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C is the midpoint of line segment AE and B is the midpoint of line

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C is the midpoint of line segment AE and B is the midpoint of line  [#permalink]

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New post 12 Jul 2017, 23:28
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

98% (01:44) correct 2% (00:47) wrong based on 66 sessions

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Posts: 188
Re: C is the midpoint of line segment AE and B is the midpoint of line  [#permalink]

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New post 13 Jul 2017, 01:22
Bunuel wrote:
C is the midpoint of line segment AE and B is the midpoint of line segment AC. If D is a point between A and E so that the length of AB equals the length of DE, what is the ratio "length of CD/length of AC"?

(A) 4/1
(B) 2/1
(C) 3/4
(D) 1/2
(E) 1/4



the answer is D

let total length be 12

AC = 6
AB = 3
DE = 3
CD= 3

CD/AC = 1/2
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Re: C is the midpoint of line segment AE and B is the midpoint of line  [#permalink]

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New post 13 Jul 2017, 02:26
Bunuel wrote:
C is the midpoint of line segment AE and B is the midpoint of line segment AC. If D is a point between A and E so that the length of AB equals the length of DE, what is the ratio "length of CD/length of AC"?

(A) 4/1
(B) 2/1
(C) 3/4
(D) 1/2
(E) 1/4


C is the midpoint of line AE...
Let AC = CE = 2x
A.................2x................C.................2x...................E

B is the midpoint of line segment AC.
AB = BC = AC/2 = x

A........x........B........x........C.................2x..................E

Now, D is a point between A & E. Also AB = DE = x, CD CE - DE = 2x - x = x

So, A........x........B........x........C........x........D.......x........E
CD = x
AC = 2x

CD/AC = 1/2

Answer D
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Re: C is the midpoint of line segment AE and B is the midpoint of line  [#permalink]

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New post 13 Jul 2017, 02:55
shashankism wrote:
Bunuel wrote:
C is the midpoint of line segment AE and B is the midpoint of line segment AC. If D is a point between A and E so that the length of AB equals the length of DE, what is the ratio "length of CD/length of AC"?

(A) 4/1
(B) 2/1
(C) 3/4
(D) 1/2
(E) 1/4


C is the midpoint of line AE...
Let AC = CE = 2x
A.................2x................C.................2x...................E

B is the midpoint of line segment AC.
AB = BC = AC/2 = x

A........x........B........x........C.................2x..................E

Now, D is a point between A & E. Also AB = DE = x, CD CE - DE = 2x - x = x

So, A........x........B........x........C........x........D.......x........E
CD = x
AC = 2x

CD/AC = 1/2

Answer D



Hi Shashankism

I solved it this way. Is it a valid way to solve this question?


Let the length be 1.

A___________B_____________C_____________D____________E


As C is the midpoint of line AE, AC=CE= 1/2

As B is the midpoint of line AC, AB=BC=1/4

We are also given that D is a point between A and E and also AB=DE=1/4

So I assume that D is also the midpoint of CE.


Therefore the ratio is: 1/4*2/1= 1/2
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Re: C is the midpoint of line segment AE and B is the midpoint of line  [#permalink]

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New post 13 Jul 2017, 03:07
1
Shiv2016 wrote:
shashankism wrote:
Bunuel wrote:
C is the midpoint of line segment AE and B is the midpoint of line segment AC. If D is a point between A and E so that the length of AB equals the length of DE, what is the ratio "length of CD/length of AC"?

(A) 4/1
(B) 2/1
(C) 3/4
(D) 1/2
(E) 1/4


C is the midpoint of line AE...
Let AC = CE = 2x
A.................2x................C.................2x...................E

B is the midpoint of line segment AC.
AB = BC = AC/2 = x

A........x........B........x........C.................2x..................E

Now, D is a point between A & E. Also AB = DE = x, CD CE - DE = 2x - x = x

So, A........x........B........x........C........x........D.......x........E
CD = x
AC = 2x

CD/AC = 1/2

Answer D



Hi Shashankism

I solved it this way. Is it a valid way to solve this question?


Let the length be 1.

A___________B_____________C_____________D____________E


As C is the midpoint of line AE, AC=CE= 1/2

As B is the midpoint of line AC, AB=BC=1/4

We are also given that D is a point between A and E and also AB=DE=1/4

So I assume that D is also the midpoint of CE.


Therefore the ratio is: 1/4*2/1= 1/2



Yes surely its a valid way to solve the problem.. But I would recommend you to take the length of AE as 4 or 8 instead of 1. As you know, you are going to divide it by 2 and again by 2 .. So better take the value in multiple of 4. The best value to be used is 4.

Also you have to reach answer somehow in the fastest possible way, so you can always use the method which u like and are very comfortable with.
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Re: C is the midpoint of line segment AE and B is the midpoint of line  [#permalink]

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New post 13 Jul 2017, 05:04
Bunuel wrote:
C is the midpoint of line segment AE and B is the midpoint of line segment AC. If D is a point between A and E so that the length of AB equals the length of DE, what is the ratio "length of CD/length of AC"?

(A) 4/1
(B) 2/1
(C) 3/4
(D) 1/2
(E) 1/4


According to question it seems that AB=BC=CD=DE
therefore the ratio will be 1/2
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Re: C is the midpoint of line segment AE and B is the midpoint of line   [#permalink] 13 Jul 2017, 05:04
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C is the midpoint of line segment AE and B is the midpoint of line

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