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If 5x = 4y, which of the following is NOT true?

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If 5x = 4y, which of the following is NOT true?  [#permalink]

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New post Updated on: 27 Feb 2017, 17:37
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A
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C
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Question Stats:

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If 5x = 4y, which of the following is NOT true?

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\)

(B) \(\frac{y}{(y – x)} = 5\)

(C) \(\frac{(x – y)}{y} = \frac{1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\)

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\)

Originally posted by vikasp99 on 26 Feb 2017, 19:31.
Last edited by mikemcgarry on 27 Feb 2017, 17:37, edited 1 time in total.
changed to proper fraction notation
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Re: If 5x = 4y, which of the following is NOT true?  [#permalink]

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New post 27 Feb 2017, 17:44
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vikasp99 wrote:
If 5x = 4y, which of the following is NOT true?

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\)

(B) \(\frac{y}{(y – x)} = 5\)

(C) \(\frac{(x – y)}{y} = \frac{1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\)

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\)

Dear vikasp99,

I'm happy to respond. :-)

There are many different ways to rearrange a ratio. The way I solved this was to scan down the list of answers. I noticed that (B) and (C) are close to reciprocals for each other, but the subtraction is in a reverse order between them. They can't both work for the values of x and y!

Think about it this way. Suppose x and y are both positive--they don't have to be, because they both could be negative, but let's just assume that they are positive. Each expression has to work for all numbers, so it must work for positive numbers! We know 5/4 = y/x, so y is a bigger positive number than x. Thus, (y - x) is positive, and (x - y) is negative.

Choice (B) has positive = positive
Choice (C) has negative = positive, so this is the one that doesn't work.

Thus, (C) is the answer.

(A), (B) (D), and (E) are all arithmetically legal rearrangements of the original equation.

Does all this make sense?
Mike :-)
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Re: If 5x = 4y, which of the following is NOT true?  [#permalink]

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New post 28 Feb 2017, 09:38
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vikasp99 wrote:
If 5x = 4y, which of the following is NOT true?

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\)

(B) \(\frac{y}{(y – x)} = 5\)

(C) \(\frac{(x – y)}{y} = \frac{1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\)

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\)


5x = 4y = 20 (Say)

So, x = 4 & y = 5

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\) ( True )

(B) \(\frac{y}{(y – x)} = 5\) ( True )


(C) \(\frac{(x – y)}{y} = \frac{-1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\) ( True )

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\) ( True )


Thus, answer must be (C)
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Re: If 5x = 4y, which of the following is NOT true?  [#permalink]

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New post 28 Feb 2017, 10:06
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vikasp99 wrote:
If 5x = 4y, which of the following is NOT true?

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\)

(B) \(\frac{y}{(y – x)} = 5\)

(C) \(\frac{(x – y)}{y} = \frac{1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\)

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\)


Another approach is to apply a nice (and often-tested) concept: \(\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}\)
For example: \(\frac{1 + 2}{5} = \frac{1}{5} + \frac{2}{5}\)

Given: 5x = 4y
Divide both sides by y to get: 5x/y = 4
Divide both sides by 5 to get: x/y = 4/5

Now let's examine each answer choice and apply the nice rule.
A) (x + y)/y = 9/5
(x + y)/y = x/y + y/y [here, we applied the above rule]
= x/y + 1
= 4/5 + 5/5
= 9/5
This checks out.

B) y/(y – x) = 5
In this case, the denominator is not a single expression, so we can't readily apply our rule.
So, let's IGNORE answer choice B for now.

C) (x – y)/y = 1/5
(x – y)/y = x/y - y/y [here, we applied the above rule]
= x/y - 1
= 4/5 - 5/5
= -1/5
No good!
Answer: C

Cheers,
Brent
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Re: If 5x = 4y, which of the following is NOT true?  [#permalink]

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New post 22 Aug 2018, 00:29
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vikasp99 wrote:
If 5x = 4y, which of the following is NOT true?

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\)

(B) \(\frac{y}{(y – x)} = 5\)

(C) \(\frac{(x – y)}{y} = \frac{1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\)

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\)


This is how I solved

Assign values to X and Y such that

5x = 4y, Here we could assign X as 4 and Y = 5

Now cross check ans

(A) (x+y)/y =9/5
=( 4+5)/5 = 9/5 SO its true

Similarly

(B) y/(y–x) =5
= 5( 5-4 ) = 5* 1 = 5 its true

(C) (x–y)/y =1/5
(4-5)/5 = -1/5 which is not the same as 1/5 hence its not true .
Ans = C





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Re: If 5x = 4y, which of the following is NOT true?   [#permalink] 22 Aug 2018, 00:29
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