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If x/y = c/d and d/c = b/a, which of the following must be true?
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18 Oct 2015, 12:57
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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?
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13 Oct 2017, 16:56
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




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Re: If x/y = c/d and d/c = b/a, which of the following must be true?
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18 Oct 2015, 13:19
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?
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18 Oct 2015, 22:12
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 TrueII. x/a = y/b TrueIII. y/a = x/b not always true answer choice C



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Re: If x/y = c/d and d/c = b/a, which of the following must be true?
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19 Oct 2015, 21:56
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?
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20 Oct 2015, 02:29
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?
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20 Oct 2015, 02:45
x/y = c/d = a/b.
option 1 & 2 are correct. Ans. c



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Re: If x/y = c/d and d/c = b/a, which of the following must be true?
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22 Oct 2015, 03:22
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
Answer is C



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Re: If x/y = c/d and d/c = b/a, which of the following must be true?
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10 Mar 2016, 03:02
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?
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28 Nov 2018, 16:35
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?
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21 Mar 2019, 17:58
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. Answer: C
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?
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22 Jul 2019, 12:49
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?
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15 Sep 2019, 19:25
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 Posted from my mobile device
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Re: If x/y = c/d and d/c = b/a, which of the following must be true?
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