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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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24 00:00

Difficulty:   15% (low)

Question Stats: 78% (01:31) correct 22% (01:54) wrong based on 1608 sessions

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If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Kudos for a correct solution.

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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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8
You can solve this by plugging in #s (see below):

QUESTION: $$\frac{x}{y}$$ = $$\frac{c}{d}$$ and $$\frac{d}{c}$$ = $$\frac{b}{a}$$

** REPHRASED: $$\frac{y}{x}$$ = $$\frac{d}{c}$$ = $$\frac{b}{a}$$

NOW, PLUG IN #S FOR VARIABLES:
> y=24, x=2, d=36, c=3, b=48, a=4 >> plug these into the *REPHRASED* above. don't you clearly see how each of these gives you a multiple of 12?

I. $$\frac{24}{2}$$ = $$\frac{48}{4}$$

II. $$\frac{2}{4}$$ = $$\frac{24}{48}$$

III. $$\frac{24}{4}$$ = $$\frac{2}{48}$$

Kudos please if you find this helpful General Discussion
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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1
Bunuel wrote:
If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Kudos for a correct solution.

x/y=c/d=a/b

I. y/x = b/a: TRUE
II. x/a = y/b: TRUE
III. y/a = x/b: Only when a=b

Ans: I+II => C
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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3
Bunuel wrote:
If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Kudos for a correct solution.

Here, y, d, c, and a are in denominator, so we can take them to be non zero and then rest would also be non zero

x/y = c/d and d/c = b/a
$$x/y = c/d = a/b$$

I. y/x = b/a True
II. x/a = y/b True
III. y/a = x/b not always true

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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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2
Bunuel wrote:
If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Kudos for a correct solution.

My Solution:

Given, x/y =c/d and d/c=b/a

If d/c=b/a then c/d =a/b, therefore we can say that x/y=a/b or y/x=b/a. Statement I is true

If x/y=a/b, then x/a=y/b. Statement II is true

As x/y=a/b, then y/a = x/b can't be true. So statement III is not true

Answer is Option C (I & II only)

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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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2
2
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

d/c = b/a implies c/d=a/b. Together with x/y = c/d --> x/y = c/d = a/b. So y/x= b/a(I is correct). By x/y = a/b --> bx=ay --> x/a = y/b(II is correct and III is not correct). The answer is, therefore, C.
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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x/y = c/d = a/b.

option 1 & 2 are correct. Ans. c
Intern  B
Joined: 25 Jul 2012
Posts: 24
Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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Given:

x/y=c/d or we can say: xd=cy or d/c=y/x --- 1

Given:

d/c=b/a --- 2

From 1 and 2, d/c=y/x=b/a

so we can say: y/x=b/a AND y/b=x/a

Manager  Joined: 03 Jan 2015
Posts: 72
Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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3
Substituting numbers for x,y,c,d,b and a is also a viable option.

Considering that $$\frac{x}{y} = \frac{c}{d}$$ $$, \frac{c}{d}$$ is a multiple of $$\frac{x}{y.}$$
Moreover, considering that $$\frac{d}{c} = \frac{b}{a}$$, $$\frac{d}{c}$$ is a multiple of $$\frac{b}{a}$$ but also the reciprocal of $$\frac{x}{y}$$.

So, let's consider the following: $$\frac{x}{y}$$ = $$\frac{4}{2}$$ = $$\frac{c}{d}$$= $$\frac{8}{4}$$ then $$\frac{d}{c}$$ = $$\frac{4}{8}$$ = $$\frac{b}{a}$$= $$\frac{8}{16}$$.

I. y/x = b/a
2/4 = 8/16 --> 2/4 is a multiple of 8/16 therefore TRUE
II. x/a = y/b
4/16 = 2/8 --> 4/16 is a multiple of 2/8 therefore TRUE
III. y/a = x/b
2/16 does not equal 4/8 therefore NOT TRUE.

Only I and II are true. The correct answer is C.
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If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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LakerFan24 wrote:
You can solve this by plugging in #s (see below):

QUESTION: $$\frac{x}{y}$$ = $$\frac{c}{d}$$ and $$\frac{d}{c}$$ = $$\frac{b}{a}$$

** REPHRASED: $$\frac{y}{x}$$ = $$\frac{d}{c}$$ = $$\frac{b}{a}$$

NOW, PLUG IN #S FOR VARIABLES:
> y=24, x=2, d=36, c=3, b=48, a=4 >> plug these into the *REPHRASED* above. don't you clearly see how each of these gives you a multiple of 12?

I. $$\frac{24}{2}$$ = $$\frac{48}{4}$$

II. $$\frac{2}{4}$$ = $$\frac{24}{48}$$

III. $$\frac{24}{4}$$ = $$\frac{2}{48}$$

Kudos please if you find this helpful This is the only approach I was able to follow.

Can someone kindly explain to me the OG's solution?
They solve for statement ii as follows:

ii. since y/x = b/a
x*(y/x = b/a)
y= xb/a
therefore ay = bx
thus y/b = x/a

I thought we couldn't infer the signs (pos/neg) of variables in questions like this?
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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Bunuel wrote:
If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Kudos for a correct solution.

We can use some convenient numbers:

x = 2, y = 3

c = 4, d = 6

b = 12, a = 8

Now we can analyze each Roman numeral:

I. 3/2 = 12/8 ?

3/2 = 3/2 → I is true.

II. 2/8 = 3/12 ?

1/4 = 1/4 → II is true.

III. 3/8 = 2/12 ?

3/8 ≠ 1/6 → III is not True.

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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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if you know properties of rations and proportions like Invertendo, etc. it becomes easier to solve this question
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?  [#permalink]

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Bunuel wrote:
If x/y = c/d and d/c = b/a, which of the following must be true?

I. y/x = b/a
II. x/a = y/b
III. y/a = x/b

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

Kudos for a correct solution.

x/y = c/d= a/b

1. y/x = b/a
True

2. x/a=y/b
True

3. y/a=x/b
Not true
Since
y/b = x/a

IMO C

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E-mail : kinshook.chaturvedi@gmail.com Re: If x/y = c/d and d/c = b/a, which of the following must be true?   [#permalink] 15 Sep 2019, 19:25
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