Lesson: Working with Percent

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%

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

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

You bet!

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

Cheers,
Brent

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

Did I accidentally writhe that somewhere?

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

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

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

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

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

Cheers,
Brent

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%)

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?