If m > 0 and x is ............

pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?

A. 100m

B. 1/100m

C. 1/m

D. 10/m

E. 10000/m

x is m percent of y => (x/y)*100 = m
Therefore, (x/y) = m/100 => (y/x) = 100/m => (y/x)*100 = 10000/m

Thus y is 10000/m percent of x.

The correct answer is E.

pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?

A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m

We have x is m percent of y.

Thus, x = m% of y

x = my/100

y = 100x/m

y = 10000x/100m

y = (10000/m)% of x

Thus, y is 10000/m percent of x.

The correct answer: E

Hope this helps!

-Jay

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Jay@ManhattanReview wrote:

pzazz12 wrote:If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x?

A. 100m
B. 1/100m
C. 1/m
D. 10/m
E. 10000/m

We have x is m percent of y.

Thus, x = m% of y

x = my/100

y = 100x/m

y = (1/m)% of x

Thus, y is 1/m percent of x.

The correct answer: C

Hope this helps!

-Jay

Jay, the correct answer to this question is E, not C.

This question is PS #194 in OG 2016, PS #181 in OG 13/2105.

santhosh_katkurwar wrote:Can someone explain with testing values approach. Also, what does it mean when questions in terms of something ? Here we need to find out in terms of m, y is what percent of x? I could write this y = ?/100 *x but i dint get it when it says in terms of x.

Here's a good general rule: if the question asks "what is p in terms of q?" that means that we want to ISOLATE p, and have it equal to some expression involving q:
p = ....q
(p equals something something q)

In this question, it's a bit more complicated, because the thing we want to isolate isn't clearly defined. Think of phrasing it this way: "what is (the percent that y is of x) in terms of m?" Let's define a new variable for (the percent that y is of x). Let's call it n. So here's what we want:
n = ...m
(n = something something m)

ALGEBRA:
If we want to do it algebraically, creating this new variable makes life a lot easier:
x is m percent of y ---> x = (m/100)y
y is what percent of x ---> y = (n/100)x

In order to get n in terms of m (but NOT in terms of x or y), we need to get rid of x and y. First, substitute what we have for x in the first equation into the 2nd:
y = (n/100)(m/100)y
y = (nm/10,000)y
Divide both sides by y:
1 = (nm/10,000)
Isolate n:
n = 10,000/m

So, we can get to answer E.

However, nearly every time I see "in terms of" in a PS question, I think about whether plugging my own numbers in might be easier. In this case - when there are 3 variables given, 1 implied - it's definitely easier! I would do things slightly differently than Mitch did (though same idea).

PLUGGING IN NUMBERS:

I'd choose an x and a y that have an easy relationship, then see what m that gives us:
x = 2
y = 10
2 is 20% of 10, so m = 20

Now what percent is 10 of 2? It's 5 times as great, so 500%. n = 500. Since n is the thing we're solving for, our target answer = 500, when we plug in 20.

A. 100m ---> 100(20) = 500? Nope.

B. 1/100m ---> 1/(100*20) = 500? Nope!

C. 1/m ---> 1/20 = 500? Nope!

D. 10/m ---> 10/20 = 500? Nope!

E. 10000/m ---> 10,000/20 = 500? YES!