Lesson: Working with Percent

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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://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?
greenlight-admin's picture

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 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://greprepclub.com/forum/25-of-1-4-of-x-3575.html#p7487


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