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


I was not able to solve this problem within 2 minutes. When given unlimited time, I was able to work it out by plugging in numbers...however, I am looking for a good strategy on how to solve this problem (and ones like it), within 2 minutes.

Thanks.

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

1. m:y = x:r

so m/y = x/r
which can be written as m/r = (x/y) * (y^2/r^2)
this clearly shows that ratio of m to r is not equal to the ratio of x to y. SUFFICIENT.

2. (m+x)/(r+y) = x/y which works out to m/r = x/y. SUFFICIENT.

So I would select choice D.

Whats the OA?

is the answer E

I think the first step is rephrase the question. It asks is the ratio of m to r = to ratio of x to y?

My rephrase was m/r = x/y? Or even a step further, by cross multiplying the two ratios, is my=rx?


Statement 1 states that m/y = x/r

This does not help us to calculate as to whether m/r is equal to x/y. So, MAYBE! (INSUFFICIENT)


Statement 2 states m+x/r+y = x/y

You can cross multiply rewriting the equation as y(m+x) = x(r+y) -----> my+yx = rx+yx
Subtracting yx from both sides, the equation then becomes my=rx, which is the rephrase of the question itself. SUFFICIENT.

I would choose B.



And just to note, the two statements will NEVER CONTRADICT EACH OTHER!! For example, one statement will NOT say that the ratio is not equal and then the second statement say the ratio IS equal. Remeber that the statements are true and NEVER LIE.

this is an absolutely wonderful response.

the content here is pretty much perfect, but i feel that it's appropriate to add a few study pointers. specifically, you should concentrate on takeaways when you study these problems: try to learn lessons that will be applicable to OTHER problems. you don't ultimately care about the solution to this one problem; you only care about what you can learn from it and then turn around and apply to other problems.

here's the most important takeaway from this problem:
* if you don't know what else to do with a proportion, cross-multiply it.

2 comments:

(1) the reason this is valuable is because there are all sorts of versions of the same proportion that LOOK different as proportions, but which are shown to be the same when cross-multiplied. for instance, ALL of the following proportions
a/b = c/d
a/c = b/d
d/b = c/a
d/c = b/a
are equivalent, as all of them multiply to give ad = bc (as do countless others, such as (a + c)/(b + d) = c/d, after cancellation).

(2) this applies only to proportions with EQUALS SIGNS in them, NOT to inequalities. if you have an inequality such as a/b < c/d, then you can't cross-multiply it unless you know the sign of the product of the two denominators, bd (because that's all cross multiplication is: multiplying by both denominators at once on both sides). if bd is positive, then the sign won't flip; if bd is negative, then the sign must flip.