: 29

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ? [#permalink] New post 22 Nov 2012, 22:06
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (03:26) correct 28% (02:24) wrong based on 36 sessions
This is problem #34 on page 238 of Manhattan GMAT's Advanced GMAT Quant book.

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

(A) [(x-1)^2]y

(B) (x+1)^2

(C) (x^2 + x +1)

(D) (x^2 + x +1)y

(E) (x^2 + x +1)(x-y)

Please see the spoiler below for my question:

[Reveal] Spoiler:
I picked 3 for x and 2 for y, but both C and E are correct for that. I redid the problem and picked 4 for x and 2 for y. That makes C the only correct answer. How can I avoid this problem in the future? If this were the real GMAT, I would have wasted a 30 seconds to a minute on this problem because I would have had to do it twice.
[Reveal] Spoiler: OA

_________________

If my post helped you, please consider giving me kudos.


Last edited by Bunuel on 23 Nov 2012, 01:00, edited 1 time in total.
Renamed the topic and edited the question.
Manhattan GMAT Discount CodesKaplan GMAT Prep Discount CodesGMAT Pill GMAT Discount Codes
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4785
Location: Pune, India
Followers: 1121

Kudos [?]: 5089 [1] , given: 164

Re: If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ? [#permalink] New post 23 Nov 2012, 19:40
1
This post received
KUDOS
Expert's post
commdiver wrote:
This is problem #34 on page 238 of Manhattan GMAT's Advanced GMAT Quant book.

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

(A) [(x-1)^2]y

(B) (x+1)^2

(C) (x^2 + x +1)

(D) (x^2 + x +1)y

(E) (x^2 + x +1)(x-y)

Please see the spoiler below for my question:

[Reveal] Spoiler:
I picked 3 for x and 2 for y, but both C and E are correct for that. I redid the problem and picked 4 for x and 2 for y. That makes C the only correct answer. How can I avoid this problem in the future? If this were the real GMAT, I would have wasted a 30 seconds to a minute on this problem because I would have had to do it twice.


When you pick numbers, it is normal for you to get 2 or even 3 options that work out. The reason for this is that we tend to pick really easy numbers so that the calculation does not get cumbersome. I do not suggest you to pick harder numbers of course; I suggest you to pick even easier numbers so that the iterations don't take time.

I picked numbers to solve this too but I took numbers in which it took me a few secs to get to the correct option.

I said to myself, 'nothing says one of them can't be 0. Let x = 1 and y = 0'
Then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = 3
(A) and (D) are outright out since they equal 0 because y is a factor in them. (B) gives 4 so out. (C) and (E) are the only possible options since they both give 3.

Now I notice that (C) and (E) differ in the product (x - y). So I want that the difference between them should not be 1 (I think you noticed this too). So now, I pick x = 2 and y = 0 (why to give up a good thing? y = 0 makes life easy)
[x^3 + (x^2 + x)(1-y) - y] / (x-y) = 14/2 = 7
Option (C) gives 7 while option (E) will give 7/2

Answer must be (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23509
Followers: 3513

Kudos [?]: 26654 [2] , given: 2714

Re: If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ? [#permalink] New post 24 Nov 2012, 05:16
2
This post received
KUDOS
Expert's post
commdiver wrote:
This is problem #34 on page 238 of Manhattan GMAT's Advanced GMAT Quant book.

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

(A) [(x-1)^2]y

(B) (x+1)^2

(C) (x^2 + x +1)

(D) (x^2 + x +1)y

(E) (x^2 + x +1)(x-y)

Please see the spoiler below for my question:

[Reveal] Spoiler:
I picked 3 for x and 2 for y, but both C and E are correct for that. I redid the problem and picked 4 for x and 2 for y. That makes C the only correct answer. How can I avoid this problem in the future? If this were the real GMAT, I would have wasted a 30 seconds to a minute on this problem because I would have had to do it twice.


ALGEBRAIC APPROACH:

\frac{x^3 + (x^2 + x)(1-y) - y}{x-y}=\frac{x^3 +x^2-x^2y+x-xy-y}{x-y}=\frac{(x^3-x^2y)+(x^2-xy)+(x-y)}{x-y}=
\frac{x^2(x-y)+x(x-y)+(x-y)}{x-y}=\frac{(x-y)(x^2+x+1)}{x-y}=x^2+x+1.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

3 KUDOS received
Intern
Intern
avatar
Joined: 21 Oct 2012
Posts: 13
Followers: 0

Kudos [?]: 27 [3] , given: 16

Re: If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ? [#permalink] New post 24 Nov 2012, 05:58
3
This post received
KUDOS
commdiver wrote:
This is problem #34 on page 238 of Manhattan GMAT's Advanced GMAT Quant book.

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

(A) [(x-1)^2]y

(B) (x+1)^2

(C) (x^2 + x +1)

(D) (x^2 + x +1)y

(E) (x^2 + x +1)(x-y)

Please see the spoiler below for my question:



[Reveal] Spoiler:
I picked 3 for x and 2 for y, but both C and E are correct for that. I redid the problem and picked 4 for x and 2 for y. That makes C the only correct answer. How can I avoid this problem in the future? If this were the real GMAT, I would have wasted a 30 seconds to a minute on this problem because I would have had to do it twice.




This can be solved quickly, if we look for cancellations in the numerator on the basis of options. The options suggests that y gets eliminated, means a rearrangement of the numerator will help us in eliminating y.

When we open up the brackets we will find that there are factors of (x-y)

x^3+x^2+x-x^2*y- xy-y (Numerator)

lets combine in factors of x-y (Since it is in denominator)
x^2 (x-y) + x(x-y) +1 (x-y)

so we get (x^2+x+1) as the final answer (because x-y cancels out in the numerator and denominator)

Answer : C
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 16

Kudos [?]: 197 [0], given: 11

GMAT ToolKit User GMAT Tests User
Re: If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ? [#permalink] New post 08 Dec 2012, 03:36
Let x=2 and y=3
= \frac{[(2)^3 + ((2)^2 + (2))(1-(3)) - (3)]}{(2-3)}
= \frac{(8 + (6)(-2) - 3)}{-1}
= \frac{-7}{-1}
= 7

(A) [(2-1)^2]3=3
(B) (2+1)^2=9
(C) (2^2 + 2 +1)=7
(D) (2^2 + 2 +1)(3)=21
(E) (2^2 + 2 +1)(2-3)=-7

Answer: C
_________________

Impossible is nothing to God.

Re: If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?   [#permalink] 08 Dec 2012, 03:36
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic 1/x+1/y=1 xy=6, then what is the value of x^2+y^2? Splendidgirl666 4 19 Jan 2012, 12:21
2 Experts publish their posts in the topic On a two dimensional coordinate plane, the curve y=x^2 - x^3 sachinrelan 2 20 Sep 2010, 02:32
If x = 3y, is x^2 > y^2? 1. y+x < x-y 2. x^2 = 9 y^2 haas_mba07 4 14 Sep 2006, 05:41
Is |x^-1 y^-1| ^ -1 > xy ? (1) xy > 1 (2) x^2 > y^2 duttsit 4 12 Dec 2005, 12:12
1 if (x1,y1,), (x2,y2) and (x3,y3)are three vertex of a MA 2 20 Feb 2005, 12:17
Display posts from previous: Sort by

If y≠x, then [x^3 + (x^2 + x)(1-y) - y] / (x-y) = ?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.