Lesson: Finding x Percent of y

Comment on Finding x Percent of y

Sir, the way you teach and your explanation are so clear and interesting that makes math fun for non math student like me.Kudos to you and your teaching.

HI BRENT,can u pls explain this problem
If a ticket increased in price by 20%, and then increased again by 5%, by what
percent did the ticket price increase in total?

gmat-admin's picture

Sure thing!

Let's say the ORIGINAL ticket price is $100

After a 20% increase, the new ticket price is $120 ($100 + 20% of $100 = $100 + $20 = $120)

After a 5% increase, the FINAL ticket price is $126 ($120 + 5% of $120 = $120 + $6 = $126)

If the ORIGINAL price was $100 and the FINAL price is $126, then the price increase is 26%

After solving some question I feel like always x or whole comes after of . So it okay presume the same .
gmat-admin's picture

I'm leery about saying "always," but I can't think of an example where the "whole" does not come after the word "of"

If course there are questions like "What is 10% of 40% of 60?" but after we calculate 40% of 60, we basically treat it like a new "whole."

If the total payroll expense of a certain business in year Y was $84,000, which was 20 percent more than in year X, what was the total payroll expense in year X ?

(A) $70,000

(B) $68,320

(C) $64,000

(D) $60,000

(E) $52,320
It's a easy question but I don't know what I doing . I used x /84000= 20/100 . What method should I use
gmat-admin's picture

If K is 20% more than W, we can write: K = 1.20W

So, with this question, we're told that year Y's payroll expenses (of $84,000) is 20% more than in year X's expenses.

So, we can write: (year Y's payroll expenses) = 1.20(year X's payroll expenses)

In other words, $84,000 = 1.20(year X's payroll expenses)

Divide both sides by 1.20 to get: $84,000/1.20 = year X's payroll expenses

Evaluate: $84,000 = year X's payroll expenses

Answer: A

In a certain furniture store, each week Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceeds $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week ?

A. $2,200
B. $3,450
C. $4,200
D. $4,250
E. $5,000
I used eliminating method I choose 5000-800. 4200 *5/100 for 210 then 450-240 gives 210 . This tell us it was right . How will I use your method in this
gmat-admin's picture

Let x = total sales

Nancy gets 5% commission on sales that exceed $800

So, commission = 5% of (x - 800)

This means TOTAL SALARY = $240 + 0.05(x - 800)

We get: $450 = $240 + 0.05(x - 800)

Subtract 240 from both sides: 210 = 0.05(x - 800)

Divide both sides by 0.05 to get: 4200 = x - 800

So, x = 5000

damn it. forgot to do the x-800 bit

In the united states 13 out of every 20 can recycled.

What percent of Cans are recycled?

pls help me understand above ques.. https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/cc-6th-percent-word-problems/e/percentage_word_problems_1
gmat-admin's picture

I'm not sure which question you'd like me to answer, so I'll do both.

QUESTION 1: In the united states 13 out of every 20 can recycled. What percent of Cans are recycled?
Part/Whole = 13/20 = 65/100 = 65%

QUESTION 2 (at https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-...): An estimated 3 out of every 25 men are left-handed. What percent of men are left-handed?
Part/Whole = 3/25 = 12/100 = 12%


Hi Brent, I need some basic help here... In the following question, I'm never sure how to properly derive 1.15 and my tendency is to go to 0.85 instead. Here's the question: "Company P had 15 percent more employees in December than it had in January. If Company P had 460 employees in December, how many employees did it have in January?" Can you please help me see how to derive "250/1.2"?
A similar step can be found on Q210 of PS in the OG 2020.
gmat-admin's picture

Question link: https://gmatclub.com/forum/company-p-had-15-percent-more-employees-in-de...

I have no idea where the 250/1.2 comes in. I don't see how we'd get to that point. I also don't see any solutions that require that calculation.
Can you show me more of the solution that mentions 250/1.2?

In the meantime, here's my full solution: https://gmatclub.com/forum/company-p-had-15-percent-more-employees-in-de...


Yulia's picture

Hi Brent,

Please explain me something.

6.4 is what percent of 16,000?

A) 0.0004%
B) 0.04%
C) 0.4%
D) 4%
E) 4.4%

What I did
x/100 * 16000 = 6.4
160x =6.4
x= 6.4/160
x=4/100>>> So I though that the answer is 4% because x= 4/100.

What am i missing?
gmat-admin's picture

Question link: https://gmatclub.com/forum/6-4-is-what-percent-of-105302.html#p1996182

In your solution x = the desired PERCENT
This is why you converted x percent to x/100

So, if x = 4/100, then the desired percent is (4/100)% (aka 0.04%)


I feel like test answer would be faster, however I did used algebraic approach to find the answer:

(?/100)180 = 45, 180? = 4500, ?=450/18 which is 25
gmat-admin's picture

Question link: https://gmatclub.com/forum/what-percent-of-180-is-223668.html

Your solution works perfectly!

your video is pretty good, reminded me a lot of basics, which really help with practicing, also I like a lot of your trick, I would need to practice more to get familiar with them. to be honest my brain is not function enough to use these tricks, like, 23 percent of 37, I would have used direct calculation, which is a headache, but instead I should use 3.7 + 3.7 + 0.27*3 : )
gmat-admin's picture

It takes time to master some of the techniques in this course. After all, for many students, this is the first time they've seen such techniques.

How do the Reinforcement Activities work?

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Study Guide

The step-by-step Study Guide will help direct your studies and ensure that you cover everything that the GMAT tests.

Free “Question of the Day” emails!