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

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.

Answer: B.
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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.

Answer: B

Let me first start off by saying that I got B, so if that is incorrect, you can ignore the rest of my post!

I put each ratio into fractions, and cross multiplied. The stem asks does m/r=x/y or in other terms, does ym=rx?

In st1, we are told m/y=x/r or rm=yx. Insuf.

In st2, we are told (m+x)/(r+y)=x/y or ym+yx=rx+yx -> ym=rx. Suff

We have: \(\frac{a}{b}=\frac{c}{d}= \frac{a-c}{b-d}= \frac{a+c}{b+d}= \frac{a+kc}{b+kd}\)
1) insuf
2) \(\frac{m+x}{r+y} =\frac{x}{y}= \frac{m+x-x}{r+y-y} = \frac{m}{r}\) suff

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).

1) m/y = x/r
mr = xy
insufficient

2) [m+x]/[r+y] = x/y
my + xy = rx + xy
my = rx
m/r = x/y
Sufficient
Ans. B
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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.

1) m/y = x/r
mr = xy
insufficient

2) [m+x]/[r+y] = x/y
my + xy = rx + xy
my = rx
m/r = x/y
Sufficient
Ans. B

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...

Hi varundixitmro2512,

You can TEST VALUES to prove that Fact 1 is insufficient. Here's how:

We're told that M, R, X and Y are POSITIVE. We're asked if M/R = X/Y. This is a YES/NO question.

1) M/Y = X/R

IF...
M = 1
Y = 1
X = 1
R = 1
Then the answer to the question.... Is 1/1 = 1/1? is YES.

IF...
M = 2
Y = 2
X = 1
R = 1
Then the answer to the question.... Is 2/1 = 1/2? is NO.
Fact 1 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

is m/r = x/y?? or is ym= rx or r = ym/x

FROM 1

m/y = x/r , mr = yx or r = yx/m true only if m=x...which we dont know .... insuff

from 2

m+x/r+y = x/y ...... this implies that m/r is in proportion to x/y i.e. m/r = x/y

to add each of the nominators and the denominators of 2 fractions to yield one of them then they must be equal .

B

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

Answer = B

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Bunnel shouldnt A be sufficent as well.. since it asks is my=xr the answer proves that my is not equal to xr hence A should be sufficent

\(mr=xy\) is not enough to say that \(my=rx\) is not true. For example, if \(m=r=x=y=1\), then both \(mr=xy\) and \(my=rx\) are true.
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hey , thanks for the explanation.
just one small query i got the answer but was just thinking aren't we getting a confirm "NO" answer from option A.
hence satisfied.

\(mr=xy\) does not necessarily mean that \(my=rx\) cannot be true. For example, consider m = r = x = y = 1 (of course there are infinitely many other possibilities). So, from (1) we can have an YES as well as a NO answer.
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