Author 
Message 
TAGS:

Hide Tags

Intern
Affiliations: IIBA
Joined: 04 Sep 2010
Posts: 49
Location: India
Schools: HBS, Stanford, Stern, Insead, ISB, Wharton, Columbia
WE 1: Information Technology (Banking and Financial Services)

Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
04 Jun 2011, 09:08
Question Stats:
43% (01:58) correct 57% (01:38) wrong based on 171 sessions
HideShow timer Statistics
Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units. What is the area of the triangle? (1) The sides of triangle ABC are in the ratio 1 : 1 : √2 (2) The hypotenuse AC is 10 units
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
~soaringAlone ~Live fast, die young and leave a marketable corpse behind !!



Retired Moderator
Joined: 16 Nov 2010
Posts: 1434
Location: United States (IN)
Concentration: Strategy, Technology

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
04 Jun 2011, 09:47
(1) The median is perpendicular to the hypotenuse, as it's an isosceles right triangle. The ratio of sides is known, and triangle ABD ~ triangle ACB AB/AC = BD/AB AB/AC = 1/root(2) = 5/AB AB = 5root(2) BC = 5root(2) So area of triangle ABC = 1/2 * 25 * 2 = 25 Sufficient (2) It is not clear if the median is perpendicular to the hypotenuse The other sides are not known either. Not Sufficient Answer  A
Attachments
Triangle.png [ 6.76 KiB  Viewed 38454 times ]
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 24 Mar 2011
Posts: 371
Location: Texas

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
04 Jun 2011, 09:54
Median divides the hypotenuse into two equal lengths, so AD = DC and forms 2 isosceles triangles. Area of triangle = 1/2 * AB*BC
so if BD =5, AD = DC = 5 Hence AC = 10
St  1 given the ratio of AB to BC to AC So we can find AB and BC = AC/sqrt(2) = 10/(sqrt(2) = 5 sqrt(2) So we can find the area of triangle = 1/2 * 5 sqrt(2) * 5 sqrt(2) = 25
St2 gives us already known information. We cannot determine the value of AB or BC from this. so insufficient.
Hence A.



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1054

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
06 Jun 2011, 03:37
a in triangles CDB and ABC,
5/AB = AB/AC giving AB^2 = 5 * 2^(1/2) thus AC can be found out and hence the area = 1/2 * AB * BC. Sufficient.
b AD = CD = 5 each. However AB and BC have no relative information given. Not sufficient.
Thus A



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6406
GPA: 3.82

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
14 Sep 2015, 03:41
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. Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units. What is the area of the triangle? 1. The sides of triangle ABC are in the ratio 1 : 1 : root 2 2. The hypotenuse AC is 10 units Transforming the original condition and the question, we have the below image. In case of the triangle we have 3 variables and 2 equations (ang B=90 degree , BD=5) thus we need 1 more equation to match the number of variables and equations. Therefore there is high probability that D is the answer. In case of 1), from 1:1:root2, we have root2*AC=5 and thus the length of AC. Then we have AB=BC=5root2, therefore the area is (1/2)(5root2)^2=25. The condition is sufficient. In case of 2), we have AC=10 but no information regarding the length of AB,BC. Therefore the condition is not sufficient. The answer is A. Normally 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 D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.
Attachments
GC DS soaringAlone Triangle ABC (20150913).jpg [ 11.92 KiB  Viewed 36181 times ]
_________________
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. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 23 Sep 2015
Posts: 4

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
23 Sep 2015, 16:52
Can someone explain why my reasoning behind St2 being sufficient is incorrect??
So we're given the line between the corner at B to the midpoint of AC, which, if you flip the triangle, is the height of the triangle. Now all you need to solve for the area is the base, which is given by the statement.



CEO
Joined: 12 Sep 2015
Posts: 3037
Location: Canada

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
23 Sep 2015, 16:58
ugur wrote: Can someone explain why my reasoning behind St2 being sufficient is incorrect??
So we're given the line between the corner at B to the midpoint of AC, which, if you flip the triangle, is the height of the triangle. Now all you need to solve for the area is the base, which is given by the statement. We can't be certain that BD is the height of the triangle. In fact, the only time it will be the height is when we have a 454590 triangle. Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails



Intern
Joined: 07 Nov 2013
Posts: 1

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
24 Sep 2015, 04:53
GMATPrepNow wrote: ugur wrote: Can someone explain why my reasoning behind St2 being sufficient is incorrect??
So we're given the line between the corner at B to the midpoint of AC, which, if you flip the triangle, is the height of the triangle. Now all you need to solve for the area is the base, which is given by the statement. We can't be certain that BD is the height of the triangle. In fact, the only time it will be the height is when we have a 454590 triangle. Cheers, Brent Why, we can prove and,in fact, we get 454590 triangle ABC



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
24 Sep 2015, 05:31
kiskinen wrote: GMATPrepNow wrote: ugur wrote: Can someone explain why my reasoning behind St2 being sufficient is incorrect??
So we're given the line between the corner at B to the midpoint of AC, which, if you flip the triangle, is the height of the triangle. Now all you need to solve for the area is the base, which is given by the statement. We can't be certain that BD is the height of the triangle. In fact, the only time it will be the height is when we have a 454590 triangle. Cheers, Brent Why, we can prove and,in fact, we get 454590 triangle ABC I dont know what you are trying to say but GMATPrepNow is correct. Statement 2 does not mention that the median is also perpendicular to the hypotenuse AC. If you are asking how can we say that ABC is 454590 triangle per statement 1, you need to remember that for any right angled triangle having sides in the ratio \(1:1:sqrt{2}\), then it MUST be 454590 triangle. This can be seen as (this proof is easiest using trigonometry but I will follow the standard GMAT treatment): lets say the sides are \(x,x, x*\sqrt{2}\). You know that angles opposite equal sides are equal. Thus, if B is the right angle such that AB=BC=x and Ac = \(x*\sqrt{2}\), then \(\angle{BAC} = \angle{BCA}=Z\) Now, per the property of any triangle, \(\angle{ABC} + \angle{BAC}+\angle{BCA} = 180\) > 90+Z+Z=180 > Z=45 >\(\angle{BAC}=\angle{BCA} = 45\) Thus triangle ABC is a 454590 triangle. We can arrive at this result using statement 2 and hence statement 2 is NOT sufficient to find the area of the triangle. Hope this helps.



Senior Manager
Joined: 07 Sep 2014
Posts: 382
Concentration: Finance, Marketing

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
10 Jun 2016, 03:15
subhashghosh wrote: (1) The median is perpendicular to the hypotenuse, as it's an isosceles right triangle.
The ratio of sides is known, and triangle ABD ~ triangle ACB
AB/AC = BD/AB
AB/AC = 1/root(2) = 5/AB
AB = 5root(2)
BC = 5root(2)
So area of triangle ABC = 1/2 * 25 * 2 = 25
Sufficient
(2)
It is not clear if the median is perpendicular to the hypotenuse
The other sides are not known either.
Not Sufficient
Answer  A triangle ABD ~ triangle ACB ???????????? Why . It doesnt follow any of the rule. Congruence of triangles Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size. 1. SAS (SideAngleSide): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. 2. SSS (SideSideSide): If three pairs of sides of two triangles are equal in length, then the triangles are congruent. 3. ASA (AngleSideAngle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.



Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
10 Jun 2016, 06:32
abrakadabra21 wrote: subhashghosh wrote: (1) The median is perpendicular to the hypotenuse, as it's an isosceles right triangle.
The ratio of sides is known, and triangle ABD ~ triangle ACB
AB/AC = BD/AB
AB/AC = 1/root(2) = 5/AB
AB = 5root(2)
BC = 5root(2)
So area of triangle ABC = 1/2 * 25 * 2 = 25
Sufficient
(2)
It is not clear if the median is perpendicular to the hypotenuse
The other sides are not known either.
Not Sufficient
Answer  A triangle ABD ~ triangle ACB ???????????? Why . It doesnt follow any of the rule. Congruence of triangles Two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size. 1. SAS (SideAngleSide): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent. 2. SSS (SideSideSide): If three pairs of sides of two triangles are equal in length, then the triangles are congruent. 3. ASA (AngleSideAngle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. If you read carefully, ~ is a symbol used for triangle SIMILARITY and not CONGRUENCY.



Manager
Joined: 24 Apr 2014
Posts: 102
Location: India
Concentration: Strategy, Operations
GMAT 1: 730 Q50 V38 GMAT 2: 750 Q48 V45
GPA: 4
WE: Information Technology (Computer Software)

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
10 Jun 2016, 07:06
soaringAlone wrote: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is 5 units. What is the area of the triangle?
1. The sides of triangle ABC are in the ratio 1 : 1 : root 2
2. The hypotenuse AC is 10 units Statement 1 tells ... triangle is isosceles . 1:1:sqrt 2 Thus can calculate the area . Statement 2 tells AC 10 and thus we can tell AD =DC=5... BUT NOTHING ABOUT THE AREA . Sent from my Le X507 using GMAT Club Forum mobile app
_________________
way to victory .....



NonHuman User
Joined: 09 Sep 2013
Posts: 8542

Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is
[#permalink]
Show Tags
28 Dec 2017, 05:27
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




Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is &nbs
[#permalink]
28 Dec 2017, 05:27






