Lesson: Working with Percent

Comment on Working with Percent

I like the idea that one strategy works with all different wordings. Thanks!

"In group 1, there are 300 people, 5% of whom have allergic wheezing and 2% of whom have nonallergic wheezing. That is, (0.05)(300) people, or 15 people, have
allergic wheezing and (0.02)(300) people, or 6 people, have nonallergic wheezing.
Therefore, in group 1, the number of people who have allergic wheezing exceeds the number who have nonallergic wheezing by 9, which is \frac{9}{6}=1.5*100%

The answer is C

I got 250% (not even an answer choice) because I did 15/6 *100 rather than 9/6 * 100. How do you know to do 15/6?
greenlight-admin's picture

You're referring to the question here: http://gre.myprepclub.com/forum/the-number-of-people-in-group-1-who-have...

You're mixing up the fact that 15 is equal to 2.5 TIMES 6 with the concept of "greater than".

For example, we can say that 12 is 200% of 6, since 12 = 200% of 6 = 2.00 x 6

However, we can't say that 12 is 200% GREATER THAN 6
To find 200% GREATER THAN 6, we need to ADD 200% of 6 TO 6

That is, 200% GREATER THAN 6 = 6 + (200% of 6) = 6 + (12) = 18

It's best to think of "greater than" in terms of PERCENT CHANGE.

Percent change = (100)(difference if values)/(original value)

So, "x is what percent greater than y?" translates into:

(100)(x - y)/2

The original question is asking "15 is what percent greater than 6?"

So, the percentage = (100)(15 - 6)/6
= (100)(9)/6
= 150%

Dear Brent,

I hope you can clarify two doubts I had when solving these problems :

1. http://gre.myprepclub.com/forum/25-of-1-4-of-x-3575.html

why (1/4)(400)(x) and not (1/4)(1/400)(x) ? (and the same in quantity B)

2. http://gre.myprepclub.com/forum/mary-paid-for-a-book-was-equal-to-the-price-of-the-book-plus-1819.html

why 1.04x dollars and not 0.04x dollars?
greenlight-admin's picture

Link for question 1: http://gre.myprepclub.com/forum/25-of-1-4-of-x-3575.html
Sorry, that was a typo. I've changed it to 1/400

Link for question 2: http://gre.myprepclub.com/forum/mary-paid-for-a-book-was-equal-to-the-pr...
If the price of the book is x dollars, then the TOTAL price (including the 4% sales tax) = 1.04x

Here's why:
If the (before tax) price = x, then...
0.04x = the 4% tax
So, the TOTAL price = x + 0.04x = 1.04x

At 7:48 I am trying to solve for P and I can not get 150. If you could work that out please I would appreciate the help!
greenlight-admin's picture

You bet!

We have (p/100)(80) = 120

One approach is to first eliminate the fraction by multiplying both sides by 100 (more on this approach here: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...)

When we do this, we get: (p)(80) = 12,000

This is the same as 80p = 12,000

Now divide both sides by 80 to get: p = 150

Does that help?


Thank you!

Can you work out this problem, please?
greenlight-admin's picture

I solved this question as below-
0 < a < b
Quantity A: a% of 1/b
Quantity B: b% of 1/a

qty A: a% *1/b
qty B : b% *1/a

qty A : a/100*1/b
qty B : b/100*1/a

qty A: .0a/b
qty B : .0b/a

qty A : smaller numerator/bigger denominator (as b>a given in shared info.)
qty B : Bigger numerator/smaller denominator (as b>a)

so qty B > qty A
Is this approach correct?
greenlight-admin's picture

That solution is fine, but converting a/100 to 0.0a is a little clunky.
For example, if a = 10%, we cannot say that a/100 = 0.010

So, here's what I'd do...

Quantity A: a% of 1/b
Quantity B: b% of 1/a

Rewrite as:
Quantity A: (a/100)(1/b)
Quantity B: (b/100)(1/a)

Quantity A: a/100b
Quantity B: b/100a

Multiply both sides by 100 to get:
Quantity A: a/b
Quantity B: b/a

Multiply both sides by b to get:
Quantity A: a
Quantity B: b²/a

Multiply both sides by a to get:
Quantity A: a²
Quantity B: b²

If 0 < a < b, then we can be certain that a² < b²
Answer: B


For that problem, aren't we able to conclude that the answer is B once you got to the below step without having to simplify any further?

Quantity A: a/b
Quantity B: b/a

Given that 0 < a < b
greenlight-admin's picture

You're absolutely right.

If 0 < a < b, then we can be certain that b/a is greater than a/b.
I could have just as well stopped at that point.


1/16 of 10% of x
How did this become the below?

Quantity B: (1/16)(10)(x)
greenlight-admin's picture

Did I accidentally writhe that somewhere?

1/16 of 10% of x = (1/16)(10/100)(x)

7th question.
i understood now. All this while i thought 1/16 was 1/16% as quantity A had the first part in percentage (25%)
greenlight-admin's picture

Good catch - thanks!
I've changed the 10 to 1/10 here: https://gre.myprepclub.com/forum/25-of-1-4-of-x-3575.html#p7487


Why isn't the answer D since we were not given the cost of the computer.

In the 2nd question below
The answer was D becuasue were not given the original price which is the same situation as the first question
greenlight-admin's picture

For the first question, I've added another solution (here https://gre.myprepclub.com/forum/gre-math-challenge-138-in-a-certain-sto...) to show that, even though we don't know the precise costs, we can still conclude that one quantity is greater than the other.

The KEY ASPECT to the first question is that we can express all 3 costs using ONE VARIABLE (z).
This allowed us to compare Quantities A and B.

Question two (https://gre.myprepclub.com/forum/the-change-in-price-of-a-pair-of-shoes-...) is much different, because we are unable to express two prices using ONE VARIABLE.

Does that help?


What makes q less than p
greenlight-admin's picture

Good question.
I've elaborated on my solution here: https://gre.myprepclub.com/forum/17-of-p-is-equal-to-18-of-q-where-p-and...



Why is the denominator 6 in the question below? In my calculations i used 15 but it's obviously wrong. Pls explain
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/the-number-of-people-in-group-1-who-hav...

The number of people who have the ailment wheezing (allergic) = 15
The number of people who have the ailment wheezing (nonallergic) = 6

We're asked: The number of people in group 1 who have the ailment wheezing (allergic) is what percent greater than the number of people in group 1 who have the ailment wheezing (nonallergic)?

In other words, 15 is what percent greater than 6?

In general, we can write the following:
If we're asked "x is what percent greater than y?"...
then the answer is (100)(x - y)/y

So, for this question, we get: (100)(15 - 6)/6


For https://gre.myprepclub.com/forum/mary-paid-for-a-book-was-equal-to-the-price-of-the-book-plus-1819.html, the book's solution makes sense but i initially only set up the first 10 > B(1.04) inequality.....would you have a different approach to this question or insights on what would make you know to set up the second 10-B(1.04) < 3?
greenlight-admin's picture

Good question. Here's my full solution: https://gre.myprepclub.com/forum/mary-paid-for-a-book-was-equal-to-the-p...


I understand how you solved the question in the beginning of the video 120/800, but wouldn't it just be faster to just use the calculator?
greenlight-admin's picture

The on-screen calculator is always an option.
Here's another way to convert 120/800 (without using a calculator)

Take: 120/800
Divide top and bottom by 4 to get: 30/200
Divide top and bottom by 2 to get: 15/100 (aka 15%)

If x > 0 which of the following expressions are equal to 3.6% of 5x12. For this question in the extra practice i went about it wrong. I understand how you got it but i was cross multiplying. How do I know what way to solve a problem like this?
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/if-x-0-which-of-the-following-expressio...

QUESTION: If x > 0 which of the following expressions are equal to 3.6% of 5x/12 ?
We can gradually transform this into an algebraic expression

OF means multiply. So, we get: Which of the following are equal to 3.6% TIMES 5x/12 ?
In other words: Which of the following are equal to (3.6%)(5x/12)?

Since k% = k/100, our question becomes: Which of the following are equal to (3.6/100)(5x/12)?

To calculate (3.6/100)(5x/12), multiply the numerators, and multiply the denominators.
We get: (3.6/100)(5x/12) = 18x/1200
Our question becomes: Which of the following are equal to 18x/1200?

Finally, to simplify 18x/1200, we can divide numerator and denominator by 6 to get 3x/200
Our question becomes: Which of the following are equal to 3x/200?

Does that help?

yes thanks

Hey i have a question its very basic..... the question is if i see (of) behind a number for example;

120 is what percent of 80?
15% of what number is 60?
what is 40% of 90?

so this means after the word (of) is whole? as in video the narrator said the number to find percentage (of) is whole.

I'm just trying to simplify it more....please and thank u for the help.
greenlight-admin's picture

Yes, the WHOLE follows the word OF.

Of the people in a certain survey, 58 percent were at most 40 years old and 70 percent were at most 60 years old. If 252 of the people in the survey
were more than 40 years old and at most 60 years old, what was the total number of people in the survey?


Hey....can u pleasse confrim if im right!

what i did was that at most means less than equal too so 58% were less than eqaul to 40 and 70 less than eqaul to 60

than people were more than 40 and less than equal to 60 somehting like 40<n<=60 all this equal to 252

so as both percetages base is of people we can subtract same base percetanges than i did was 70 - 58 = 12%

and as 12% of total = 252 hence total = 2100
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/58-percent-were-at-most-40-years-old-an...
Your solution is perfect.

Here's a similar approach:
Let x = the total population
Property: (number of people 40 or less) + (number of people between 40 and 60) = (number of people 60 or less)
Substitute to get: (58% of x) + 252 = (70% of x)
Simplify: 0.58x + 252 = 0.70x
Rearrange: 252 = 0.12x
Solve: x = 252/0.12 = 2100


Hey Brent thank you for the above reply but i have another question.....i started to plug in values and got D as i had both a and b as answers in.....but what u did made sense...however my issue is this question doesnt feel gre like its to ambigiuos like i used th eplug in appraoch....and how do i knw how to solve like u
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/x-and-y-are-integers-greater-than-5-x-i...
In my opinion, this could be a valid GRE question.

Testing values shouldn't yield a different answer. Can you tell me what values you plugged in?

first i took a case where i took x = 20 and y = 10 where i got A and than i took y = 10 and x = 6 as (x>5) and i got B hence i did D
greenlight-admin's picture

Key property: If you want to test values, those values must meet the conditions specified in the question.
The question tells us that: x is y percent of x², so any values you test must meet that given condition.

The values first pair of values you chose (x = 20 and y = 10) don't work.
When we plug these values into the given information we get: 20 is 10 percent of 20²
Simplify to get: 20 is 10% of 400, when 20 is actually 5% of 400.

Your other pair of values (y = 10 and x = 6) also don't satisfy the given information.
When we plug in these values, we get: 10 is 6 percent of 10²
Simplify to get: 10 is 6% of 100, which also isn't true.

Damn this was a sneaky question i understand now thank u soooo much

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