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Point A, B, and C all lie on a line. Point D is the midpoint of and E
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14 Feb 2023, 07:29
14 Feb 2023, 07:29
1
Expert Reply
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Question Stats:
71% (01:34) correct
28% (02:47) wrong based on 14 sessions
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Point A, B, and C all lie on a line. Point D is the midpoint of \(\overline{AB}\) and E is the midpoint of BC; \(\overline{AB}=4\) and \(\overline{BC}=10\). Which of the following could be the length of \(\overline{AE}\)?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Re: Point A, B, and C all lie on a line. Point D is the midpoint of and E
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19 Feb 2023, 14:06
19 Feb 2023, 14:06
1
Expert Reply
OE
The trick to this problem is recognizing that there is more than one possible arrangement for the points on the number line. Because BC is longer than AB, A could be either in between B and C or on one side of B with C on the other side of B,
Using the information about the midpoints (D and E) and the lengths of the line segments, you can fill in all the information for the two number lines:
GRE (3).jpg [ 7.7 KiB | Viewed 966 times ]
You can see that AE has two possible lengths: 1 and 9, however 1 is the only option that is an answer choice.
The trick to this problem is recognizing that there is more than one possible arrangement for the points on the number line. Because BC is longer than AB, A could be either in between B and C or on one side of B with C on the other side of B,
Using the information about the midpoints (D and E) and the lengths of the line segments, you can fill in all the information for the two number lines:
Attachment:
GRE (3).jpg [ 7.7 KiB | Viewed 966 times ]
You can see that AE has two possible lengths: 1 and 9, however 1 is the only option that is an answer choice.
gmatclubot
Re: Point A, B, and C all lie on a line. Point D is the midpoint of and E [#permalink]
19 Feb 2023, 14:06
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