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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]

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14 May 2010, 19:38

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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]

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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]

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06 Jan 2012, 20:43

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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]

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03 Oct 2015, 08:51

I too have my doubts related to first option being insufficient. All we need to answer in yes or no way.. Then why statement 1 is insufficient??\ Please provide an explanation...

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

We can rephrase this as . . . REPHRASED target question:Does m/r = x/y?

We may find it useful to take the equation m/r = x/y and cross-multiply to get my = rx. This allows us to rephrase the target question in one more way . . . RE-REPHRASED target question:Does my = rx?

Statement 1: The ratio of m to y is equal to ratio of x to r In other words, m/y = x/r This LOOKS similar to m/r = x/y (one of our target questions), but it is not the same. There are several values of m, r, x and y that satisfy this condition. Here are two: Case a: m = r = x = y = 1, in which case m/r = x/y Case b: m = 1, y = 2, x = 3 and r = 6, in which case m/r ≠ x/y Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The ratio of m+x to r+y is equal to the ratio of x to y. In other words, (m+x)/(r+y) = x/y Cross multiply to get: y(m+x) = x(r+y) Expand: ym + yx = xr + xy Subtract xy from both sides to get: ym = xy Perfect, we've shown that ym = xy, and this is one of our REPHRASED target questions. Since we can answer the RE-REPHRASED target question with certainty, statement 2 is SUFFICIENT