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If m, r, x and y are positive, the ratio of m to r equal to the ratio x to y?

Is \(\frac{m}{r}=\frac{x}{y}\)? Is \(my=rx\)?

(1) the ratio of m to y is equal to the ratio of x to r --> \(\frac{m}{y}=\frac{x}{r}\) --> \(mr=xy\). Not sufficient.

(2) the ratio of m + x to r + y is equal to the ratio of x to y --> \(\frac{m+x}{r+y}=\frac{x}{y}\) --> cross multiply --> \(my+xy=rx+xy\) --> \(my=rx\). Sufficient.

Re: How do you solve this in 2 minutes? [#permalink]
14 May 2010, 19:38

1

This post received KUDOS

vannbj wrote:

If m, r, x, and y are positive is the ratio of m to r equal to the ratio of x to y? 1) the ratio of m to y is equal to the ratio of x to r 2) the ratio of m + x to r + y is equal to the ratio of x to y

A. statement 1 alone is sufficient but statement 2 is not sufficient B. statement 2 alone is sufficient but statement 1 is not sufficient C. Both statements Together are sufficient but neither is sufficient alone D. Each Statement alone is sufficient E. Statements 1 and 2 Together are not sufficient

Can anyone help me understand why 1 is insuff? I understand that when you cross multiply 1, you get mr=xy, while the question wants to see xr=my, which 2 provides. Still, I don't see the difference between mr=xy and xr=my.

Sorry for the poor explanation, I just don't understand why 2 is insuff.

Can anyone help me understand why 1 is insuff? I understand that when you cross multiply 1, you get mr=xy, while the question wants to see xr=my, which 2 provides. Still, I don't see the difference between mr=xy and xr=my.

Sorry for the poor explanation, I just don't understand why 2 is insuff.

Try digits. Let m=5 r=4 x=2 y=10

mr=xy (5*4=2*10), but xr not equal to my (2*4 and 5*10).

Re: If m, r, x, and y are positive, is the ratio of m to r equal [#permalink]
20 Dec 2011, 11:31

is the ratio of m to r equal to the ratio of x to y? or is m/r=x/y or is m/x=r/y Statement 1: m/y=x/r or m/x= y/r. So NO. Sufficient. Can Someone please tell, what am i doing wrong for statement 1.

Re: If m, r, x, and y are positive, is the ratio of m to r equal [#permalink]
06 Jan 2012, 20:43

1

This post received KUDOS

BDSunDevil wrote:

is the ratio of m to r equal to the ratio of x to y? or is m/r=x/y or is m/x=r/y Statement 1: m/y=x/r or m/x= y/r. So NO. Sufficient. Can Someone please tell, what am i doing wrong for statement 1.

I think you are assuming that r/y can never equal y/r. If y = 1, r = 1, then r/y = y/r.

Such values can show that Statement 1 is sufficient to answer the equation. However, for some other values, Statement 1 will not be sufficient to answer the question. That is why it is INSUFFICIENT.

Statement 2, on the other hand, will always be sufficient because after cross multiplication, the xy will cancel out from both sides of the equation, giving us only the equation my = xr. This is sufficient to answer the question regardless of the values that each of the variables takes. That is why it is SUFFICIENT.

Re: If m, r, x and y are positive, the ratio of m to r equal [#permalink]
09 Oct 2013, 12:43

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Re: If m, r, x and y are positive, the ratio of m to r equal [#permalink]
21 Oct 2014, 07:17

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