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

It is currently 19 Oct 2019, 11:22

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

The two lines y = x and x = -4 intersect on the coordinate plane. If z

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58445
The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

Show Tags

New post 17 Jul 2015, 01:25
1
6
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (02:28) correct 25% (02:15) wrong based on 146 sessions

HideShow timer Statistics

The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.

_________________
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2597
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

Show Tags

New post 17 Jul 2015, 02:51
1
1
Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.



The area enclosed by the 2 lines and the x-axis is a right triangle with coordinates (0,0), (-4,0) and (-4,-4). Thus z = 0.5*4*4 = 8 ---> 6z = 48 ----> Surface area of a cube with side l = 6l^2

Thus 6l^2 = 48 ---> l =\(2\sqrt{2}\) , D is the correct answer.
Manager
Manager
avatar
Joined: 20 Jul 2011
Posts: 79
GMAT 1: 660 Q49 V31
GMAT ToolKit User
Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

Show Tags

New post 17 Jul 2015, 10:36
Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.



Line y = x, is a line passing through Ist and IInd Quadrant via origin. And Line x = -4 is a vertical line.
The area intersecting these two lines is a triangle with base = 4 and height = 4. Hence the area, z = 1/2 * 4 * 4 = 8

Given, Surface area of Cube = 6 * side^2 = 6z ==> side^2 = 8
side = 2\sqrt{2}

Option D
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

Show Tags

New post 18 Jul 2015, 06:12
2
Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.


Recommendation : Draw the graph in all questions of Co-ordinate Geometry

Answer: Option D
Attachments

File comment: www.GMATinsight.com
Sol 11.jpg
Sol 11.jpg [ 127.37 KiB | Viewed 1745 times ]


_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58445
Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

Show Tags

New post 19 Jul 2015, 13:25
Bunuel wrote:
The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

A. 16
B. 8√2
C. 8
D. 2√2
E. (√2)/3

Kudos for a correct solution.


800score Official Solution:

The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.

The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , or answer choice (D).
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13277
Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z  [#permalink]

Show Tags

New post 20 Dec 2018, 21:43
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 Club Bot
Re: The two lines y = x and x = -4 intersect on the coordinate plane. If z   [#permalink] 20 Dec 2018, 21:43
Display posts from previous: Sort by

The two lines y = x and x = -4 intersect on the coordinate plane. If z

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne