Lesson: Percent Increases and Decreases

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Great video! Just letting you know the first related resource says Manhattan Prep but links to Gmat Club!
gmat-admin's picture

Thanks! It's actually both :-)
It's a question on GMAT Club that's created by Manhattan Prep. The questions listed as GMAT Club are questions created by the people at GMAT Club.

This question seems ambiguous to me. I assumed the reference to the net result was to Hilda's profits, meaning the answer would be 18% (her profits are the same as if she had sold at regular price after paying $118 for the product). Who cares what % decrease the sale price is compared to the wholesale price.
gmat-admin's picture

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

I can see how "net" could cause confusion, since the word has more than one meaning. In this case, "net" refers to the combined effect of the price increase and decrease. I believe we'd have to add a word like "profit" in order to convey the meaning that you're suggesting.

Point taken though - thanks!

maybe another way to think about it

1*1.2*0.85 = 1.02

therefore 2% increase

gmat-admin's picture

Yes, that's basically what we're doing in the video. Except we're starting with 100 rather than 1.

How do you know or go about determining the difficulty levels for the practice problems? Will the harder ones only appear if you continuously get the previous problems correct?
gmat-admin's picture

Are you're referring to what happens during the official practice tests (the GMATPrep tests)?

On the official practice tests (and on test day), the questions you see are based on your success rate on previous questions. So, if you keep answering questions correctly, you will see harder and harder questions.

Conversely, if you keep getting questions wrong, then you'll be given easier and easier questions.

For more on the GMAT's scoring algorithm, watch https://www.gmatprepnow.com/module/general-gmat-strategies/video/1251

Sorry let me rephrase using this as an example: 'GMAT practice question (difficulty level: 650 to 800) - Manhattan Prep'

How would you know this is a 650-800 level GMAT quant difficulty question?
gmat-admin's picture

Those categorizations are my best guess at the difficulty levels. I've been teaching the GMAT for quite a while, so I have a good idea of what kinds of questions cause difficulties for students. Also, the practice questions in the Official Guide for GMAT Review are ordered in ascending difficulty, which also helps me gauge difficulty levels.

Of course, I can't be super accurate and say a question is a 590-level question, which is why I provide a range.

Hi Brent,

Please help me with the solution:

Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/3 what percent of the total number of the remaining employees would then be clerical?
(A) 25 %
(B) 22.2 %
(C) 20 %
(D) 12.5 %
(E) 11.1 %
gmat-admin's picture

If 1/3 of the 3,600 employees are clerical, then there are 1200 clerical workers.

If 1/3 of the clerical staff are laid off, then 400 of the 1200 clerical workers are laid off.

This means there are 800 clerical workers remaining.

Since 400 workers were laid off, the NEW employee population = 3600 - 400 = 3200

"What percent of the total number of the remaining employees would then be clerical?"

Of the 3200 workers, 800 are clerical workers

800/3200 = 1/4 = 25%

Answer: A

The cost C of manufacturing a certain product can be estimated by the formula C = 0.03 rst², where r and s are the amounts, in pounds, of the two major ingredients and t is the production time, in hours. If r is increased by 50 %, s is increased by 20 %, and t is decreased by 30 %, by approximately what percent will the estimated cost of manufacturing the product change ?

(A) 40% increase
(B) 12% increase
(C) 4% increase
(D) 12% decrease
(E) 24% decrease
gmat-admin's picture

Let's plug in some nice values of r, s and t, and then see what happens when we make the given changes.

Let's try r = 10, s = 10 and t = 10

So, cost = 0.03rst² = 0.03(10)(10)(10²) = 3000

If r is increased by 50 %, then r = 15
If s is increased by 20 %, then s = 12
If t is decreased by 30 %, then t = 7
So, NEW cost = 0.03rst² = 0.03(15)(12)(7²)

Let's use some ESTIMATION....

= (0.03)(180)(7²)
= (3/100)(180)(7²)
= (540/100)(7²)
≈ (5.5)(7²)
≈ (5.5)(50)
≈ 275

So, the original cost was $300 and the new cost is $275

This is a DECREASE, so eliminate A, B and C

Percent change = (100)(change)/original
= (100)(300 - 275)/300
= 25/3
≈ 8 1/3%
≈ 8.333%

The closest answer is D, so it must be correct.

Dear Brent,

Thank you for the reinforcement activity questions. They represent a great pool of questions for various difficulty levels. Though I was able to solve (and understand the explanation for) most of the questions above, this particular question perplexed me and I am still unable to understand the explanations provided underneath the question. Kindly help me understand it in a better and simpler manner if possible. Thanks.

Here's the question for your reference:

A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Was the salesman's commission larger than his base salary last year?

(1) If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year.

(2) The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.

Thanks and Regards,
gmat-admin's picture

Glad to help.
Here's my step-by-step solution: http://www.beatthegmat.com/income-t285243.html#798714


Hi Brent, Could you please help me solve this question by assuming some values?

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?
(1) x > y
(2) xy/100 < x - y
gmat-admin's picture

There's a nice discussion (by several experts) here: http://www.beatthegmat.com/og-13-127-t288372.html

If you have any questions about those approaches, I'm happy to help.


Sir is thera any other easy way to remember the question

By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?

A. 73%
B. 56%
C. 41%
D. 37%
E. 29%
gmat-admin's picture

Here's one approach:

Given: (4/5)(x) = 1
Divide both sides by 4/5 to get: x = 5/4

So, one option is to determine by what percent 5/4 is greater than 4/5
However, working with fractions can be a pain, so we could also go this route:
5/4 = 25/20 and 4/5 = 16/20

Since both values have the same denominator, we can determine by what percent 25 is greater than 16 (a little easier)
This is the same as the percent increase from 16 to 25

Percent increase = (100)(new - old)/old
= (100)(25 - 16)/16
= (100)(9)/16
≈ 56%

Answer: B


Hi Brent,
I find it difficult to solve this problem. I am not clear with the successive percent change calculations. Could you please help me out? Also if you have answered this question elsewhere please share the link.

Thanks in advance.
gmat-admin's picture

Here's my solution: https://gmatclub.com/forum/each-year-for-4-years-a-farmer-increased-the-...

Please let me know if you'd like me to elaborate on any parts of my solution.


A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.

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