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

You are Genius Bunuel.. I waas getting so confused in this , thankew so much...

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

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!

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.

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:

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

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.

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.

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.



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

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

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:
\(\frac{10,000}{m}\) = \(w\)

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.

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

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".

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

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

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?

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.

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