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

 It is currently 05 Dec 2019, 12:47

### 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

# In the figure shown above, x is the length of side BD of triangle ABD.

Author Message
Current Student
Status: Chasing my MBB Dream!
Joined: 29 Aug 2012
Posts: 1096
Location: United States (DC)
WE: General Management (Aerospace and Defense)
In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

25 Feb 2016, 05:05
1
10
00:00

Difficulty:

65% (hard)

Question Stats:

63% (01:23) correct 37% (01:48) wrong based on 209 sessions

### HideShow timer Statistics

In the figure shown above, x is the length of side BD of triangle ABD. If D is a point that lies on line AC and x is an integer, what is the value of x?
A 2
B 3
C 4
D Either 3 or 4
E Cannot be determined

Attachment:

Problem.PNG [ 11.92 KiB | Viewed 3178 times ]

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Become a GMAT Club Premium member to unlock discounts

MBA, Class of 2020,
Math Expert
Joined: 02 Sep 2009
Posts: 59561
Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

25 Feb 2016, 05:16
2
2
Gnpth wrote:

In the figure shown above, x is the length of side BD of triangle ABD. If D is a point that lies on line AC and x is an integer, what is the value of x?
A 2
B 3
C 4
D Either 3 or 4
E Cannot be determined

Attachment:
Problem.PNG

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

For triangle ABD: (2 - 2) < x < (2 + 2) --> 0 < x < 4;
For triangle BCD: (4 - 2) < x < (4 + 2) --> 2 < x < 6.

From above: 2 < x < 4. Since x is an integer then x = 3.

Intern
Joined: 09 Mar 2016
Posts: 18
WE: Information Technology (Computer Software)
Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

24 Mar 2016, 00:00
Current Student
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

04 Apr 2016, 15:11
Superb Question Team E-gmat => here from the two triangles using the triangle inequality law => x => 1,2,3 or 3,4,5 => x=3 is the only intersection..
Hence B
_________________
Manager
Joined: 09 Jul 2013
Posts: 107
Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

05 Apr 2016, 09:51
First, we know that the length can be determined, since with the measures given, the triangles are well defined. We have an isosceles triangle with two sides of length 4 and one side of length 2. The line BD bisecting AC can only have one possible length. So answers D and E are out.

Now, line BD can't have a length of 4, since it would have to be on top of BC for that to be true. Answer C is out.

If BD had a length of 2, then triangle ABD would be an equilateral triangle, with each interior angle = 60. But we know that angle BAD > 60 since triangle ABC is isosceles, and AB is the short side. Answer A is out.

_________________
Dave de Koos
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

### Show Tags

11 Nov 2016, 05:39

In the figure shown above, $$x$$ is the length of side $$BD$$ of triangle $$ABD$$. If $$D$$ is a point that lies on line $$AC$$ and $$x$$ is an integer, what is the value of $$x$$?

A. $$2$$
B. $$3$$
C. $$4$$
D. Both $$3$$ and $$4$$ are possible values for $$x$$
E. Cannot be determined

Take a stab at this fresh question from e-GMAT. Post your analysis below.

Official Solution to be provided after receiving some good analyses.
_________________
Manager
Joined: 28 Jun 2016
Posts: 205
Concentration: Operations, Entrepreneurship
Re: In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

### Show Tags

11 Nov 2016, 10:46
EgmatQuantExpert wrote:

In the figure shown above, $$x$$ is the length of side $$BD$$ of triangle $$ABD$$. If $$D$$ is a point that lies on line $$AC$$ and $$x$$ is an integer, what is the value of $$x$$?

A. $$2$$
B. $$3$$
C. $$4$$
D. Both $$3$$ and $$4$$ are possible values for $$x$$
E. Cannot be determined

Take a stab at this fresh question from e-GMAT. Post your analysis below.

Official Solution to be provided after receiving some good analyses.

AB=2 and BC=4

So 2<=x<4

So x can be 2 or 3.

Now consider triangle BCD.

4-2<x<4+2

2<x<6

From above statements, definitely x has to be 3.

IMO B

Sent from my iPhone using GMAT Club Forum mobile app
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4121
Re: In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

### Show Tags

11 Nov 2016, 16:35
2
Top Contributor
EgmatQuantExpert wrote:

In the figure shown above, $$x$$ is the length of side $$BD$$ of triangle $$ABD$$. If $$D$$ is a point that lies on line $$AC$$ and $$x$$ is an integer, what is the value of $$x$$?

A. $$2$$
B. $$3$$
C. $$4$$
D. Both $$3$$ and $$4$$ are possible values for $$x$$
E. Cannot be determined

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .
difference between sides A and B < third side < sum of sides A and B

Consider ∆ABC
The two known sides have lengths 2 and 2
So, applying the above rule, 2 - 2 < x < 2 + 2
In other words, 0 < x < 4
IMPORTANT: We're told that x is an integer.
So the possible values of x are 1, 2 and 3

Now consider ∆BDC
The two known sides have lengths 4 and 2
So, applying the above rule, 4 - 2 < x < 4 + 2
In other words, 2 < x < 6
Since x is an integer, the possible values of x are 3, 4, and 5

So, x must be 1, 2 or 3 AND x must be 3, 4 or 5
Since x = 3 is the only value that satisfies both conditions, x must equal 3

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Math Expert
Joined: 02 Aug 2009
Posts: 8282
In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

11 Nov 2016, 20:13
EgmatQuantExpert wrote:

In the figure shown above, $$x$$ is the length of side $$BD$$ of triangle $$ABD$$. If $$D$$ is a point that lies on line $$AC$$ and $$x$$ is an integer, what is the value of $$x$$?

A. $$2$$
B. $$3$$
C. $$4$$
D. Both $$3$$ and $$4$$ are possible values for $$x$$
E. Cannot be determined

Take a stab at this fresh question from e-GMAT. Post your analysis below.

Official Solution to be provided after receiving some good analyses.

My analysis
1) there can only be one value of x, be it integer or noninteger ..
2) the value of x should be $$\sqrt{6}$$..
3) would look forward for your solution that makes 3 as answer..

Chetan...

acegmat123 now on why answer shud be $$\sqrt{6}$$

Drop a perpendicular from B to AD, say at E..
From ∆ABE and ∆BCE, you can find AE by equating BE in both..
AE is 0.5..
Take ∆ABE, AB is 2, AE is 0.5,so BE will be $$\sqrt{3.75}$$...
Now in ∆BDE, BE is $$\sqrt{3.75}$$, DE is 1.5, so BD or x = $$\sqrt{3.75+1.5^2}$$=$$\sqrt{6}$$..
_________________
Manager
Joined: 28 Jun 2016
Posts: 205
Concentration: Operations, Entrepreneurship
Re: In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

### Show Tags

11 Nov 2016, 20:38
chetan2u wrote:
EgmatQuantExpert wrote:

In the figure shown above, $$x$$ is the length of side $$BD$$ of triangle $$ABD$$. If $$D$$ is a point that lies on line $$AC$$ and $$x$$ is an integer, what is the value of $$x$$?

A. $$2$$
B. $$3$$
C. $$4$$
D. Both $$3$$ and $$4$$ are possible values for $$x$$
E. Cannot be determined

Take a stab at this fresh question from e-GMAT. Post your analysis below.

Official Solution to be provided after receiving some good analyses.

My analysis
1) there can only be one value of x, be it integer or noninteger ..
2) the value of x should be $$\sqrt{6}$$..
3) would look forward for your solution that makes 3 as answer..

Chetan...

Can you please explain how you got x=$$\sqrt{6}$$.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Non-Human User
Joined: 09 Sep 2013
Posts: 13709
Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

### Show Tags

02 Apr 2018, 08:10
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: In the figure shown above, x is the length of side BD of triangle ABD.   [#permalink] 02 Apr 2018, 08:10
Display posts from previous: Sort by