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# If A, B, C, and D are positive numbers such that the ratio of A to B

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Joined: 02 Sep 2009
Posts: 56306
If A, B, C, and D are positive numbers such that the ratio of A to B  [#permalink]

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28 Mar 2018, 02:58
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25% (medium)

Question Stats:

82% (01:53) correct 18% (02:54) wrong based on 41 sessions

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If A, B, C, and D are positive numbers such that the ratio of A to B is 3 to 4, the ratio of B to D is 8 to 5, and the ratio of C to D is 3 to 2, what is the ratio of A to C?

(A) 4 to 5
(B) 5 to 4
(C) 5 to 9
(D) 9 to 5
(E) 16 to 5

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Re: If A, B, C, and D are positive numbers such that the ratio of A to B  [#permalink]

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28 Mar 2018, 03:24
Bunuel wrote:
If A, B, C, and D are positive numbers such that the ratio of A to B is 3 to 4, the ratio of B to D is 8 to 5, and the ratio of C to D is 3 to 2, what is the ratio of A to C?

(A) 4 to 5
(B) 5 to 4
(C) 5 to 9
(D) 9 to 5
(E) 16 to 5

We'll expand the ratios to a common multiple to solve the question.
This is a Precise approach.

We'll first write things out clearly:
A:B = 3:4
B:D = 8:5
C:D = 3:2

We can comapre A:B to B:D by multiplying A:B by 2 --> A:B:D = 6:8:5
We can next compare B:D to C:D by multiplying C:D by 2.5 --> C:D = 7.5:5 so B:C:D = 8: 7.5 : 5
Then A:C = 6 : 7.5 = 12:15 = 4:5

(A) is our answer.
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Re: If A, B, C, and D are positive numbers such that the ratio of A to B  [#permalink]

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29 Mar 2018, 17:36
Bunuel wrote:
If A, B, C, and D are positive numbers such that the ratio of A to B is 3 to 4, the ratio of B to D is 8 to 5, and the ratio of C to D is 3 to 2, what is the ratio of A to C?

(A) 4 to 5
(B) 5 to 4
(C) 5 to 9
(D) 9 to 5
(E) 16 to 5

We have the following:

A : B = 3 : 4

Multiplying by 2, we have:

A : B = 6 : 8

and

B : D = 8 : 5

Thus:

A : D = 6 : 5

We also are given that:

C : D = 3 : 2

Multiplying A to D ratio by 2 and C to D ratio by 5, we have:

A : D = 12 : 10

and

C : D = 15 : 10

So, A : C = 12 : 15 = 4 : 5.

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Re: If A, B, C, and D are positive numbers such that the ratio of A to B   [#permalink] 29 Mar 2018, 17:36
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# If A, B, C, and D are positive numbers such that the ratio of A to B

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