what percent is x of y

[jay.mathew]

What percent is x of y?

(1) x = 3y

(2) x - y = 6

I've always assumed that the word 'of' meant 'times'. So when I saw this question I tried to rephrase the question stem to the following:
z/100 = xy

That is we need to know the value of x and y in order to figure out z.

However, the answer explanation suggests that 'of' in this context actually means 'divided by'. It provides the following example:

To answer the question "What percent is 3 of 4," we would simply take 3/4 and multiply it by 100.

Once again, I'd rephrase this to:
z/100 = 3 x 4
z = 12 x 100
Therefore z = 1200.
And we can conclude that 1200% is 3 of 4

As a result I chose answer choice E, but the official answer is A. I'm a little confused about this.

Can somebody please explain to me when we should interpret 'of' to mean 'times' and when we should interpret 'of' to mean 'divided by'?

[mgshorr]

First of all, Statement 2 alone can be dismissed. So you are left with A,C,E.

Secondly, you are given that x=3y.

Because we are dealing with just percents, we do not need actual numbers for X or Y in this scenario.

We know that 3*Y = X, no matter what Y and X are.

Therefore, X is 3 times larger than Y, and 300% larger accordingly.





***To change the problem around a bit, think of it like this:

Imagine that you are told 2X=Y...
Then you could figure that X=Y/2, or X is equal to one-half Y. If X is equal to one-half Y, than it is 50% of Y.

[jay.mathew]

Hi mgshorr, thanks for the reply.

However...didn't you just change the question? I can understand how your solution would answer the question 'X is what percent of Y?'. But the question actually says 'What percent is X of Y?'. Aren't these two questions fundamentally different? Or is there something I'm missing?

[RonPurewal]

Hi mgshorr, thanks for the reply.

However...didn't you just change the question? I can understand how your solution would answer the question 'X is what percent of Y?'. But the question actually says 'What percent is X of Y?'. Aren't these two questions fundamentally different? Or is there something I'm missing?

hmm, yeah, this problem has sloppy writing.

it should be written in one of the following 2 ways:
"what percent of y is x?"
or
"x is what percent of y?"

i'll submit this problem for revision.

--

by the way:
are you a non-native speaker of english?
just wondering - my instinct is that native speakers of english would process this question in the intended way without hesitation, while non-native speakers (who would rely on literal rules such as "of means multiplication") would be more likely to have trouble with it.
either way, it's essentially our fault, since it's not terribly well written. thanks for bringing it to our attention.

[jay.mathew]

Hi Ron,

I'm actually a native speaker (born and raised in Australia). If its any consolation, I'm a musician, so it could just be a non-native/musician problem. Regardless, I've discovered that I make fewer mistakes when I follow the literal rules, so I've made it a point to always convert the problem into an equation. It had worked for me 100% of the time...up until now.

Thanks for the clarification.

Jay

[albert.chi]

I know I might be over thinking this, but should there be something in the question stem that says that xy != 0? (xy does not equal zero?)

1) x = 3y
>> I would assume that dividing by y where y = 0 would be incorrect?

[Kweku.Amoako]

when u are asked:

what % of 10 is 6 what do u do?

(6/10) *100 right

would you say this is a different question and if so how would do it

what % is 6 of 10 ?

in any case there are two things you need to determine to answer the question
1) the "part"
2) and the "whole"

in a statement like x of Y, you usually consider the "of Y" as the whole. So this question is really simple. Figure out the whole and the part . If you do that should end up with an expression x/y or y/x ....in any case you will notice statement 2 does not help you find either but statement one does

[jay.mathew]

when u are asked:

what % of 10 is 6 what do u do?

I would make z the value we want to determine:

z/100 x 10 = 6
z/10 = 6
z = 60
Therefore 60% of 10 is 6

what % is 6 of 10 ?

would you say this is a different question and if so how would do it

Yes, in my opinion it is a different question.

z/100 = 6 x 10
z = 6000
Therefore 6000 percent = 6 x 10 = 60

in any case there are two things you need to determine to answer the question
1) the "part"
2) and the "whole"

in a statement like x of Y, you usually consider the "of Y" as the whole. So this question is really simple. Figure out the whole and the part . If you do that should end up with an expression x/y or y/x ....in any case you will notice statement 2 does not help you find either but statement one does

Right...and basically what I've been trying to understand is whether it is appropriate to assume (as you have done) that "of" means "divided by". If we cannot assume this, then I don't see how the answer can be determined, even with both of the statements taken together.

[Kweku.Amoako]

common sense tells me that when I have two numbers x and y and I know one is a % of the other(in other words one is a fraction of the other) , then the answer is always x/y * 100 or y/x* 100 ......

I'm hesitant to make that assumption because I will be relying on key words rather than meaning to determine a mathimatical operation.

Let me follow your reasoning for a sec...you are not being consistent in the us of the word "is" and "of"

in case one: what % "of 10" "is 6"

you correctly did (% = z/100) * "of 10" = "is 6"

notice you implied "of 10" is the whole and "is 6" is the part

case 2: what % "is 6" "of 10"

you did (% = z/100) = "of 10" * "is 6" ...how does 6 of 10 translate to 6*10

where is the consistency? two same expressions "of 10 " and "is 6" just reversed in a sentence in your case warranted a different mathimatical operation in each case

If I am forced to make an assumption then I will say specifically with fractions "of" signals a whole(notice i didn't say division) and "is" signals a part. just like in sentence correction "some(x) of the the men(y) are good" means x is a fraction of y( of the men ).

tx

[jay.mathew]

common sense tells me that when I have two numbers x and y and I know one is a % of the other(in other words one is a fraction of the other) , then the answer is always x/y * 100 or y/x* 100 ......

Unfortunately, my common sense is fallible. Consequently, I'd rather rely on a more foolproof method, so that I don't misinterpret the question.

Let me follow your reasoning for a sec...you are not being consistent in the us of the word "is" and "of"

No offense, but I believe that by following the rules I'm actually the one being more consistent.

in case one: what % "of 10" "is 6"

you correctly did (% = z/100) * "of 10" = "is 6"

notice you implied "of 10" is the whole and "is 6" is the part

No, I implied that 'of' meant 'times' and 'is' meant '='.

case 2: what % "is 6" "of 10"

you did (% = z/100) = "of 10" * "is 6" ...how does 6 of 10 translate to 6*10

'6 of 10' translates to '6 x 10' when 'of' means 'times'.

It basically comes down to how we interpret the usage of 'of' in this context. I'd never heard/seen this type of usage before, hence the query. I actually thought it was a trick question rather than a simple one.

Now, in no way am I advocating that the word 'of' always means 'times'. If I had added the word 'out' to the question I would have interpreted it differently:

What percent is x out of y?

In this case, I'm happy to concede that the question translates to z/100 = x/y, because I recognise that 'out of' means 'divided by'. Take for example the following phrase:

'5 out of 10 people drink milk every day'.

We wouldn't say '5 of 10 people drink milk every day'. Having said that, I doubt a question would use the words 'out of' in the first place. The question would most likely just use '/' symbol or express 'x/y' as a fraction using a graphic.

Either way, Ron admitted that this question was poorly worded, so I'm happy to leave it at that.

[Ben Ku]

Hi Jay, I think using the phrase "out of" would indeed clarify the question. I agree with Ron that the wording is sloppy. Almost always, the literal translation of "of" is multiplication.

[hisabness]

First of all, Statement 2 alone can be dismissed. So you are left with A,C,E.

Secondly, you are given that x=3y.

Because we are dealing with just percents, we do not need actual numbers for X or Y in this scenario.

We know that 3*Y = X, no matter what Y and X are.

Therefore, X is 3 times larger than Y, and 300% larger accordingly.





***To change the problem around a bit, think of it like this:

Imagine that you are told 2X=Y...
Then you could figure that X=Y/2, or X is equal to one-half Y. If X is equal to one-half Y, than it is 50% of Y.

It's 200% larger

3Y-Y / Y = 2

Not important, but you should be careful when using the phrase larger than

[Ben Ku]

hisabness makes an good point on being precise on wording.

"x is 300% of y" is translated to x = 3y.
However, "x is three times larger than y" means x = 3y + y = 4y. "Larger than y" means in addition to y.

[toddrinaldo]

I understand that statement one is true if X or Y are both non-zero integers, but what if X is Zero? Should I not think about if a number can be Zero on the exam? What would If X=0 thne Y=0, All that tells me is that Y and X are =

[tim]

totally correct. this is an old problem and clearly has a few issues..