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If point X is on line segment AB, all of the following may be true EXC

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V
Joined: 02 Sep 2009
Posts: 46129
If point X is on line segment AB, all of the following may be true EXC [#permalink]

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New post 06 Mar 2018, 21:58
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

88% (00:24) correct 12% (00:22) wrong based on 41 sessions

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Joined: 16 May 2017
Posts: 51
Location: India
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Re: If point X is on line segment AB, all of the following may be true EXC [#permalink]

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New post 07 Mar 2018, 08:50
[quote="Bunuel"]If point X is on line segment AB, all of the following may be true EXCEPT

(A) AX=XB

(B) AX > XB

(C) AX < XB

(D) AB > XB

(E) AX + XB < AB[/quote

IMO E since , length of AX + XB should be equal to AB,it cannot be less than AX+XB.
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If point X is on line segment AB, all of the following may be true EXC [#permalink]

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New post 25 Mar 2018, 06:28

Solution



The length of AX and XB may vary according to the placing of the point of X on the line segment AB.

To understand it more clearly, let us see the following cases:

(A) AX=XB
AX can be equal to XB if x is the mid-point of AB.

Image

(B) AX > XB[/u]

Image
(C) [u]AX < XB


Image
(D) AB > XB

If the point X lies inside the points, A and B, then AB >XB.

Image

(E) AX+XB<AB
    • If the point X lies inside the points, A and B, then as clear from the above diagrams that AX+XB is always equal to AB.

    • If points X lies outside A and B:
      o AX=AB+XB…….(1)
      o After addition of XB with AB, we get AX. Hence, AX is greater than AB.
         AX>XB
        Hence, AX+XB>AB.
Image
Answer: E
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If point X is on line segment AB, all of the following may be true EXC   [#permalink] 25 Mar 2018, 06:28
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If point X is on line segment AB, all of the following may be true EXC

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