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

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

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
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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.
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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masland wrote:
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).
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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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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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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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.
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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??\
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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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,
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
LM wrote:
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

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
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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LM wrote:
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

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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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Bunuel wrote:
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.

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
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
venmic wrote:
Bunuel wrote:
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.

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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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
Bunuel wrote:
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.

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.
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Re: If m, r, x and y are positive, the ratio of m to r equal to the ratio [#permalink]
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Nikhil30 wrote:
Bunuel wrote:
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.

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