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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

## 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

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