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

 It is currently 11 Dec 2019, 23:36

### 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

# Which of the following equals x + xy + (x + xy)y?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59676
Which of the following equals x + xy + (x + xy)y?  [#permalink]

### Show Tags

21 Nov 2019, 00:47
00:00

Difficulty:

25% (medium)

Question Stats:

85% (01:31) correct 15% (01:29) wrong based on 40 sessions

### HideShow timer Statistics

Which of the following equals $$x + xy + (x + xy)y$$?

(A) $$x(1 + y)^2$$

(B) $$x(2 + y + y^2)$$

(C) $$2x(1 + y) + y$$

(D) $$2xy(1 + y)$$

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

_________________
Senior Manager
Joined: 13 Feb 2018
Posts: 492
GMAT 1: 640 Q48 V28
Which of the following equals x + xy + (x + xy)y?  [#permalink]

### Show Tags

21 Nov 2019, 01:04
1
2 ways to solve. First pure algebra (my least beloved thing and most needed on Gmat ) and second brute force (I like to waste up to 5 minutes brute-forcing everything )

1) Algebra
x+xy+(x+xy)y
Open the brackets: $$x+xy+xy+xy^2$$=$$x+2xy+xy^2$$
factor out common variable: $$x(1+2y+y^2)$$
Observe that $$1+2y+y^2=(1+y)^2$$
So we have $$x(1+y)^2$$
Look for such option

2) Brute force
Open the brackets: $$x+xy+xy+xy^2$$=$$x+2xy+xy^2$$
Open the brackets for every answer choice to see the match

Hope you will choose the first option and score 700+ on actual test
Have a nice day
L
Manager
Joined: 16 Feb 2015
Posts: 160
Location: United States
Concentration: Finance, Operations
Re: Which of the following equals x + xy + (x + xy)y?  [#permalink]

### Show Tags

21 Nov 2019, 21:06
Bunuel wrote:
Which of the following equals $$x + xy + (x + xy)y$$?

(A) $$x(1 + y)^2$$

(B) $$x(2 + y + y^2)$$

(C) $$2x(1 + y) + y$$

(D) $$2xy(1 + y)$$

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

Explanation:
Approach, opening the brackets, taking common out as in option, common is out
= x + xy + (x+xy).y
= x + xy + xy + xy^2
Taking x (common out)
= x (1+ 2y + y^2)
= x ( 1 + y)^2--- Option A

Please give kudos, if you find my explanation good enough
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8678
Location: United States (CA)
Re: Which of the following equals x + xy + (x + xy)y?  [#permalink]

### Show Tags

24 Nov 2019, 19:08
Bunuel wrote:
Which of the following equals $$x + xy + (x + xy)y$$?

(A) $$x(1 + y)^2$$

(B) $$x(2 + y + y^2)$$

(C) $$2x(1 + y) + y$$

(D) $$2xy(1 + y)$$

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

We can factor out x + xy first, and we have:

(x + xy)(1 + y)

Now we can factor out x from the first factor:

x(1 + y)(1 + y)

x(1 + y)^2

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: Which of the following equals x + xy + (x + xy)y?   [#permalink] 24 Nov 2019, 19:08
Display posts from previous: Sort by