GMAT Trick on percentage

Question

I remember that I ran into some tricky questions on percentages. it is tricky because I wasn't sure if it was asking x%, or the x itself. For instance, the two questions below:

6.4 is what percent of 16,000? 
 0.004%
 0.04%
 0.4%
 4%
 4.4%'

6.4 is x percent of 16,000? what is x? 
 0.004%
 0.04%
 0.4%
 4%
 4.4%

The answer to the first question is 0.04%, the second question should be 4%, right?

Does any one remember any other type of tricky expressions in calculating percentage?

VeritasPrepBrian · Accepted Answer

Hey yufenshi:

Actually those two questions say exactly the same thing, and that brings up a decent strategic point for word problems. Quite often, the language of mathematics gives you the equation just in word form. On this problem, consider that:

"Is" means =
"per" means "divided by" or /
"cent" means 100
"What" is the unknown, which we can call x
"Of" is multiplication, or *

So 6.4 is what percent of 16000, mathematically, is:

6.4 = x/100 * 16000
6.4 = 16000x/100
6.4 = 160x
6.4/160 = x
4/100 = x
4/100 = x, so x = .04

I'm a big fan of using the language to set up the math for you, so if this makes sense to you I'd definitely recommend it!

Sarang · Answer

Remember the formula- Percentage = (part/whole)* 100

Q:-6.4 is what percent of 16,000? which means 
A:-% = (6.4/16000)*100 = 0.04%

Q:-6.4 is x percent of 16,000? what is x?
A:-x percent of 16000 means x/100 of 16000 in value.
6.4 = (x/100) * 16000 
 =0.04

walkerme13 · Answer

Yes. I used the exact same strategy.

x/100 * 16000 = 6.4

as x% of 16000 is equal to 6.4 and therefore to find x using this algebraic equation is x = (6.4/16000) * 100 = 0.04

yufenshi · Answer

Hi Brian,

I thinik my problem is to understand exactly what was asked. In the first case, "6.4 is what percent of 16,000"? the official answer is 0.04%. In the second question, 6.4 is x percent of 16,000? what is x? the answer to the second question is 4%. I think the first question is not clear as to what it was asking. if what percent means x%, is it asking for the x%, or is it asking for the x? Do I make sense?

0.004%
0.04%
0.4%
4%
4.4%'

VeritasPrepBrian · Answer

Hey yufenshi,

I hear you - and that's where I think the "language of math" example is so important. Those two questions are EXACTLY the same. Let's look at it with smaller, easier to digest numbers:

4 is what percent of 16?

vs.

4 is x percent of 16? What is x?

Well, we know that 4 is 25% of 16, so the first answer is clearly 25.

The second asks the same thing: 4 = x/100 * 16
So multiply both sides by 100 to get rid of the denominator to get: 400 = x * 16
Divide both sides by a common 4 to get: 100 = x * 4
Divide by 4 again to finish the job: 25 = x

Because the original question asks "what percent" we're already solving for the integer that goes next to the % symbol so we don't need to multiply (or divide) by 100...we've already accounted for the fact that it's a percentage, so the answer is 25%.

In your two questions, the only difference is that #2 replaces the word "what" with the variable "x". But that's just algebra - that's how we solve for something by taking the question "what" and turning it into a variable:

What plus two is 4?
x + 2 = 4

The question you're asking - "what" - is the variable.

yufenshi · Answer

Hi, Brian,

I am confused:
4 is what percent of 16?
"Well, we know that 4 is 25% of 16, so the first answer is clearly 25."

Thought it should be 25%?

VeritasPrepBrian · Answer

Yes, but either works because we're already talking about percent. Percent is a unit of measure, is one way to think about it.

If I asked:

I'll pay you $20 and hour for two hours of work, how many dollars will it cost?

You could say: 40. And you'd be right because I asked in terms of dollars.

Or you could say: 40 dollars. And you're still right, because you're using the correct term of measure.

Either works, even though 40 dollars is 4000 cents or 42.75 in Canadian dollars or 32 British pounds (or whatever the exchange rates are nowadays). If the question is in terms of dollars, you can answer with just the number or you can clarify by including the units.

Now, with percents, as with dollars and cents, it's important to make sure that you're carrying the right units, as taking 10% of y doesn't mean you multiply it by 10 - you actually multiply by 10/100. But as long as you track whether you're within the proper units you can answer that question above as 25 (because the question already asked for "what percent" or you could tack on the % symbol to repeat the question and say "25%".

Does that help? I like that you're being careful with those units...

yufenshi · Answer

Hi Brian,

Thanks for the explanation, but no. I don't understand.

for the question " 6.4 is what percent of 16,000? "
0.004%
0.04%
0.4%
4%
4.4%'

In asking "what percent", the answer can't be both 0.04% and 4%. I need to understand by "what percent", they were asking for the x% (in this case, it is equal to 0.04%), or merely the x in front of the percent (in this case, it would be 4%, or 0.04).

VeritasPrepBrian · Answer

Like I said, it's the same exact question in each form you asked it originally. 6.4 is 0.04% of 16,000 so the answer is 0.04%.

The GMAT won't ask you to take a percent of a percent as your answer. If they ask "10 is what percent of 100?", the correct answer will be listed as 10% (and not 1000% under the assumption that you'll divide by 100 because of the word "percent").

Do you have the Official Guide 12th edition? If so, please check the following page/problem numbers for evidence of how they list answers in this way:

p. 184, #223
p. 184, #220
p. 179, #187
p. 169, #124
p. 168, #115
p. 167, #109
p. 164, #111

The answer choices each include the percent symbol as does the question, but only to indicate that "percent" is the unit.

walkerme13 · Answer

Oh. Thanks for the useful info and the questions. Now I can practice those questions as well.

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GMAT Trick on percentage

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