# Lesson: Introduction to Percent

## Comment on Introduction to Percent

### Great shortcuts - I would of

Great shortcuts - I would of never thought of those tricks and tips.

### Hi Brent,

Hi Brent,

Can you please explain this question, I guess something is missing in question. If we remove 2 more apples remaining apples will be 96 i.e. 96%, so not sure how ans is 50

https://gmatclub.com/forum/there-are-100-apples-in-a-bag-of-which-98-are-green-and-the-rest-red-228471.html "There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green?"

----------------------
START
We start with 98 green apples and 2 red apples (TOTAL = 100).
98/100 = 98%.
So, 96% of the apples are green.
-----------------------
REMOVE APPLES PHASE
Once we remove 50 green apples, we are left with:
48 green apples and 2 red apples (TOTAL = 50)
So, 48 of the 50 apples are green.
48/50 = 96/100 = 96%.
So, 96% of the apples are green.
-----------------------
Does that help?

Cheers,
Brent

### Hi Brent.

Hi Brent.

https://gmatclub.com/forum/if-mn-0-and-25-percent-of-n-equals-37-1-2-percent-of-m-what-is-the-220305.html

Can you help explain the steps involved in coming to this answer in the above mentioned GMAT club post:

25 percent of n equals 37(1/2) percent of m
In other words, 1/4 of n equals 3/8 of m
We get: n/4 = 3m/8

What is the value of 12n/m?
Take n/4 = 3m/8
Cross-multiply to get: (8)(n) = (3m)(4)
Simplify: 8n = 12m
Divide both sides by m to get: 8n/m = 12 [ALMOST THERE!!!]
Multiply both sides by 1.5 to get: 12n/m = 18 ### You bet!

You bet!

25 percent of n equals 37(1/2) percent of m
[given information from the question]

In other words, 1/4 of n equals 3/8 of m
[25% = 1/4 and 37.5% = 3/8, so I just replaced each percent with their fraction equivalents]

We get: n/4 = 3m/8
[1/4 of n = (1/4)(n) = (1/4)(n/1) = n/4]
[3/8 of n = (3/8)(n) = (3/8)(n/1) = 3n/8]

What is the value of 12n/m?
[This is what the question asks us]

Take n/4 = 3m/8
Cross-multiply to get: (8)(n) = (3m)(4)
[we're applying a nice rule that says: If a/b = c/d, then ad = bc]
[more on this technique here: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

Simplify: 8n = 12m
[(8)(n) = 8n, and (3m)(4)= 12m]

Divide both sides by m to get: 8n/m = 12
[The question asks for the value of 12n/m]
[So, dividing both sides of our equation by m help make the left side of our equation resemble 12n/m]

Multiply both sides by 1.5 to get: 12n/m = 18
[8 x 1.5 = 12]
[So, this step causes the left side of our equation to become 12n/m]

Does that help?

Cheers,
Brent

### Perfect perfect.

Perfect perfect.
how to use the shortcut with denominators larger than 100.
for example, 37/120
thanks ### Great question!

Great question!

Here are two options:

Option 1: divide numerator and denominator by 10 to get 3.7/12 (then follow the steps covered in the video)
To get a denominator of 100, we must multiply 12 by a number a bit bigger than 8 (8+)
Multiply 3.7 by 8+ to get approximately 24
So, 37/120 = 3.7/12 ≈ 24/100 ≈ 24%

Option 2: try to make the denominator 1000
Take, for example, the fraction 111/253
253 is close to 250
So, to get a denominator of 1000, we multiply numerator and denominator by a number a bit less than 4
We get 111/253 ≈ 444/1000 ≈ 44.4/100 ≈ 44.4%

Does that help?

Cheers,
Brent

### Hi Brent ,

Hi Brent ,

https://gmatclub.com/forum/a-dishonest-dealer-claims-to-sell-a-product-at-its-cost-pric-160822.html

In this question , why is 56.2% wrong ?I dont understand the explanations given there

Thankyou ! This question has already been categorized as "Poor Quality"
The reason for this is that the words "he added 20% impurities to the product" is ambiguous.

Skip this questions. There are 1000's of GMAT-quality practice questions to work on. This one is not worth your time.

Cheers,
Brent

### https://gmatclub.com/forum/in

https://gmatclub.com/forum/in-the-football-league-of-2010-manu-won-40-of-their-games-268209.html

in my attempt to answer the question, i went this route and ended up nowhere. can you please explain to me why i ended up nowhere although the logic seems to be right.

(0.4X + 0.6(3x))/4x *100

i think it is because there is one variable in a function that does not equal anything. even if we make it equals to Y where Y is the percent of total won games, we need two equations since we have two variables.

i feel like my approach is logically sound but mathematically wrong. i just can't lock it down on why it is wrong. "In the football league of 2010, ManU won 40% of their games. In 2011 they won 60% of their Games. If there were thrice as many games played in the second as in the first, What percentage of the games did ManU win the 2 Years?"

Let x = number of games in 2010
So, 3x = number of games in 2011

Number of WINS = 0.4x + 0.6(3x)
= 0.4x + 1.8x
= 2.2x

TOTAL number of games = 4x

So, win percentage = (2.2x/4x)(100)
= (2.2/4)(100)
= 220/4
= 55%

As you can see, these are the same values you used.
So, I'm assuming you made an arithmetic error.

Cheers,
Brent

### https://gmatclub.com/forum

https://gmatclub.com/forum/there-are-100-apples-in-a-bag-of-which-98-are-green-and-the-rest-red-228471.html

is it possible to solve this question by probability ? As far as I can tell, we can't use probability in a meaningful way here, other than to say that P(select green apple) = 98/100, but this is the same as saying that 98 of the 100 apples are green.

That said, perhaps another student will see this post and come up with a useful way to use probability.

Cheers,
Brent

### Wow! amazing shortcuts!

Wow! amazing shortcuts!

### Hi Brent,

Hi Brent,

I have a general question regarding simple interest rates. If we are given that two people have invested a certain amount into their accounts and are asked to determine who collects the greater interest after one year, would it be impossible to determine with just the below information?:

1) Amount invested by A is greater than amount invested by B
2) Interest rate for A is lower than interest rate for B

Apologies in advance if the post is not under the correct topic as I couldn't find the interest rate video lesson.

Thanks ### Placing the question here is

Placing the question here is fine. It's definitely related to percents.

To answer your question, neither statement alone is enough to determine who collects the most interest.
The statements combined are still insufficient information.

Consider these two possible cases:
CASE I: A invests \$100 at 1% interest, and B invests 50\$ at 20% interest. In this case, A receives \$1 in interest, and B receives \$10 in interest.
CASE II: A invests \$100 at 15% interest, and B invests 50\$ at 20% interest. In this case, A receives \$15 in interest, and B receives \$10 in interest. 