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Current Student P
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In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

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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 ]

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Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

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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.

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Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

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Current Student D
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]

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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
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Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

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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.

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In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

### Show Tags 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.

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Re: In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

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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

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Re: In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

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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

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

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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 = $$\sqrt{3.75+1.5^2}$$=$$\sqrt{6}$$..
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Re: In the figure shown above, x is the length of side BD of triangle ABD  [#permalink]

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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=$$\sqrt{6}$$.

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Re: In the figure shown above, x is the length of side BD of triangle ABD.  [#permalink]

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