If m 0 and x is m percent of y, then, in terms of m, y is

Question

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

Bunuel · Accepted Answer

x is m percent of y translates to:

y*\frac{m}{100}=x ;
 \frac{y}{x}=\frac{100}{m}

y is what percent of x translates to:

x*\frac{?}{100}=y ;

?=\frac{y}{x}*100 .

Since from the above  \frac{y}{x}=\frac{100}{m}  then:

?=\frac{y}{x}*100=\frac{100}{m}*100=\frac{10,000}{m} .

Answer: E.

PareshGmat · Answer

x is m percent of y, means

x = \frac{my}{100}

y = \frac{100}{m} * x  .................... (1)

Lets say y is "a" percent of x, which means

y = \frac{"a" x}{100}  ..................... (2)

Equating (1) & (2)

\frac{100x}{m} = \frac{"a" x}{100}

"a" = \frac{100*100}{m}

Answer = E

ishdeep18 · Answer

You are Genius Bunuel.. I waas getting so confused in this :!:

, thankew so much...

ankur1901 · Answer

key to solve such problems is to know the below basic rule

To convert Fraction to % => Multipy by 100
eg 1/4 = 25%

To convert % to Fraction => Divide by 100
eg 25% = 25/100 = 1/4

russ9 · Answer

Hi Bunuel,

I was with you for almost all of the problem but I lost you in the end. It's the last bit of conversion that screws me up. Let me try with some numbers.

X is m % of Y
If m = 10 and Y = 100, then X = 10.

The question asks, y is what percent of x. Meaning, 100 is what percent of x. I would write that as, 100 = (z/100)(10), this gives me Z as 1,000 %. Correct?

Based on that method, I picked A because 100 * M = 100 * 10 = 1,000.

I know that i'm screwing up on the last part. Would appreciate your help.

Thanks!

Bunuel · Answer

For your numbers both A and E fit. For plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing VALUES.

We're told that M > 0 and X = M% of Y. We're asked Y is what percent of X.

IF...
M = 50
Y = 20
X = 10

20 is 200% of 10. So we're looking for an answer that equals 200 when M = 50. There's only one answer that matches...

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

Ekland · Answer

x is m% of y.
Say 50 = 50% of 100 respectively.

100 is what percent of 50?
That's 200%. 
Now only E gives you 200.

You didn't have to solve it.

JeffTargetTestPrep · Answer

To solve we want to first create a word translation from the information in the problem stem. We are given that x is m percent of y. We can express this as:

x = (m/100)y

x = my/100

We are next asked, in terms of m, y is what percent of x? This can be expressed as:

y/x * 100 = ?

We need to manipulate our first equation until we isolate y/x.

x = my/100

Multiplying the entire equation by 100 we have:

100x = my

Then divide both sides by x:

100 = my/x

Then divide both sides by m:

100/m = y/x

The final step is to multiply both sides of the equation by 100.

100/m * 100 = y/x * 100

10,000/m = y/x * 100

Answer is E.

GMATCoachBen · Answer

Please see the table below — direct word-for-word translation works very well here, because once you know the basic process, it can be done without thinking or hesitation, much like the fluency of translating a foreign language that you know well.

https://lh3.googleusercontent.com/XoWDUGPmqkpL5lDfFttJxWMsAB9wxmu9AaF6kZPa1XTUvHGYO2O1bYPXg0KBhWR01BuRWex0lzQofbATTing9SluqQ48aH_ic-1J4baD_041ECc2CcgAqeF8XUgaM4QKegIvJzpkXls6qRONSB8JIX6QSKlbiYzn_ayi9PkfG8M0X_Mw6WEHGZ-rzKcIAOA4iuG9-u2arNIf-p7YK6e705Rl96h5Xqc_aplEZwi0QiF8P4jFhbApQs2UOWGic2DEcgfV05X_y7ThuIeliXo7HhJ47olGk89BS5cNqyJSYnaNEGnms6U99HtUgEAK_8B7RXeJA2gGXdPzlLlq5OuXS2mh_FB8tjs3oSk4w6JNumsYy4bz6sPaNNigXUmJ0nAvVn7eefMFC5TiNqn-lhyl2AEhAvSLHD4e1bpCTouJp3vFH3piOEapW8MvndnNgYcIpbJUwT-NaZRINYzbGTRWpiI5CeWanjD3jpGrtPdvOAvHUjSifd2RSa-btt7EnrqrQbf_Fi_9AZG01-iepctDc9CI8-EtOMQ0mSzJbofxGnYZZMSVkpQyFSAV4D_bFQ_cGN5eFPokopjAkVkwDy8AAcdmrVRNtfXH1v_jzhKXDngH9Mx1D5RyE2POWwASQA9rf_Cw2V5TSnkacglxkeybtgzoLnORZpnyYE1kbBV26QdvT3wiUQbg7AJEWPkIDlFMABPYltu6tG01F4BFAUftJHagYQ=w188-h316-no?authuser=0

x  =  \frac{m}{100}*y

y  =  \frac{w}{100}*x

As a habit, ask ourselves: what are we solving for? We need to find "what", which is "w". (This example illustrates that using "w" is a good habit for "what", because the variable "x" is already taken. It's often helpful to label variables with the first letter of what they represent, such as a=apples, c=cost.)

To be most efficient, substitute "x" from the 1st equation into the 2nd equation:
 y  =  \frac{w}{100}*\frac{m}{100}*y

Since we are multiplying on both sides, we can cross off the "y" on each side:
1 =  \frac{w}{100}*\frac{m}{100}

We can multiply by 100 twice on both sides:
10,000 =  w*m

Finally, divide by m:
   \frac{10,000}{m}    =  w

Bambi2021 · Answer

Number plugging is dangerous on this question.

If x = 10, m = 10, y = 100

then y = 1000 % of x

Both A and E gives the correct answer. In your case though, you happened to pick the numbers wisely.

EMPOWERgmatRichC · Answer

Hi Bambi2021,

When dealing with multiple variables in this type of 'story problem', if you're going to TEST VALUES, then it's typically a good idea to choose DIFFERENT values for the variables. In your example, you chose the same number for X and M. Would you run into this same situation if you chose two different values? 
 
GMAT assassins aren't born, they're made,
Rich

Bambi2021 · Answer

Thanks for the input Rich. I will have that in mind. On this question I chose x and y first, instinctively as 10 and 100. Then m became 10 and I was left with A and E. I like these kind of questions though, when they make something extremely basic into something quite tricky. Actually I think it could almost be classified as common sense knowing how to take percentages "in reverse".

EMPOWERgmatRichC · Answer

Hi Bambi2021,

You bring up a really good point. Understanding ratios, percents and percent change are all fundamental concepts in Business School (and beyond) - which is why you'll face a number of questions on Test Day that "test" your understanding of those ideas.

GMAT assassins aren't born, they're made,
Rich

Elite097 · Answer

ThatDudeKnows   JeffTargetTestPrep   Bunuel  how do you know that x and y are positive? How can we divide variables without that info?

ThatDudeKnows · Answer

Elite097

There are variables in the question that are repeated in the answer choices, so my approach here would undoubtedly be to simply Plug In.
x=1
y=2
m=50
y is 200% of x, so we want to plug those numbers into the answer choices and get 200.

A. 100m = 100(50) = 5000 Wrong.
B. 1/100m = 1/5000 Wrong. 
C. 1/m = 1/50 Wrong.
D. 10/m = 10/50 Wrong.
E. 10000/m = 10000/50 = 200

Answer choice E.
Correct answer, took about 15 seconds, and very low risk of making a silly mistake. I know you asked about the "real" math, but I just don't see why you'd go that route in the first place!

Okay, now back to your question. m is a percentage derived by dividing x by y and multiplying by 100, and m is greater than 0. That means that either x and y are both positive or x and y are both negative. Does that help you with whatever "real" math approach you were taking?

ScottTargetTestPrep · Answer

In this question, x and y can be positive or negative, the answer wouldn't change. The only problem would be if one of those variables were 0, but that cannot happen either. First, since m > 0, if either x or y were 0, then the other variable would also be 0. If x and y were both 0, then there is no single value of m which satisfies "x is m percent of y". In fact, if both x and y were 0, then all the answer choices would be correct.

Abolnasr · Answer

Assume Y = a% of X
We’re solving for a

Y = aX/100

Also as X is m percent of Y then X= mY/100
Y= 100X/m (Given)

100X/m=aX/100

Divide both by X

100/m=a/100

Multiply by 100

10,000/m=a

harryzhang · Answer

i found the other methods to be a bit hard to understand (for me), so i wanna share my methods here as well

there are two methods:

(1) plugging in numbers (almost always works!)

note: this method is quite "dangerous" as the plug-in method will likely have more than one answer to work  (albeit it does usually limit the choices to be 2 or 3 max) , so   make sure to go through all choices   and   try picking more obscure numbers

a good example here is if m = 10, x = 100, y = 1000
x (100) is m (10%) of y (1000)
y (1000) is ?% of x (100)
? = 100m or 10000/m 
answer would be A OR E

if we pick more obscure combos like say m = 50, y = 20, x = 10
x (10) is m (50%) of y (20)
y (20) is ?% of x (10)
? = 200, so 4m (which doesnt work for A)
only E (10000/m = 10000/50 = 200) would work here

(2) use variables

the key is "m percent of" can be rewritten as m% or m/100 because 3 percent of sth. = 3% or 3/100 of sth.

after reading the prompt, i note down:

m > 0
x = m% * y 
 x = (m/100) * y (key step) 
then i rewrite the equation in the form of y since that's the question:
y = x / (m/100)
y = x * (100/m) OR y = (100/m) * x

the question is asking, y = __% * x
 btw, the symbol % can really be seen as "/100"
 
plugging things in, y = (100/m) * x would be y = (100/m) * 100% * x since 100% = 1
thus, y = (100/m) * 100% * x = y = (10000/m)% * x

here we have (10000/m) as the final answer

If m > 0 and x is m percent of y, then, in terms of m, y is

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