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

 It is currently 17 Oct 2019, 16:12

### 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

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

# What is the length of segment BC?

Author Message
TAGS:

### Hide Tags

SVP
Joined: 29 Aug 2007
Posts: 1946
What is the length of segment BC?  [#permalink]

### Show Tags

Updated on: 09 Oct 2019, 21:23
6
22
00:00

Difficulty:

65% (hard)

Question Stats:

49% (01:10) correct 51% (01:11) wrong based on 630 sessions

### HideShow timer Statistics

What is the length of segment BC?

(1) Angle ABC is 90 degrees.
(2) The area of the triangle is 30.

Attachment:

Triangle.jpg [ 28.62 KiB | Viewed 31428 times ]

_________________
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Originally posted by GMAT TIGER on 08 May 2008, 21:28.
Last edited by Bunuel on 09 Oct 2019, 21:23, edited 3 times in total.
Edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: What is the length of segment BC?  [#permalink]

### Show Tags

18 Jul 2012, 05:11
10
4
Responding to a pm.

What is the length of segment BC?

(1) Angle ABC is 90 degrees. $$BC=\sqrt{13^2-5^2}$$. Sufficient.

(2) The area of the triangle is 30. Consider the diagram below:
Attachment:

ABC.png [ 6.06 KiB | Viewed 16140 times ]
Notice that segment $$AB_2$$ is the mirror reflection of segment $$AB_1$$ around the vertical line passing through point A. Now, if the height of triangles $$ACB_1$$ and $$ACB_2$$ is $$\frac{60}{13}$$, then the area of both triangles is $$area=\frac{1}{2}*base*height=\frac{1}{2}*13*\frac{60}{13}=30$$. So, as you can see we can have different lengths of segment CB ($$CB_1$$ and $$CB_2$$). Not sufficient.

Hope it's clear.
_________________
##### General Discussion
Senior Manager
Joined: 24 Feb 2008
Posts: 333
Schools: UCSD ($) , UCLA, USC ($), Stanford
Re: What is the length of segment BC?  [#permalink]

### Show Tags

08 May 2008, 21:32
1
A

1. Suff since it's a 5-12-13 triangle
2. Insuff because the height to side 5, which can be calculated to be 12 may not necessarily be the leg.
_________________

Best AWA guide here: http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
CEO
Joined: 17 Nov 2007
Posts: 3071
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: What is the length of segment BC?  [#permalink]

### Show Tags

12 May 2008, 00:37
6
Hi all!

My 2 cents....

Let imagine AB and AC as sticks bounded in point A by a hinge. So, we can move AB relatively to AC and change angle BAC form 0 to 180. The area of ABC triangle will change form 0 (angle BAC=0) through maximum value 12*5*13=32.5 (angle BAC=90) to 0 (angle BAC=180). If you imagine that, It will be obvious that for 0<area<32.5 we will get two possible value of BC and for area=32.5 we will get only one value of BC. In our case area=30<32.5. Therefore, the second condition is insufficient.
_________________
HOT! GMAT Club Forum 2020 | GMAT ToolKit 2 (iOS) - The OFFICIAL GMAT CLUB PREP APPs, must-have apps especially if you aim at 700+ | Limited Online GMAT/GRE Math tutoring
Senior Manager
Joined: 06 Jan 2008
Posts: 435
Re: What is the length of segment BC?  [#permalink]

### Show Tags

15 May 2008, 09:14
2
What a bliss! I was being jerk!
For those who did not understand Walker's expln, check out this link.
(Interactive triangle)
http://www.mathopenref.com/heronsformula.html
For there are 2 triangles with the area 30.
1: 5,13,12 (For acute angle)
2: 5,13,15.5... (Not 15.5) ( For obtuse angle)
see the attachment. Thank you all
Attachments

traingle.doc [39.5 KiB]

Intern
Joined: 07 Jan 2005
Posts: 3
Location: New York
Re: What is the length of segment BC?  [#permalink]

### Show Tags

25 Aug 2009, 14:08
3
We can keep the fact in mind that triangles between two parallel lines have same area.(draw a line ll to AC / BC's value will vary and still satisfy the area being constant at 30 ,as base and height in this case are constant (AC) and distance between ll lines remain the same , which in this case would be the height of the triangle)

Heron's formula makes one jump to a quick conclusion about statement 2 being sufficient but an important point is overlooked by the fact using it to find the value of BC would give some polynomial ( x3 or x4 or whatever ....) and that will lead to multiple values of x
(at least 2 in this case ).
Hence insufficient.

Statement 1 is sufficient
Hence A
Intern
Status: NOT READY TO GIVE UP
Joined: 24 Apr 2013
Posts: 21
Location: India
Concentration: Strategy, Marketing
GMAT Date: 10-30-2013
WE: Engineering (Other)
Re: What is the length of segment BC?  [#permalink]

### Show Tags

12 Oct 2013, 21:08
hoping_for_stern wrote:
We can keep the fact in mind that triangles between two parallel lines have same area.(draw a line ll to AC / BC's value will vary and still satisfy the area being constant at 30 ,as base and height in this case are constant (AC) and distance between ll lines remain the same , which in this case would be the height of the triangle)

Heron's formula makes one jump to a quick conclusion about statement 2 being sufficient but an important point is overlooked by the fact using it to find the value of BC would give some polynomial ( x3 or x4 or whatever ....) and that will lead to multiple values of x
(at least 2 in this case ).
Hence insufficient.

Statement 1 is sufficient
Hence A

Answer Should Be "D" since area is equals= 0.5*A*B*SinQ; so from here we can get the included angle between the given two sides and then use Cosine law to get the third side easily.....

+1 KUDDUS if I'm Right
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: What is the length of segment BC?  [#permalink]

### Show Tags

13 Oct 2013, 03:40
himang wrote:
hoping_for_stern wrote:
We can keep the fact in mind that triangles between two parallel lines have same area.(draw a line ll to AC / BC's value will vary and still satisfy the area being constant at 30 ,as base and height in this case are constant (AC) and distance between ll lines remain the same , which in this case would be the height of the triangle)

Heron's formula makes one jump to a quick conclusion about statement 2 being sufficient but an important point is overlooked by the fact using it to find the value of BC would give some polynomial ( x3 or x4 or whatever ....) and that will lead to multiple values of x
(at least 2 in this case ).
Hence insufficient.

Statement 1 is sufficient
Hence A

Answer Should Be "D" since area is equals= 0.5*A*B*SinQ; so from here we can get the included angle between the given two sides and then use Cosine law to get the third side easily.....

+1 KUDDUS if I'm Right

That's not correct. The answer to this question is A, not D.

The formula you posted is correct: $$Area=\frac{1}{2}BA*CA*sinA$$ --> $$sinA=\frac{12}{13}$$, but from this we cannot calculate angle $$A$$, as $$sin A=Sin (180-A)$$. Meaning that this won't give us ONLY one value for angle A, thus we won't have ONLY one value for CB --> A can be acute angle, making B right angle AND making CB equal to 12 OR A can be obtuse angle, making B acute angle AND making CB greater then 12.

Check here: what-is-the-length-of-segment-bc-63639-20.html#p1105437

Hope it helps.
_________________
Manager
Joined: 18 May 2014
Posts: 54
Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
Re: What is the length of segment BC?  [#permalink]

### Show Tags

18 May 2014, 10:04
4
(1) Angle ABC is 90 degrees.
Since ABC is right angled at B, we can easily find the length of BC using Pythagoras Theorem; SUFFICIENT.

(2) The area of the triangle is 30.
Although Heron's formula is out of GMAT scope, but still let me clarify it here that why statement 2 is NOT sufficient.

Let us assume that BC = x
Then s = (5 + 13 + x)/2 = (18 + x)/2 = 9 + (x/2)
Now area of triangle, A = √[s(s - a)(s - b)(s - c)] or A² = [s(s - a)(s - b)(s - c)]
(30)² = [9 + (x/2)] * [9 + (x/2) - 5] * [9 + (x/2) - 13] * [9 + (x/2) - x]
900 = [9 + (x/2)] * [4 + (x/2)] * [-4 + (x/2)] * [9 - (x/2)]
900 = [81 - (x/2)²][(x/2)² - 16]
Let (x/2)² = y
900 = [81 - y][y - 16]
900 = 81y - y² + 16y - 1296
y² - 97y + 2196 = 0
y² - 36y - 61y + 2196 = 0
y(y - 36) - 61(y - 36) = 0
(y - 61)(y - 36) = 0
y = 36, 61
(x/2)² = 36, (x/2)² = 61, which clearly implies that we are getting 2 values of x, which means 2 values of BC. So, statement 2 is NOT sufficient.

I hope that helps.
Intern
Joined: 23 Apr 2014
Posts: 20
Re: What is the length of segment BC?  [#permalink]

### Show Tags

26 May 2015, 11:26
We dont know whether it is a right angle triangle
Hence stmt 1- ab is 9 not suff as we dont know the length of the other side
Stmt 2 also insuff similarly
Combining we get
The triangle can be 4 4 9 or 9 9 4 but 4 4 9 is not possible since the 3rd side of the triangle cannot be greater than the sum of the other two sides

Hence C
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15271
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the length of segment BC?  [#permalink]

### Show Tags

27 May 2015, 22:07
Hi kasturi72,

In Fact 1, we're told that angle ABC is a RIGHT ANGLE. With the two sides that we're given in the prompt (5 and 13), we CAN determine the length of the missing side (it's 12), so THAT information is SUFFICIENT to answer the question.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Joined: 15 Feb 2016
Posts: 59
GMAT 1: 710 Q48 V40
Re: What is the length of segment BC?  [#permalink]

### Show Tags

29 Aug 2016, 13:31
2
GMAT TIGER wrote:
Attachment:
Triangle.jpg
What is the length of segment BC?

(1) Angle ABC is 90 degrees.
(2) The area of the triangle is 30.

This is such a shrewd trap type. I hope to God I don't fall for it in the exam.

A alone is sufficient but when you come down to B you tend to use the information that you got from A. Also I was thinking how smart I am to already know the pythagorean triplet and Bam!
_________________
It is not who I am underneath but what I do that defines me.
Intern
Joined: 14 Jan 2019
Posts: 12
Re: What is the length of segment BC?  [#permalink]

### Show Tags

09 Oct 2019, 21:12
Hi, I believe the answer should be D. If we change the angle from 90 to any other angles the height changes and it can not keep the area 30 considering the length of 2 sides are 5 and 13.
Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: What is the length of segment BC?  [#permalink]

### Show Tags

09 Oct 2019, 21:20
emonmisra wrote:
Hi, I believe the answer should be D. If we change the angle from 90 to any other angles the height changes and it can not keep the area 30 considering the length of 2 sides are 5 and 13.

Please check under the spoiler in original post, OA is not D, it's A. Please read the thread to see WHY it's not D.
_________________
Manager
Joined: 28 Feb 2014
Posts: 171
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: What is the length of segment BC?  [#permalink]

### Show Tags

09 Oct 2019, 22:29
GMAT TIGER wrote:

What is the length of segment BC?

(1) Angle ABC is 90 degrees.
(2) The area of the triangle is 30.

Attachment:
Triangle.jpg

(1) If it is right angle triangle, we can consider pythagorean triplet 5-12-13. Sufficient
(2) We dont know the height of the given triangle and therefore cannot find BC. Insufficient

A is correct
Re: What is the length of segment BC?   [#permalink] 09 Oct 2019, 22:29
Display posts from previous: Sort by