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## Comment on

Working with Percent## I like the idea that one

## "In group 1, there are 300

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?

## You're referring to the

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

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://greprepclub.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://greprepclub.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?

## Link for question 1: http:/

Link for question 1: http://greprepclub.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://greprepclub.com/forum/mary-paid-for-a-book-was-equal-to-the-price...

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

## You bet!

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?

Cheers,

Brent

## Thank you!

## Can you work out this problem

http://greprepclub.com/forum/geoff-used-630-to-buy-a-new-guitar-this-amount-was-15-perc-1899.html

## You bet!

You bet!

Here's my solution: http://greprepclub.com/forum/geoff-used-630-to-buy-a-new-guitar-this-amo...

Cheers,

Brent

## I solved this question as

0 < a < b

Quantity A: a% of 1/b

Quantity B: b% of 1/a

Solution:

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?

## That solution is fine, but

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...

Given:

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)

Simplify:

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

Cheers,

Brent

## For that problem, aren't we

Quantity A: a/b

Quantity B: b/a

Given that 0 < a < b

## You're absolutely right.

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.

Cheers,

Brent

## 1/16 of 10% of x

How did this become the below?

Quantity B: (1/16)(10)(x)

## Did I accidentally writhe

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%)

## Good catch - thanks!

Good catch - thanks!

I've changed the 10 to 1/10 here: https://greprepclub.com/forum/25-of-1-4-of-x-3575.html#p7487

Cheers,

Brent

## https://greprepclub.com/forum

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

In the 2nd question below

https://greprepclub.com/forum/the-change-in-price-of-a-pair-of-shoes-marked-down-by-3062.html

The answer was D becuasue were not given the original price which is the same situation as the first question

## For the first question, I've

For the first question, I've added another solution (here https://greprepclub.com/forum/gre-math-challenge-138-in-a-certain-store-...) 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://greprepclub.com/forum/the-change-in-price-of-a-pair-of-shoes-mar...) is much different, because we are unable to express two prices using ONE VARIABLE.

Does that help?

Cheers,

Brent

## https://greprepclub.com/forum

What makes q less than p

## Good question.

Good question.

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

Cheers,

Brent

## Thanks

## Why is the denominator 6 in

https://greprepclub.com/forum/the-number-of-people-in-group-1-who-have-the-ailment-wheezi-1911.html

## Question link: https:/

Question link: https://greprepclub.com/forum/the-number-of-people-in-group-1-who-have-t...

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?

ASIDE:

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

Cheers,

Brent

## For https://greprepclub.com

## Good question. Here's my full

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

Cheers,

Brent

## I understand how you solved

## The on-screen calculator is

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%)

## f x > 0 which of the

## Question link: https:/

Question link: https://greprepclub.com/forum/if-x-0-which-of-the-following-expressions-...

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