ratio

[Viper83]

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

1. ratio of m to y is equal to ratio of x to r.

2. ratio of m+x to r+y is equal to ratio of x to y.

B

[clock60]

my try
is m/r=x/y, or is m*y=x*r
(1)m/y=x/r, it can be true that m*y=x*r in case m=r=x=y.(1=1) but it may not true if there are different values for m,r,x,y, so insuff
(2) (m+x)/(r+y)=x/y after little transforming
my+xy=xr+xy from here we can cancel xy and left with my=xr. so suff

[Frankenstein]

Hi,
Is m/r = x/y ?
From(1): m/y = x/r
Insufficient
From(2): (m+x)/(r+y) = x/y => y(m+x) = x(r+y) => my+xy = rx+xy =>my = rx =>m/r = x/y
Sufficient

Hence B

[tpr-becky]

This may be one that is more easily worked with numbers than algebra for some people.

is m/r = x/y? all numbers are positive and we are working within ratios

1) if m = 2, y = 3, x = 4 and r = 6 then 2/3 = 4/6 BUT 4/3 does not equal 2/6
However all the numbers could be the same - if they are all 2 then 2/2 = 2/2

thus, we do not always know whether the ratio will be the same and the answer is BCE.

2) if you pick x = 2 and y = 3 then in order to make m+x/r+y = 2/3 you have to pick multiples of each x and y for m and r - m must be 4 and r is 6 or , m is 8 and r is 12

working a little with the numbers shows you that statement 2 is sufficient.