Lesson: Percent Increases and Decreases

There are 2 ways to handle a decrease of 30%. We can find 30% of the original value and then subtract that amount from the original value, or we can just find 70% of the original value.

Here's another way to think of it. Let's say there are 100 people in a room. If 30% of those people leave, how many are remaining? Well, if 30% have left, then we know that 70% of the people are remaining. 70% of 100 = 70 people are remaining. Alternatively, 30% of 100 = 30. 100 - 30 = 70. Same answer, two ways to think of it.

I believe you are confusing "300% of" with "300% increase" and "300% more than"

300% of 50 is 150.
300% of 60 is 180.
300% of 11 is 33.

If 50 is increased by 300%, then we take 50 and add 300% of 50 to it. So, 50 increased by 300% is 200.
Likewise, 60 increased by 300% is 240.
And 11 increased by 300% is 44

On a similar note, 200 is 300% greater than 50.
And 44 is 300% greater than 11
And 4000 is 300% greater than 1000

So, in your approach, you are not treating the increase as a 300% increase. The question tells us that the new population is 300% MORE THAN the old population. However, in your approach, you are saying that the new population is 300% OF the old population. In other words, you are saying that the new population is THREE TIMES old population.

You're referring to the question that starts at 3:45 in the video.

The "net result" in this instance refers to the TOTAL (combined) effect of all the changes put together.

For example, if I gave you 8 apples, then took 3 apples away from you, then gave you 2 apples and then took away 1 apple, then the NET RESULT would be the same as giving you 6 apples.

In the Hilda question, increasing the wholesale price by 20% and then decreasing the resulting price by 15% has the same effect (NET RESULT) as increasing the wholesale price by 2%

Does that help?

Link to the first question: http://gre.myprepclub.com/forum/jack-and-jill-each-bought-the-same-tv-se...

Why is adding 8.5% tax is the same as multiplying by 1.085?

Let x = the PRE-TAX price of the TV
So, 0.08x = the 8% tax on the TV
So, the TOTAL price = x + 0.08x = 1.08x

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Link to second question: http://gre.myprepclub.com/forum/qotd-21-from-2011-to-2012-jack-s-annual-...

You're correct when you say that Arnie’ salary IS 115.8% of Jack’s salary. HOWEVER, the question asks "Arnie’s salary was what percent GREATER THAN Jack’s salary?"

Other examples: "X is 116% OF Y" is the same as saying "X is 16% greater than Y"

And "X is 180% OF Y" is the same as saying "X is 80% greater than Y"

And "X is 245% OF Y" is the same as saying "X is 145% greater than Y"
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"Finally, a last doubt, when a question asks me to round to the nearest 0.1%, does it simply mean that I am asked to white a percentage value rounded to the first decimal digit?"

That's correct!

Cheers,
Brent

Hi Deepak,

Your method is perfect - nice work!

Here's my full solution (it's a little different from yours): https://gre.myprepclub.com/forum/a-full-glass-of-juice-is-a-mixture-of-2...

Cheers,
Brent

That's a perfectly valid approach, Deepak.

Cheers,
Brent

"feet" is the plural of "foot"
1 foot
2 feet
3 feet
However, when used in hyphen form (as in 12-foot board),we use "foot" for everything (yes, English is a lawless language!)

So, if 4 feet are removed from the 12-foot board, the board now has length 8.

Percent decrease = 100(difference in values)/ORIGINAL value

The length changes from 12 to 8 (so the original length
= 100(12 - 8)/12
= 33.333...%

Cheers,
Brent

If k is 25% greater than x, then we can say: k = 1.25x

Likewise, if k is 45% greater than x, then we can say: k = 1.45x

And, if k is 113% greater than x, then we can say: k = 2.13x

If k is 40% LESS than x, then we can say: k = 0.6x

Now let's examine the question...

Let B = Bob's PRESENT weight
Let S = Sara's PRESENT weight
"Bob is 30 pounds heavier than Sara."
We can write: B = S + 30 (as you have)

Adding 30 to each weight, we get:
Bob's NEW weight = B + 30
Sara's NEW weight = S + 30

ASIDE: If S = Sara's PRESENT weight, then S+30 = her NEW weight.
You said S+60 = Sara's weight, but this represents a weight gain of 60 pounds.

"Bob's weight is 25% greater than Sara's weight."
In other words: (Bob's NEW weight) = 1.25(Sarah's NEW weight)
We can write: B + 30 = 1.25(S + 30)

We now have a system of two equations:
B = S + 30
B + 30 = 1.25(S + 30)

When we solve this system, we get: S = 90 and B = 120

So, Sarah's PRESENT weight is 90 pounds, and Bob's PRESENT weight is 120 pounds

Does that help?

Cheers,
Brent

Let's say the sales for 2008 totaled $100
So, the sales for 2009 = $105 (after a 5% increase)
And the sales for 2010 = $99.75 (after a 5% decrease)
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Question: In store D, the dollar amount of sales for 2009 was approximately what percent of the dollar amount of sales for 2010?
A) 105%
B) 106%
C) 95%
D) 104%
E) It cannot be determined from the information given.
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We get: 105/99.75 ≈ 105/100 ≈ 105%

Answer: A

Cheers,
Brent

We can use that formula when we want to say that a certain quantity is comprised of a certain amount of one thing.

For example, if a team of 8 people is comprised of 3 males, then we can say: 3/8 = p/100
When we solve that equation for p, we'll get the percentage of the team members who are male.

Does that help?

Cheers,
Brent

Question link: http://www.urch.com/forums/gre/153587-please-help-detail-explanation.html

The word "glass" doesn't have any specific measurement associated with it.
So, we can't say that the glass must hold 8 oz of liquid.

I hope that helps.

Cheers,
Brent

Question link: https://gre.myprepclub.com/forum/joan-bought-a-calculator-at-a-discounte...

I think you meant to say 105/0.7

Here's how I'd calculate 105/0.7 in my head"

105/0.7 = 105/(7/10)
= 105 x (10/7)
= 1050/7
= (700 + 350)/7
= 700/7 + 350/7
= 100 + 50
= 150

Cheers,
Brent

You're referring to the question that begins at 3:45 of the above video.

Let $100 - the original price

20% INCREASE
New price = (1 + 20/100)($100)
= (1 + 0.2)($100)
= (1.2)($100)
= $120

15% DECREASE
Final price = (1 - 15/100)($120)
= (1 - 0.15)($120)
= (0.85)($120)
$102

Final price = $102

Cheers,
Brent

Question link: https://gre.myprepclub.com/forum/kathleen-s-weekly-salary-was-increased-...

Great question!

There's a bit of algebra going on here. The technique is called simplifying expressions, and it's covered later in the Algebra module here: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Also, it's important to note that, if a term does not have a coefficient, then the coefficient is assumed to be 1.
For example, x = 1x and k² = 1k²

So, the equation: x + 0.08x = 237.60
Is the same as the equation: 1x + 0.08x = 237.60

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Aside: If two terms have the same variable, we can combine their coefficients. For example:
3x + 4x = 7x
8w² - 2w² = 6w²
k + k + k = 1k + 1k + 1k = 3k
----------------------------

Likewise, 1x + 0.08x = 237.60 can be simplified to 1.08x = 237.60

Does that help?

Cheers,
Brent

Question link: https://gre.myprepclub.com/forum/if-a-b-c-2-and-c-decreases-by-20-while-...

Be careful. We're not decreasing 5² by 20%; we're decreasing 5 by 20%. Here's why:

In my solution, I let c = 5

The question tells us that c decreases by 20%
20% of 5 is 1.
5 - 1 = 4
So, if we decrease 5 by 20%, we get 4.
In other words, c decreases from 5 to 4

This means, c² now equals 4², which equals 16

Does that help?

Question link: https://gre.myprepclub.com/forum/if-a-b-c-2-and-c-decreases-by-20-while-...

For my first set of values, I used a = 2500, b = 100 and c = 5

We are then told that c decreases by 20%.
Since c = 5, we must decrease 5 by 20%
5 decreased by 20% equals 4.

Does that help?

Solution link: https://gre.myprepclub.com/forum/quantitative-2290.html#p4753
Sorry, I mixed up the words GREATEST and SMALLEST in my original solution. I've edited to show the proper solution.

To answer your other questions, we know that a must be greater than 4.1.
While 4.2 is greater than 4.1, there are numbers smaller than 4.2 that are still greater than 4.1.
For example, 4.11 is greater than 4.1.
Likewise, 4.10000000000000000000000000000001 is greater than 4.1
In fact, if we keep adding more zeros, a can get super close to 4.1, which is why I just used 4.1 as a possible value of a.

Conversely, we know that a is less than 8.5.
So, a could equal 8.4999999999999999999999
If we keep adding more 9's, a can get super close to 8.5, which is why I just used 8.5 as a possible value of a.

You're absolutely right; GRE Prep Club moved all of their contents to a different domain, but they neglected to add the necessary redirects.
My programmer is now working to change the all of the links on our site. He should be done with that in a few hours, at which point everything should be running again.
Sorry for the inconvenience!

Question link: https://gre.myprepclub.com/forum/gre-math-challenge-35-ms-smith-got-an-8...

By the "multiplier method," are you referring to the property that says increasing a value by 8% is the same as multiplying that value by 1.08?
If so, that strategy won't work for this question.

Why not? Because the question tells us: Ms. Smith got an 8 percent cost of living raise of $20 per week.
Here, we are given the actual dollar increase.
In other words, of the given information tells us that: 8% of Ms. Smith's old weekly salary = $20
So, if we let x = Ms. Smith's old weekly salary, then our equation becomes: 8% of x = 20, which we can solve for x.