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# If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

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Math Expert
Joined: 02 Sep 2009
Posts: 43792
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a? [#permalink]

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12 Oct 2017, 02:40
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Question Stats:

72% (00:54) correct 28% (00:45) wrong based on 43 sessions

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If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

A. 1 : 3
B. 3 : 1
C. 3 : 4
D. 1 : 1
E. 4 : 3
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43792
Re: If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a? [#permalink]

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12 Oct 2017, 02:46
Bunuel wrote:
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

A. 1 : 3
B. 3 : 1
C. 3 : 4
D. 1 : 1
E. 4 : 3

$$\frac{1}{2}*b = c$$, thus $$b = 2c$$;
$$a = 2b = 4c$$.
$$4c = 3d$$, thus $$d = \frac{4c}{3}$$.

$$\frac{d}{a}=\frac{\frac{4c}{3}}{4c}=\frac{4c}{3}*\frac{1}{4c}=\frac{1}{3}$$.

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VP
Joined: 26 Mar 2013
Posts: 1427
Re: If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a? [#permalink]

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12 Oct 2017, 03:06
Bunuel wrote:
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

A. 1 : 3
B. 3 : 1
C. 3 : 4
D. 1 : 1
E. 4 : 3

Let b=6.......then a =12, c=3, d=4

$$\frac{d}{a} =\frac{4}{12}= \frac{1}{3}$$

VP
Joined: 22 May 2016
Posts: 1329
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a? [#permalink]

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12 Oct 2017, 08:21
Bunuel wrote:
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

A. 1 : 3
B. 3 : 1
C. 3 : 4
D. 1 : 1
E. 4 : 3

a is the greatest of three:
a = 2b, b = 2c, so a > c

d's relation to a is not evident in an instant, so I picked a larger multiple of the coefficients 2, 3, and 4

Let a = 36
a = 2b
36 = 2b
b = 18

1/2 * b = c
b = 2c
18 = 2c
c = 9

4c = 3d
36 = 3d
d = 12

Ratio of d to a

$$\frac{12}{36} =\frac{1}{3} = (1:3)$$

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Re: If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a? [#permalink]

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16 Oct 2017, 15:47
Bunuel wrote:
If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?

A. 1 : 3
B. 3 : 1
C. 3 : 4
D. 1 : 1
E. 4 : 3

We can multiply the equation 1/2*b = c by 4 and we have:

2b = 4c

Since a = 2b:

a = 4c

Since 4c = 3d:

3d = a

So, d/a = 1/3

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Re: If a = 2b, 1/2*b = c, and 4c = 3d, then what is the ratio of d to a?   [#permalink] 16 Oct 2017, 15:47
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