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

 It is currently 23 Oct 2018, 11:23

### 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

# Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
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
5
00:00

Difficulty:

85% (hard)

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

_________________

~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
2
(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

St-2 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
GMAT 1: 760 Q51 V42
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
2
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 one-and-only 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 Resources-30 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
1
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 45-45-90 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 45-45-90 triangle.

Cheers,
Brent

Why, we can prove and,in fact, we get 45-45-90 triangle ABC
Current Student
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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 45-45-90 triangle.

Cheers,
Brent

Why, we can prove and,in fact, we get 45-45-90 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 45-45-90 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 45-45-90 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 45-45-90 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 (Side-Angle-Side): 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 (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

3. ASA (Angle-Side-Angle): 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
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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 (Side-Angle-Side): 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 (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.

3. ASA (Angle-Side-Angle): 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 .....

Non-Human 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.
_________________
Re: Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is &nbs [#permalink] 28 Dec 2017, 05:27
Display posts from previous: Sort by

# Triangle ABC is right angled at B. BD, the median to hypotenuse AC, is

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.