Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 07 Sep 2010
Posts: 327

In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
04 Sep 2012, 05:06
1
This post received KUDOS
3
This post was BOOKMARKED
Question Stats:
25% (02:03) correct
75% (01:16) wrong based on 220 sessions
HideShow timer Statistics
In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
+1 Kudos me, Help me unlocking GMAT Club Tests
Last edited by Bunuel on 30 Mar 2014, 11:14, edited 1 time in total.
Added the OA.



Intern
Joined: 28 Aug 2012
Posts: 46
Location: Austria

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
04 Sep 2012, 05:43
Statement (1): We know all 4 sides. But we don't know any angle. There is more than one way to draw this quadrilateral. > not sufficient Statement (2): Again, there's one info too few. We would need one more angle or the fourth side. There is more than one way to draw this quadrilateral > not sufficient
Both statements together are sufficient. We can draw two triangles ABC and CDA. ABC is an isosceles rectangular triangle. What's important here is that CD and DA are longer than AB and BC. If this would not be the case, we could draw two quadrilaterals, one with angle CDA being smaler than 180 degrees, the other one with angle CDA being greater than 180 degrees.
We could mirror/flip triangle CDA anyways, but this way, the angle ABC would not longer be 90 degrees, but 270 degrees (the 90 degrees would then be "outside".



Intern
Joined: 09 Jan 2012
Posts: 3

Challenge Problem from Manhattan GMAT [#permalink]
Show Tags
04 Sep 2012, 14:28
In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
I was able to solve the datasufficiency question using the 1 and 2 but the OA is E.My Approach is given below. GMAT club members kindly check and let me know whether there is anything wrong with my approach.
Area of quadrilateral=1\2 *d1(p1+p2) d1=lenght of one digaonal;p1=lenght of perpendicular from one vertex.p2=lenght of perpendicular from opp vertex to the diagonal. 1.Using 1. In traingle ADC of quadrilateral ABCD AD=DC. Draw perpendicular say DE from vertex D onto diagonal AC of quadrilateral.Now traingles ADE and CDE are congruent traingles AAS congruency(<DAE=<DCA ;<DEA=<DEC=90 ;AD=DC), so AE=EC.But we cant calculate length of diagonal AC from the info, hence it is insufficient.
2.Using this info we can calculate the length of diagonal AC from pythagoras theorem.Lenghth of other perpendicular drawn from vertex B on AC say BF can be found out using the same procedure as above ie by AAS congruency.But we cant calculate lenght of other perpendicular drawn from vertex D with this infro.Hence this is aslo insufficient.
Using (1)+(2) we get Length of diagonal and lenght of perpendicular DE and BF (E and F will be the same point as from AAS congruency of two traingles we get AE+EC =AC and AF=FC=AC).Hence both together are sufficeint to answer the problem.
Let me know your views on this problem.



Manager
Joined: 05 Mar 2012
Posts: 62

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
05 Sep 2012, 14:47
I believe it's E.
Statement 1 is not sufficient because we don't know if angle ABD is acute or obtuse.
Statement 2 is not sufficient because of aforementioned reasons.
Even with both statements we still have nothing about the angle ABD.



Manager
Joined: 30 Sep 2009
Posts: 120

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
07 Sep 2012, 04:44
if we know four sides of the quadrilateral we can find its area...
s=a+b+c+d/4
area =sqrt of s*(sa)*(sb)*(sc)*(sd) ....
so answer A ...
Am i missing something.....



Manager
Status: Retake.. The OG just loves me too much.
Joined: 18 Jun 2012
Posts: 69
Location: India
WE: Information Technology (Consulting)

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
10 Sep 2012, 11:57
1
This post received KUDOS
i guess with both, statements 1 and 2 together, you are able to determine the area of the given quadrilateral. please refer to the image attached.. Attachment:
quadABCD.jpg [ 19.47 KiB  Viewed 11216 times ]
you can see that once you have the 2nd condition, you can find the diagonal AC of the quad. and when you calculate the length of the diagonal, you end up getting an equilateral triangle ADC on the other side. So, 1 you have a right triangle and 2 you have an equilateral triangle, the areas of both of which can be calculated. Thus, I would go with option C.
_________________
Live Life the Way YOU Love It !! GmatPrep1 [10/09/2012] : 650 (Q42;V38)  need to make lesser silly mistakes. MGMAT 1 [11/09/2012] : 640 (Q44;V34)  need to improve quant pacing and overcome verbal fatigue.



Manager
Joined: 02 Jun 2011
Posts: 108

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
11 Sep 2012, 12:42
imhimanshu wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Please post your reasoning. I go with answer 'D' as both the sentences are sufficient to give the answer.



Director
Joined: 24 Aug 2009
Posts: 503
Schools: Harvard, Columbia, Stern, Booth, LSB,

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
10 Oct 2012, 05:21
imhimanshu wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Please post your reasoning. From stem AB = BC = 2^1/2 CD = 2 1) AD = 2 > This can form a KITE if we knew the angles but since there is no info about the angles included >Insufficient 2) One of the triangle is right angle triangle but no info about the shape of other triangle >Insufficient. 1+2) If we combine both we get KITE ( a combination of 2 Isosceles Right angle triangles) > Sufficient Answer C Note : Not able to include the diagram, you have to imagine.
_________________
If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth Game Theory
If you have any question regarding my post, kindly pm me or else I won't be able to reply



Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
10 Oct 2012, 10:59
imhimanshu wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Please post your reasoning. To the best of my knowledge, on the GMAT only convex polygons are considered, except maybe the cases when a drawing is supplied. This is just another example when Manhattan is going overboard.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
30 Mar 2014, 09:17
imhimanshu wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Please post your reasoning. I'm going with C here. Please provide OA ok? Here's my reasoning Statement 1 we have that AD which is the diagonal of the right triangle formed in the polygon is 2 therefore knowing two sides and one angle is sufficient to know the measures of the right triangle but thing is we don't know about BC is this side perpendicular to AB or not? Insufficient Statement 2 only tells us that the angle in ABC is 90 degrees but still no way to find the area of the other right triangle. Now with both statements together we know the area of the right triangle and we know that AB is perpendicular to BC hence the area of the given square is 2 which added to the area of the right triangle can provide the total area of the figure Answer is thus C Please let me know if this is sound reasoning Cheers J
Last edited by jlgdr on 07 Apr 2014, 05:51, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
30 Mar 2014, 11:16
jlgdr wrote: imhimanshu wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Please post your reasoning. I'm going with A here. Please provide OA ok? Here's my reasoning Statement 1 we have that AD which is the diagonal of the right triangle formed in the polygon is 2 therefore knowing two sides and one angle is sufficient to know the measures of the right triangle but thing is we don't know about BC is this side perpendicular to AB or not? Insufficient Statement 2 only tells us that the angle in ABC is 90 degrees but still no way to find the area of the other right triangle. Now with both statements together we know the area of the right triangle and we know that AB is perpendicular to BC hence the area of the given square is 2 which added to the area of the right triangle can provide the total area of the figure Answer is thus C Please let me know if this is sound reasoning Cheers J The correct answer is E: Attachment:
quadrophenia3.jpg [ 9.69 KiB  Viewed 9305 times ]
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 10 Mar 2014
Posts: 245

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
17 Apr 2014, 11:36
Bunuel wrote: jlgdr wrote: imhimanshu wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
Please post your reasoning. I'm going with A here. Please provide OA ok? Here's my reasoning Statement 1 we have that AD which is the diagonal of the right triangle formed in the polygon is 2 therefore knowing two sides and one angle is sufficient to know the measures of the right triangle but thing is we don't know about BC is this side perpendicular to AB or not? Insufficient Statement 2 only tells us that the angle in ABC is 90 degrees but still no way to find the area of the other right triangle. Now with both statements together we know the area of the right triangle and we know that AB is perpendicular to BC hence the area of the given square is 2 which added to the area of the right triangle can provide the total area of the figure Answer is thus C Please let me know if this is sound reasoning Cheers J The correct answer is E: Attachment: quadrophenia3.jpg Hi Bunnel, When I use st1 and st2 I get one 454590 triangle. and another one an equilateral triangle with site 2. I can get area of quadrilateral by adding both the areas. I choose C but official ans is E. Please clarify. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
18 Apr 2014, 02:45
PathFinder007 wrote: Bunuel wrote: jlgdr wrote: In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°.
I'm going with A here. Please provide OA ok?
Here's my reasoning
Statement 1 we have that AD which is the diagonal of the right triangle formed in the polygon is 2 therefore knowing two sides and one angle is sufficient to know the measures of the right triangle but thing is we don't know about BC is this side perpendicular to AB or not? Insufficient
Statement 2 only tells us that the angle in ABC is 90 degrees but still no way to find the area of the other right triangle.
Now with both statements together we know the area of the right triangle and we know that AB is perpendicular to BC hence the area of the given square is 2 which added to the area of the right triangle can provide the total area of the figure
Answer is thus C
Please let me know if this is sound reasoning Cheers J The correct answer is E: Attachment: quadrophenia3.jpg Hi Bunnel, When I use st1 and st2 I get one 454590 triangle. and another one an equilateral triangle with site 2. I can get area of quadrilateral by adding both the areas. I choose C but official ans is E. Please clarify. Thanks Not sure how to clarify better than the diagram: As you can see both those figure satisfy all the conditions and have different areas. Thus the answer must be E. Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 15 Mar 2013
Posts: 7

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
19 Apr 2014, 01:30
Thanks for clarification. But i think second figure is not a convex polygon(because interior ABC angle is 270 and not less than 180). And in GMAT I guess we are concerned about convex polygon only? And if we agree that second figure is valid, then can we say ans is C? Also i feel is it really possible to draw such diagram with precision in exam ? Any alternative way to build the thought process for exam? Thanks. Manoj Parashar



Math Expert
Joined: 02 Sep 2009
Posts: 39702

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
21 Apr 2014, 05:09
manojISB wrote: Thanks for clarification. But i think second figure is not a convex polygon(because interior ABC angle is 270 and not less than 180). And in GMAT I guess we are concerned about convex polygon only? And if we agree that second figure is valid, then can we say ans is C? Also i feel is it really possible to draw such diagram with precision in exam ? Any alternative way to build the thought process for exam? Thanks. Manoj Parashar Yes, OG defines a quadrilateral as a polygon with four sides. Next, it says that the term "polygon" will be used to mean a convex polygon, that is, a polygon in which each interior angle has a measure of less than 180°. Hence this question violates GMAT definition of a quadrilateral, which makes the question/solution presented by MGMAT flawed. I wouldn't worry about this question at all.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 08 Apr 2012
Posts: 453

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
29 Jun 2014, 11:09
Is there a set of details that we must know in order to find the area of a quadrilateral?



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15985

Re: In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
24 Sep 2015, 02:15
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



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3460
GPA: 3.82

In quadrilateral ABCD, sides AB and BC each have length √2, [#permalink]
Show Tags
24 Sep 2015, 03:35
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. In quadrilateral ABCD, sides AB and BC each have length √2, while side CD has length 2. What is the area of quadrilateral ABCD? (1) The length of side AD is 2. (2) The angle between side AB and side BC is 90°. In the original condition, there are 5 variables (4 sides and 1 diagonal line) and 3 equations(sides AB and BC each have length √2, while side CD has length 2) and thus we need 2 more equations to match the number of variables and equations. Since there is 1 equation each in 1) and 2), the best answer is C by our DS definition. However, this type of question always shows the diagram in actual exam. If diagram is not shown, E is the answer because we don't know the alphabetical orders of vertices (ABCD? ACBD? BDAC?) Normally for cases where we need 2 more equations, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly 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




In quadrilateral ABCD, sides AB and BC each have length √2,
[#permalink]
24 Sep 2015, 03:35








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


9


Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is

Bunuel 
7 
15 Feb 2017, 07:10 

3


The lengths of the sides of triangle ABC are such that AB = x + 2, BC

Bunuel 
4 
02 Mar 2015, 07:24 

13


In the quadrilateral ABCD, side AD is parallel to side BC.

siddharthvaid 
14 
03 Nov 2016, 11:54 

11


If ABCD is a quadrilateral, is AB=BC=CD=DA ?

tt11234 
11 
17 Apr 2017, 11:31 

4


If ABCD is a quadrilateral, is AB=BC=CD=DA ?

Illuminati 
7 
27 Jun 2012, 01:39 



