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In the figure shown above, x is the length of side BD of triangle ABD.
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25 Feb 2016, 04:05
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13
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00:00
A
B
C
D
E
Difficulty:
65%
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Question Stats:
62%
(01:50)
correct
38%
(02:22)
wrong
based on 170
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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
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired.
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Re: In the figure shown above, x is the length of side BD of triangle ABD.
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25 Feb 2016, 04:16
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Expert Reply
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
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.
Re: In the figure shown above, x is the length of side BD of triangle ABD.
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04 Apr 2016, 14:11
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 _________________
Re: In the figure shown above, x is the length of side BD of triangle ABD.
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05 Apr 2016, 08:51
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.
In the figure shown above, x is the length of side BD of triangle ABD
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11 Nov 2016, 04:39
Expert Reply
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. _________________
Re: In the figure shown above, x is the length of side BD of triangle ABD
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11 Nov 2016, 09:46
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.
Re: In the figure shown above, x is the length of side BD of triangle ABD
[#permalink]
11 Nov 2016, 15:35
2
Kudos
Expert Reply
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
In the figure shown above, x is the length of side BD of triangle ABD.
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11 Nov 2016, 19:13
Expert Reply
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..
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 = \(\sqrt{3.75+1.5^2}\)=\(\sqrt{6}\).. _________________
Re: In the figure shown above, x is the length of side BD of triangle ABD
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11 Nov 2016, 19:38
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=\(\sqrt{6}\).
Thanks in advance!!
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Re: In the figure shown above, x is the length of side BD of triangle ABD.
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19 Apr 2021, 11:56
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