Forum Home > GMAT > Quantitative > Problem Solving (PS)
It is currently 20 May 2024, 22:07 |
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.
JOIN GMAT CLUB
Become part of our 1M+ member community!
GMAT Registration Benefits:
-
Vast Question Bank:
Practice thousands of GMAT questions with top expert solutions.
-
Error Tracking:
Identify and improve upon mistakes efficiently using our Error Log.
-
Expert Support:
Get the latest tips and news from our top GMAT professionals.
-
Sing up now
- it’s free and easy!
GMAT Club Timer Informer
Hi GMATClubber!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
-
We’ll give you
learn more
an estimate of
your score -
We’ll provide
learn more
personalized question
recommendations -
Your score will improve
learn more
and your results
will be more realistic
Is there something wrong with our timer? Let us know!
Thanks! I'll try it now
Add Mistakes & Note
Request Expert Reply
ConfirmCancel
'; } sliderBody += '
'; if(events[i].landing_uri) { sliderBody += '
'; if (events[i].partner_logo) { sliderBody += ''; } sliderBody += ''; } else { sliderBody += '
'; if (events[i].partner_logo) { sliderBody += ''; } sliderBody += ''; } sliderBody += '
'; sliderBody += '
'; sliderBody += '
' + events[i].start_date_formatted_main_min + '
'; sliderBody += '
'; if(events[i].landing_uri) { sliderBody += '
'; } else { sliderBody += '
'; } if( events[i].start_time ) { sliderBody += '
'; sliderBody += ''; sliderBody += '
' + events[i].start_time_formatted + ' ' + events[i].utc_start + '
'; if( events[i].end_date_formatted && events[i].end_date_formatted ) { sliderBody += ' - '; sliderBody += '
' + events[i].end_time_formatted + ' ' + events[i].utc_end + '
'; } sliderBody += '
'; } else { sliderBody += '
'; sliderBody += '
' + events[i].utc_start + '
'; sliderBody += '
'; } sliderBody += '
'; sliderBody += '
'; if( events[i].short_description ) { sliderBody += '
'; sliderBody += events[i].short_description; sliderBody += '
'; } sliderBody += '
'; sliderBody += '
'; sliderBody += ''; } return sliderBody += '';}function createNavigation(currentSlide, events){ if( events[currentSlide-1] ){ $('.previousEvent .flex-prev').show(); $('#prevName').text(events[currentSlide-1].name_cutted); $('#prevPartner').text(events[currentSlide-1].partner_name); $('#prevDate').html(events[currentSlide-1].start_date_formatted); } else{ $('.previousEvent .flex-prev').hide(); } if( events[currentSlide+1] ){ $('.nextEvent .flex-next').show(); $('#nextName').text(events[currentSlide+1].name_cutted); $('#nextPartner').text(events[currentSlide+1].partner_name); $('#nextDate').html(events[currentSlide+1].start_date_formatted); } else{ $('.nextEvent .flex-next').hide(); }}function createEventList() { var href; var eventList = '
- '; for (var j = 0; j < events.length; j++) { href = events[j].landing_uri ? events[j].landing_uri : 'http://www.facebook.com/' + events[j].eid; eventList += '
- '; eventList += ''; eventList += ''; eventList += ''; eventList += '
'; eventList += '
' + '' + events[j].start_date_formatted_main_min + '' + '
'; eventList += '
'; eventList += '' + '
' + events[j].name + '
' + ''; if(events[j].icon_type){ if(events[j].icon_type === 'download'){ eventList += '' } else if(events[j].icon_type === 'external_link'){ eventList += '' } else if(events[j].icon_type === 'webinar'){ eventList += '' } } eventList += ''; eventList += '
'; }; eventList += '
'; document.getElementById('EVENTSLIST').innerHTML = eventList;}function getEventIndexByDate( inDate, events, approximate ){ var indexes = []; for( var i=0; i
Events & Promotions
May 21
Unlock Your Career Potential with Carnegie Mellon's MS in Product Management
May 20
Humanities / Social Science Passages - GMAT Focus Reading Comprehension Series (Part 2)
May 25
Exclusive GMAT Strategy Webinar
May 25
Score 100th Percentile in GMAT Focus Verbal
May 26
Ace Arithmetic on the Current GMAT & the GMAT Focus Edition
May 26
The GMAT Club Podcast - Experiential Learning at NYU Stern
May 26
Turbocharge Your GMAT Focus Prep with Live Online Classes
Jun 11
MBA Spotlight Fair
May 21
07:30 AM PDT
-
08:30 AM PDT
Are you curious about the dynamic field of Product Management and how it can shape your career trajectory? Join Carnegie Mellon for an insightful conversation about the MS in Product Management (MSPM) ...
May 20
08:30 AM PDT
-
09:30 AM PDT
Master the RC on GMAT Club's with Manhattan Prep. Join the Live!
May 25
11:00 AM IST
-
01:00 PM IST
In this webinar, Rajat Sadana, GMAT Club’s #1 rated expert will help you create a personalized study plan so that each one of you can visualize your journey to a top GMAT Focus Score.
May 25
01:00 PM EDT
-
02:00 PM EDT
Think a 100% GMAT Focus Verbal score is out of your reach? TTP will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
May 26
11:00 AM IST
-
01:00 PM IST
Attend this session to evaluate your current skill level, learn process skills, and solve through tough Arithmetic questions
May 26
See AlsoA Summary of Triangle Congruence12:00 PM PDT
-
01:00 PM PDT
In this podcast, we talk to Lindsay Loyd, Executive Director, of MBA Admissions at NYU Stern, Hunter Brickey, NYU Stern alumnus and Daisy Cheng, a current student at NYU Stern, and more.
May 26
01:00 PM EDT
-
02:00 PM EDT
The Target Test Prep team is excited to announce multiple live online classes for GMAT Focus test-takers in May. Our 40-hour LiveTeach program will take your GMAT Focus score to the next level.
Jun 11
05:30 AM PDT
-
12:00 PM PDT
Register for the GMAT Club Virtual MBA Spotlight fair, the biggest MBA fair of the year. You will have a chance to hear Admissions directors from almost every Top 20 program speak, network with peers, and more.
Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]Updated on: 19 Jan 2013, 04:44
11
Kudos
129
Bookmarks
';$(this).html(tpl);});};}function store_answer( answer ){var timer_duration = 0;//timer_offset = 0;if(timer_stop_time !== null && timer_start_time !== null){timer_duration = Math.floor( ( timer_stop_time.getTime() - timer_start_time.getTime() ) / 1000);}var url = "/forum/timer.php?topic_id=82126&user_id=1&timer_duration=" + timer_duration + "&timer_answer=" + answer + "&r=" + Math.random() + "&sid=39d48f3dbced2bdbc3ca48cea333abf5";sendAjax( "GET", url, callbackStoreAnswer );}var timer_offset = 0;function timer_click(){if ( timer_id == 0 ){//document.getElementById('timer_button').src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/timer_stop.png";document.getElementById('timer_button').src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/timer_pause_btn.png";document.getElementById('timer_message').innerHTML = "";var i = 0;$('.statisticWrap').each(function() {var sumbol = '', value = 0;switch(i){case 0:{sumbol = 'a';value = 11;}break;case 1:{sumbol = 'b';value = 12;}break;case 2:{sumbol = 'c';value = 13;}break;case 3:{sumbol = 'd';value = 14;}break;case 4:{sumbol = 'e';value = 15;}break;}$(this).removeClass('correctAnswer');var tpl = '
'+sumbol.toUpperCase()+'
';$(this).html(tpl);i++;});timer_start_time = new Date();timer_start_time.setTime(timer_start_time.getTime() - timer_offset);document.getElementById('timer_display').classList.add('playing');if(timer_offset > 0)timer_loop();elsedocument.getElementById('timer_display').innerHTML = "00:00";timer_id = setInterval( timer_loop, 200 );selected_answer = null;//document.getElementById('timer_button').style.visibility = 'hidden';//document.getElementById('timer_abcde_block').style.display = 'none';}else{timer_stop_time = new Date();timer_offset = timer_stop_time.getTime() - timer_start_time.getTime();clearInterval( timer_id );timer_id = 0;document.getElementById('timer_button').src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/timer_play_btn.png";document.getElementById('timer_display').classList.remove('playing');if(selected_answer !== null)store_answer(0);}}function blink_right_answer(){var element = document.getElementById( 'timer_answer_'+'Official Answer and Stats are available only to registered users.Register/Login.'.toLowerCase() );if ( element != null ){if( element.style.visibility == "hidden" ){element.style.visibility = "visible";} else {element.style.visibility = "hidden";}}}function timer_loop(){var current_time = new Date();var timer_elapsed = 0;var timer_minutes = 0;var timer_seconds = 0;timer_elapsed = current_time.getTime() - timer_start_time.getTime();timer_elapsed = Math.floor(timer_elapsed / 1000);timer_minutes = Math.floor(timer_elapsed / 60);timer_seconds = timer_elapsed - timer_minutes * 60;if( timer_minutes < 10 ){timer_minutes= "0" + timer_minutes;}if( timer_seconds < 10 ){timer_seconds = "0" + timer_seconds;}document.getElementById('timer_display').innerHTML = timer_minutes + ":" + timer_seconds;}function write_timer_message( message ){document.getElementById( 'timer_message' ).innerHTML = message;}/*** !!!*/function write_timer_difficulty( percentile ){// console.log( 'write_timer_difficulty - in_percentile = ' + percentile);if(percentile > 0){var tpl_status = '';if(percentile>0 && percentile<=29){tpl_status += '';tpl_status += '';tpl_status += '';}else if(percentile>=30 && percentile<=69){tpl_status += '';tpl_status += '';tpl_status += '';} else if(percentile>=70 && percentile<=99){tpl_status += '';tpl_status += '';tpl_status += '';}var tpl = '';tpl += '
Difficulty:
';tpl += '
';tpl += '';tpl += tpl_status;tpl += '';tpl += '';tpl += ''+getLabelPercentile(percentile)+' ('+getLabelPercentileStatus(percentile)+')';tpl += '
';document.getElementById( 'timer_difficulty' ).innerHTML = tpl;}}/*** !!!*/function getLabelPercentileStatus(in_percentile){var status = 'low';if(in_percentile >= 0 && in_percentile <= 29) {status = 'low';}else if(in_percentile >= 30 && in_percentile <= 69){status = 'medium';} else if(in_percentile >= 70 && in_percentile <= 99){status = 'hard';}return status;}function getLabelPercentile( in_percentile ){var percentile = '0%';if(in_percentile >= 0 && in_percentile <= 9){percentile = '5%';} else if(in_percentile >= 10 && in_percentile <= 19){percentile = '15%';}else if(in_percentile >= 20 && in_percentile <= 29){percentile = '25%';}else if( in_percentile >= 30 && in_percentile <= 39){percentile = '35%';}else if( in_percentile >= 40 && in_percentile <= 49){percentile = '45%';}else if(in_percentile >= 50 && in_percentile <= 59){percentile = '55%';}else if(in_percentile >= 60 && in_percentile <= 69){percentile = '65%';}else if(in_percentile >= 70 && in_percentile <= 79){percentile = '75%';}else if(in_percentile >= 80 && in_percentile <= 89){percentile = '85%';}else if(in_percentile >= 90 && in_percentile <= 99){percentile = '95%';}return percentile;}function enable_timer_answer_group(){if ( show_answer_id != 0 ){clearInterval( show_answer_id );show_answer_id = 0;}var element = document.getElementById( 'timer_answer_' + 'Official Answer and Stats are available only to registered users.Register/Login.'.toLowerCase() );if ( element != null ){element.style.visibility = "visible";}//document.getElementById('timer_button').style.visibility = 'visible';//document.getElementById('timer_abcde_block').style.display = 'block';if( document.getElementById( 'timer_answer_1' ) ){document.getElementById( 'timer_answer_1' ).disabled = false;}if( document.getElementById( 'timer_answer_2' ) ){document.getElementById( 'timer_answer_2' ).disabled = false;}if( document.getElementById( 'timer_answer_3')){document.getElementById( 'timer_answer_3').disabled = false;}if ( document.getElementById( 'timer_answer_a' ) ){document.getElementById( 'timer_answer_a' ).src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/buttons/a_white.png";document.getElementById( 'timer_answer_a' ).onclick = function() { timer_answer( 11 ) };}if ( document.getElementById( 'timer_answer_b' ) ){document.getElementById( 'timer_answer_b' ).src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/buttons/b_white.png";document.getElementById( 'timer_answer_b' ).onclick = function() { timer_answer( 12 ) };}if ( document.getElementById( 'timer_answer_c' ) ){document.getElementById( 'timer_answer_c' ).src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/buttons/c_white.png";document.getElementById( 'timer_answer_c' ).onclick = function() { timer_answer( 13 ) };}if ( document.getElementById( 'timer_answer_d' ) ){document.getElementById( 'timer_answer_d' ).src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/buttons/d_white.png";document.getElementById( 'timer_answer_d' ).onclick = function() { timer_answer( 14 ) };}if ( document.getElementById( 'timer_answer_e' ) ){document.getElementById( 'timer_answer_e' ).src="https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/theme/images/viewtopic/buttons/e_white.png";document.getElementById( 'timer_answer_e' ).onclick = function() { timer_answer( 15 ) };}}/* Timer Mod End-------------- */
Difficulty:
95%(hard)
Question Stats:
47%(02:19)correct53%(02:14) wrongbased on1126sessions
HideShowtimer Statistics
Attachment:
Rhombus.gif [ 1.37 KiB | Viewed 86650 times ]
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD
Originally posted by crejoc on 09 Aug 2009, 10:03.
Last edited by Bunuel on 19 Jan 2013, 04:44, edited 1 time in total.
OA added.
request expert reply
Most Helpful Reply
Re: Rhombus[#permalink]15 Jun 2010, 13:38
30
Kudos
23
Bookmarks
Expert Reply
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).
So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.
(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.
(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.
(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.
Answer: C.
Attachments
untitled.JPG [ 3.95 KiB | Viewed 83044 times ]
_________________
New to the GMAT CLUB Forum?
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Re: Rhombus hard problem[#permalink]25 Oct 2009, 04:42
7
Kudos
1
Bookmarks
'B' meets only one condition for a rhombus which is Parellelism. but it does not prove that all sides of ABDE are equal. Please see the attachment which suggests that 'B' only is not correct. We also need 'A' to prove all sides are equal. Hope it clarifies.
Attachments
General Discussion
Re: Rhombus hard problem[#permalink]Updated on: 15 Aug 2009, 12:05
1
Kudos
[quote="crejoc"]Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD
to prove that it is a rhombus, we need to prove that it is a paralellogram with equal opposite angles and all sides =.
from 1
draw the diagonal bd would split the abcd rhombus into 2 similar triangles , both eqelateral all angles = 60, however as long as we dont know whether ae is // to bd or we know angles dae or aed we can not deduce that opposit sides of abde are equal or parallel.....insuff
from 2
obviously not suff
both
suff...C
Re: Rhombus hard problem[#permalink]15 Aug 2009, 12:08
sandipchowdhury wrote:
whould you please explain why not B ?
to prove a shape to be a rhombus:
1)opposite sides are //
2) all sides are equal
and ( only to deferenciate it from a square):
3) opposite angles are =
to prove to be a squaresame as above however all angles have to be = in measure and a such each = 90 degrees
Re: Rhombus hard problem[#permalink]22 Oct 2009, 06:48
1
Bookmarks
I don't understand why not B.
question stem has given CDE is parallel to AB --> DE is parallel to AB
and S2 give AE is parallel to DB , so for ABDE, we have the condition that opposite sides are parallel is met.
How we know that opposite angles are not equal - can someone draw such figure ?
Re: Rhombus[#permalink]15 Jun 2010, 14:09
AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE)
Bunuel, all sides have to be equal as the question stem states that C, D and E are on the same line. And it also states that BD is parallel to AE. Try drawing any kind of rhombus with the following conditions and all sides will be equal. So why do we need statement A? Am I missing something?
Re: Rhombus[#permalink]15 Jun 2010, 14:24
3
Kudos
Expert Reply
study wrote:
AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE)
Bunuel, all sides have to be equal as the question stem states that C, D and E are on the same line. And it also states that BD is parallel to AE. Try drawing any kind of rhombus with the following conditions and all sides will be equal. So why do we need statement A? Am I missing something?
From your reasoning above it's not clear how you came to the conclusion that alls sides must be equal.
Actually I don't even need to try drawing, to state that there are infinite # of cases possible for AE to be parallel to BD and ABDE not to be a rhombus. Just try to increase or decrease diagonal BD and leave everything else the same (AE||BD): you'll always have a parallelogram but in only one case a rhombus, when BD=AB.
_________________
New to the GMAT CLUB Forum?
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Re: Rhombus hard problem[#permalink]Updated on: 17 Oct 2010, 04:29
6
Kudos
1
Bookmarks
anandnat wrote:
I still don't understand why B is wrong. Can we safely say that the diagonal will never equal the side? If this is true, then with B, we always get a firm answer that ABDE is never a rhombus. Hence imo the answer is B. Math experts please help!
anandnat,
With statement 2, we can conclude that since AE is parallel to BD, therefore triangle ABD is mirror image of AED (similar triangle). We have, AD is equal to AB. With all this, we can assert that ED is equal to AB and AE is equal to BD.
In other way, to cut the long story short:-
From st 2, we can come closer to only this much.. ..
ABD and AED are two similar "Isosceles" triangles, Joined together. But, we need to prove that all four sides are equal.
I have drawn one such example here:
Hope that helps!
Attachments
Rhombus1.jpg [ 6.48 KiB | Viewed 70017 times ]
Rhombus1.jpg [ 6.48 KiB | Viewed 69995 times ]
Re: Rhombus hard problem[#permalink]19 Oct 2010, 20:25
1
Kudos
1
Bookmarks
I will explain why B) is not sufficient
Pls refer the attached diagram
AE || BD is not sufficient to judge whether BD = DC or BD = BC because for AEDB to be a rhombus , AE = ED = DB= BA
From A) we can deduce
DC = CB = BD (diagonal of the rhombus) as angle B = angle C = angle D = 60 deg.
Now from the statement of the question , DC = AB as it is a rhombus , so DB = AB
Since from A) we deduce DB = AB and from 2) we know that AE = DB as C , D , E lies on a straight line
Hence combining (A) and (B) , we know that AEDB is always a RHOMBUS
Note that if angle BCD not equal to 60 degrees , then AEDB would not have been a RHOMBUS
Hope the above explanation is now clear
Attachments
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]10 May 2012, 14:47
I still don't understand this question. "AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. " I understand how paralellogram --> BD=AE and AB=DE, but how does AE||BD and BA||DA imply it is a paralellogram with opposite sides equal?
Manager
Joined: 02 Sep 2012
Posts: 161
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE:Architecture (Computer Hardware)
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]18 Jan 2013, 20:51
1
Kudos
Can some1 pls explain me how from st1 people derive BD=AB.Can anyone pls explain elaborately
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]19 Jan 2013, 04:54
4
Kudos
Expert Reply
skamal7 wrote:
Can some1 pls explain me how from st1 people derive BD=AB.Can anyone pls explain elaborately
(1) The measure of angle BCD is 60 degrees. Since given that BC=DC, then <DBC=<BDC --> <DBC+<BDC+<BCD=180 degrees --> x+x+60=180 --> x=60 degrees. We have that triangle BCD is equilateral, thus BD=BC=DC. We know that AB=BC=CD=AD, thus BD=AB.
Hope it's clear.
_________________
New to the GMAT CLUB Forum?
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Manager
Joined: 28 Jul 2011
Posts: 225
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE:Accounting (Commercial Banking)
Re: Rhombus[#permalink]20 Jan 2013, 23:39
Bunuel wrote:
Attachment:
untitled.JPG
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).
So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.
(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.
(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.
(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.
Answer: C.
Bunnel,
In Statement 2 How can you say ABDE is ||gm without knowing whether AB and DE are ||el.... we just know that AE and BD are ||el
Re: Rhombus[#permalink]21 Jan 2013, 05:14
1
Kudos
Expert Reply
mydreammba wrote:
Bunuel wrote:
Attachment:
untitled.JPG
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).
So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.
(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.
(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.
(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.
Answer: C.
Bunnel,
In Statement 2 How can you say ABDE is ||gm without knowing whether AB and DE are ||el.... we just know that AE and BD are ||el
We know that points C, D, and E are on the same line and since CD||AB, then the same line DE is also parallel to AB.
Hope it's clear.
_________________
New to the GMAT CLUB Forum?
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Senior Manager
Joined: 13 Aug 2012
Posts: 334
Concentration: Marketing, Finance
Schools: Full Time MBA (A$)
GPA: 3.23
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]29 Jan 2013, 08:13
crejoc wrote:
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
(1) The measure of angle BCD is 60 degrees.
(2) AE is parallel to BD
I think the rubber band technique is effective. If you can stretch a side or dimension and come up with different results, then the information is INSUFFICIENT.
1. If BCD is 60 then BAD is also 60. Then we are left with two angles from left to right with 120 each. Imagine a straight line cutting the rhombus in half horizontally, what we got are two equilateral triangles ABD and BCD. For ABDE to become a rhombus, AE, BD,DE, and AE must have equal sides. Imagine pulling the line CDE a little longer through pt. E, then we could distort the figure and come up with a non-rhombus quadrialeteral. We could push it back and we could estimate a rhombus.
INSUFFICIENT.
2. Now imagine your rhombus ABCD and make it narrower, this will make BD and AE's lengths shorter than the size of a side of rhombus ABCD. Imagine your rhombus a little wider and this will make BD and AE's lengths longer. By rubber band technique, we know that we are not sure if ABDE is a rhombus.
INSUFFICIENT.
Together:
We know that ABD and BCD are equilateral triangles forming rhombus ABCD. Thus, line BD would be equal to all the sides of the rhombus.
Now we know that BD and AE are parallel each other fixed by the bordering lines of BA and CDE. Hence, BD = AE.
All the sides of the rhombus are equal to BD then also to AE.
To close the deal, AB and DE must be equal to become a rhombus. Since AE and BD are two parallel lines with equal length then, we are certain that AB and DE are also equal in length.
Answer: C
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]17 Nov 2013, 11:47
Hi Bunuel,
I think the answer to this Q shd be B. My soln is as follows:
let angle BAD be X, angle ABC be Y. Therefore since ABCD is a rhombus, angle BCD will be X and angle CDA will be Y. Also all the sides are equal of this rhombus, i.e., AB=AD=CD=BC. Now draw BD. Further, in the Q it is given that CDE is a straight line, that means AB is parallel to CDE. Therefore, we can say that angle ADE is X (alternate angles). Now acc. to second stmt, AE is parallel to BD. Let angle DAE =Z. Consequently, angle ADB =Z (alternate angles). Then angle BDC = Y-Z and angle ABD= Z (because AB=AD). That means X+Z+Z = 180. Therefore, in triangle DAE, angle A = Z and angle D =X. From this, we can calculate that angle AED = Z. This means AD=DE. And therefore because triangle ABD is similar to traingle ADE, BD will also be equal to AE. Thus all sides are equal. And we do not need any specific angle value.
Please help! as to why B cant be the answer. GMAT in two days!!
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]17 Nov 2013, 12:13
1
Kudos
Expert Reply
noorshergill wrote:
Hi Bunuel,
I think the answer to this Q shd be B. My soln is as follows:
let angle BAD be X, angle ABC be Y. Therefore since ABCD is a rhombus, angle BCD will be X and angle CDA will be Y. Also all the sides are equal of this rhombus, i.e., AB=AD=CD=BC. Now draw BD. Further, in the Q it is given that CDE is a straight line, that means AB is parallel to CDE. Therefore, we can say that angle ADE is X (alternate angles). Now acc. to second stmt, AE is parallel to BD. Let angle DAE =Z. Consequently, angle ADB =Z (alternate angles). Then angle BDC = Y-Z and angle ABD= Z (because AB=AD). That means X+Z+Z = 180. Therefore, in triangle DAE, angle A = Z and angle D =X. From this, we can calculate that angle AED = Z. This means AD=DE. And therefore because triangle ABD is similar to traingle ADE, BD will also be equal to AE. Thus all sides are equal. And we do not need any specific angle value.
Please help! as to why B cant be the answer. GMAT in two days!!
First of all when making such posts please attach a diagram. It's hard to follow all that angles in your explanation.
As for your solution: where did you prove that BD is equal to AB? In rhombus all sides must be equal.
_________________
New to the GMAT CLUB Forum?
- Posting Rules: QUANTITATIVE | VERBAL.
Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant
Questions' Bank By Tags and Difficulty: GMAT Club's Complete Questions' Bank
My Signature Questions' Collection:
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Re: Quadrilateral ABCD is a rhombus and points C, D, and E are[#permalink]17 Nov 2013, 13:16
Thanx Bunuel, noticed my error... and thanx a ton fr quick reply too
Manager
Joined: 26 Sep 2013
Posts: 149
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Rhombus[#permalink]15 Dec 2013, 16:42
Bunuel wrote:
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).
So ABCD is a rhombus means AB=BC=CD=AD.
ABDE to be a rhombus it must be true that AB=BD=DE=AE.
(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.
(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.
(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.
Answer: C.
How do you know that BD=AB from 1?? Is there some hidden calculations done in there? All I see is BCD=60, you don't know the measures of any other angles so it doesn't really tell you anything
gmatclubot
Re: Rhombus[#permalink]
15 Dec 2013, 16:42
Moderator:
Announcements Tuck at Dartmouth Latest Posts |