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Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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05 May 2011, 08:37
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Let d > c > b > a. If c is twice as far from a as it is from d, and b is twice as far from c as it is from a, then (d  b)/(d  a) = ? A. 2/9 B. 1/3 C. 2/3 D. 7/9 E. 3/2
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Last edited by Bunuel on 19 Nov 2013, 03:05, edited 1 time in total.
Renamed the topic and edited the question.

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Re: If d > c > b > a [#permalink]
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05 May 2011, 08:44
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Draw a number line and label with x and y. You would have: a b c d    y 2y x  2x Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y. Now you can calculate d b and d a d  b= x +2y = 7/2 y d  a = x + 2x = 3x = 9/2y Dividing both you get: 7/9 Answer D
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Re: If d > c > b > a [#permalink]
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05 May 2011, 09:06
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Better to draw a number line, from 1st statement > ca = 2x and dc = x; da = 3x from 2nd statement > ba = y and cb = 2y i.e. ca = y+2y = 3y
From the 2 underlined eqs; 2x = 3y
d  b = x + 2y (dc = x and cb = 2y) d a = 3x
d  b/da = x + 2y/3x
substituting the value, = 7x/9x = 7/9 Answer is D.

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Re: If d > c > b > a [#permalink]
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05 May 2011, 17:34
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<2x><x> abcd
<y><2y>
3y = 2x
\((db)/(da) = (3xy)/(3x) = 7/9\)
Answer is D.

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Re: If d > c > b > a [#permalink]
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11 May 2011, 08:06
I tried algebra, took me some time to figure out. c  a = 2(dc) => 3c = 2d + a cb = 2(ba) => c + 2a = 3b d  a = d  (3c  2d) = 3d  3c d  b = d  (c+2a)/3 = (3d  c  2a)/3 = [3d  c  2(3c  2d)]/3 = (7d  7c)/3 => (db)/(da) = 7/3/3 = 7/9 Answer  D
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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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kannn wrote: Let d > c > b > a. If c is twice as far from a as it is from d, and b is twice as far from c as it is from a, then (d  b)/(d  a) = ?
A. 2/9 B. 1/3 C. 2/3 D. 7/9 E. 3/2 OK, this may get a bit complicated I suggest giving variables 'x' and 'y' to each and then solve. We don't even need smart numbers for this one So we have a(y)b(2y)c(x)d (2x) Now we have that 3y = 2x So, y = 2x/3 db/da = 3xy/3x which will translate to 1  y/3x Replace y and one will get 7/9 Answer is thus D Hope it helps! Cheers! J

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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06 May 2014, 16:38
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For me this problem turns easy if we pick up some numbers. For example, lets start assuming that a = 0 and c = 6
If c is twice as far from a as it is from d, then d should be 9. acd 0 6 9
Then we have that b is twice as far from c as it is from a, so b must be 2 abcd 0 2 6 9
Then just replace: (92)/9=7/9

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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08 Jul 2014, 07:59
Let a=0 d=3x c=2x b=2x/3 solve as per the relation = 7/9
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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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10 Jul 2014, 10:32
Nayimoni wrote: Draw a number line and label with x and y. You would have:
a b c d    y 2y x  2x
Before calculating recognize it would be more effcient to express x or y in terms of the other. here 2x = 3y so x =3/2 y.
Now you can calculate d b and d a
d  b= x +2y = 7/2 y
d  a = x + 2x = 3x = 9/2y
Dividing both you get: 7/9
Answer D Hi I could not understand highlighted part...Can you pls elaborate ??? Thanks

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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30 Nov 2014, 12:44
kannn wrote: Let d > c > b > a. If c is twice as far from a as it is from d, and b is twice as far from c as it is from a, then (d  b)/(d  a) = ?
A. 2/9 B. 1/3 C. 2/3 D. 7/9 E. 3/2 When i first wrote two equations 2(dc) = ca & 2(ba) = bc and tried to solve, i realized its taking a lot of time...hence shifted to plugin method
Let a=1 b=2 ...hence c = 4 d=5.5 from the given realtionship.
So db / da = 3.5/4.5 = 7/9
Hence Answer D. Please give kudos, if this helps.

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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03 Dec 2014, 05:49
jlgdr wrote: kannn wrote: Let d > c > b > a. If c is twice as far from a as it is from d, and b is twice as far from c as it is from a, then (d  b)/(d  a) = ?
A. 2/9 B. 1/3 C. 2/3 D. 7/9 E. 3/2 OK, this may get a bit complicated I suggest giving variables 'x' and 'y' to each and then solve. We don't even need smart numbers for this one So we have a(y)b(2y)c(x)d (2x) Now we have that 3y = 2x So, y = 2x/3 db/da = 3xy/3x which will translate to 1  y/3x Replace y and one will get 7/9 Answer is thus D Hope it helps! Cheers! J Hello, could you explain these steps? db/da = 3xy/3x which will translate to 1  y/3x Replace y and one will get 7/9 Kind regards, Lax

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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17 Jan 2015, 09:11
Spidy001 wrote: <2x><x> abcd
<y><2y>
3y = 2x
\((db)/(da) = (3xy)/(3x) = 7/9\)
Answer is D. awesome !! Kudos !!
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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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17 Jan 2015, 12:44
Ans D
take distance between c and d as x=>distance between b and c is 2x take distance between a and b as y=>distance between a and c is 2y
with this we will get 3y=2x
BD = X+4X/3 = 7x/3
AD= 3X
=>BD/AD = 7/9

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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13 Jan 2016, 09:22
Number line says that ratio is 1>x>2/3
only option is 7/9
D

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Re: Let d > c > b > a. If c is twice as far from a as it is from [#permalink]
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