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

It is currently 17 Jun 2019, 21:59

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

Points M and P lie on square LNQR, and LM = LQ. What is the

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

Hide Tags

 
Intern
Intern
avatar
Joined: 23 Jan 2013
Posts: 6
Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post Updated on: 25 Oct 2013, 09:11
3
30
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:43) correct 24% (01:47) wrong based on 952 sessions

HideShow timer Statistics

Attachment:
Untitled2.png
Untitled2.png [ 7.24 KiB | Viewed 29560 times ]
Points M and P lie on square LNQR, and LM = PQ. What is the length of the line segment PQ?

(1) \(PR=\frac{4\sqrt{10}}{3}\)
(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.

Originally posted by Pmar2012 on 25 Oct 2013, 08:46.
Last edited by Bunuel on 25 Oct 2013, 09:11, edited 2 times in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55631
Re: Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post 25 Oct 2013, 09:09
16
9
Image
Points M and P lie on square LNQR, and LM = PQ. What is the length of the line segment PQ?

(1) \(PR=\frac{4\sqrt{10}}{3}\). We know two sides (PR and PQ) in right triangle PQR, thus we can find the third side PQ. Sufficient.

(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1. Say LM = PQ = x, then the area of the shaded region is 2*(1/2*4*x)=4x. The area of unshaded region is 4*4-4x=16-4x. Thus we have that (unshaded)/(shaded)=(16-4x)/4x=2/1. We can find x. Sufficient.

Answer: D.
_________________
General Discussion
Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 415
Re: Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post 11 Dec 2013, 09:53
Points M and P lie on square LNQR, and LM = PQ. What is the length of the line segment PQ?

(1) PR=\frac{4\sqrt{10}}{3}

This is pretty self explanatory. Sufficient.

(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.

Because we know that LM = PQ, and that the figure is a square, we know that both shaded triangles are equal to one another. We know that the total area of the square (including the shaded triangles) = 16. If the ratio of unshaded to shaded is 2:1 we can set up an equation.

x:16 = 2:3 Where x represents the unshaded portion relative to the entire square and 2:3 represents the ratio given to us.

x = 32/3. Now we can find the remaining area of the triangles (which are both equal to one another). Finally, we plug in the area and the one given base length (4) into the area of a triangle formula to get the missing length (i.e. PQ or ML.) Sufficient.

D
Manager
Manager
User avatar
Joined: 05 Jul 2015
Posts: 97
Concentration: Real Estate, International Business
GMAT 1: 600 Q33 V40
GPA: 3.3
Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post 21 Nov 2015, 19:19
1
Easy solution:

A) Obviously sufficient because a^2+b^2=c^2

B) The white to gray is 2:1 so the gray is 1/3 of the total area. The area is 4*4. So the missing line segment is (4/3).

ANS: D
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7462
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post 26 Nov 2015, 08:00
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.

Points M and P lie on square LNQR, and LM = PQ. What is the length of the line segment PQ?

(1) PR=410 − − √ 3
(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.

We can know PQ if we know PR, so there is one variable (PR), and 2 equations are given by the conditions, so there is high chance (D) will be the answer.
For condition 1, from (4 sqrt 10/3)^2-4^2=PQ^2. PQ=4/3. This is sufficient
For condition 2, if the ratio of the area is 2:1, the height is the same, so NP:PQ=2:1, and PQ=4/3 so this is sufficient as well, and the answer becomes (D).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
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.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
avatar
B
Joined: 23 Dec 2013
Posts: 142
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Reviews Badge
Re: Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post 22 Jul 2017, 19:17
1
Pmar2012 wrote:
Attachment:
Untitled2.png
Points M and P lie on square LNQR, and LM = PQ. What is the length of the line segment PQ?

(1) \(PR=\frac{4\sqrt{10}}{3}\)
(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.


The goal is to find then length of PQ.

Statement 1) PR = 4sqrt(10)/3

By the Pythagorean theorem, we can determine that x^2 + 4^2 = 16/9*10

x^2 = 160/9-16

x^2 = 17.77-16

Sufficient.

Statement 2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.

Let PQ = x

The area of the shaded region is 2(1/2*4*x) = 4x

The total area of the square is 4^2 = 16

16 - 4x = unshaded

(16-4x)/(4x) = 2/1

16-4x = 8 x

16 = 12x
4 = 3x
4/3 = x

Sufficient.
Director
Director
User avatar
V
Joined: 12 Feb 2015
Posts: 862
Re: Points M and P lie on square LNQR, and LM = LQ. What is the  [#permalink]

Show Tags

New post 01 Jan 2019, 11:00
St1:- Apply pythagoras theorem as the lengths of two sides are given and one is missing.

St2:- Apply the formula for area of a triangle formula to find the length of the side.

Option D is the correct answer
_________________
"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"
GMAT Club Bot
Re: Points M and P lie on square LNQR, and LM = LQ. What is the   [#permalink] 01 Jan 2019, 11:00
Display posts from previous: Sort by

Points M and P lie on square LNQR, and LM = LQ. What is the

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


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