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shashankism
Bunuel
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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shashankism
Bunuel
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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Bunuel
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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