vikasp99 wrote:

If 5x = 4y, which of the following is NOT true?

(A) \(\frac{(x + y)}{y} = \frac{9}{5}\)

(B) \(\frac{y}{(y – x)} = 5\)

(C) \(\frac{(x – y)}{y} = \frac{1}{5}\)

(D) \(\frac{4x}{5y} = \frac{16}{25}\)

(E) \(\frac{(x + 3y)}{x} = \frac{19}{4}\)

Dear

vikasp99,

I'm happy to respond.

There are many different ways to rearrange a ratio. The way I solved this was to scan down the list of answers. I noticed that (B) and (C) are close to reciprocals for each other, but the subtraction is in a reverse order between them. They can't both work for the values of x and y!

Think about it this way. Suppose x and y are both positive--they don't have to be, because they both could be negative, but let's just assume that they are positive. Each expression has to work for all numbers, so it must work for positive numbers! We know 5/4 = y/x, so y is a bigger positive number than x. Thus, (y - x) is positive, and (x - y) is negative.

Choice (B) has positive = positive

Choice (C) has negative = positive, so this is the one that doesn't work.

Thus, (C) is the answer.

(A), (B) (D), and (E) are all arithmetically legal rearrangements of the original equation.

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)