Lesson: Working with Percent

Comment on Working with Percent

Should we learn both ways or the first method is sufficient for gmat
gmat-admin's picture

Make sure you are familiar with all of the ways to express percents.

I am having a lot of trouble recognizing the percent - part - and whole. I continuously put the values in the wrong spots.
gmat-admin's picture

For the Townville question. I wrote 120/800 = x/100, then divided 800 by 8 to get the denom of 100, and 120 by the same 8 to get the numerator of 15, getting 15/100, yielding the same answer. Would you say this is a valid, timely way to solving similar problems using this method?
gmat-admin's picture

Your approach is perfect! In fact, later in the module, we discuss this exact same approach.

For others reading this, here's what kingerikclusters did:

Take: 120/800
Divide top and bottom by 8 to get the EQUIVALENT fraction 15/100, which equals 15% (done!)

This is the fastest/easiest approach, whereas some (many) students will resort to long division to calculate 120 ÷ 800 = 0.15, which equals 15%

Nice work!


Hi Brent,

I did not understand the second part of this answer. Grateful for more clarifiactions please.

If x is 8/3 percent of y, y is what percent of x?

A. 3/8
B. 37.5
C. 375
D. 3,750
E. 3.75
x is 8/3 percent of y
Let's plug in some nice values for x and y that satisfy the above conditions.
We know that 8/3 is 8/3 percent of 100.
So, x = 8/3 and y = 100 works

y is what percent of x?
In other words, 100 is what percent of 8/3?
Rewrite as 100 is what percent of 2 2/3?
Well, 100 is about 40 TIMES 2 2/3
If we express 40 as a percent we get 4000%
So, our answer will be close to 4000
gmat-admin's picture

Question link: https://www.beatthegmat.com/if-x-is-8-3-percent-of-y-y-is-what-percent-o...

Here's another way to look at it.

We can see that 8/3 and y = 100 satisfies the condition that x is 8/3 percent of y.

The question asks "y is what percent of x?"

In other words, "100 is what percent of 8/3?"

Or we can ask "100 is what percent of 2.7?" (since 8/3 ≈ 2.7)

Well, we know that 2.7 is 100% of 2.7

So, 27 is 1,000% of 2.7

And 270 is 10,000% of 2.7

Since 100 lies between 27 and 270, we know that the correct answer is between 1,000% and 10,000%

Answer: D

Does that help?


Yulia's picture

Hi Brent,
I also have a question.

x = (8/3)/100 * y

x = 8/300 * y

y = 300/8 * x

y = 37.5 * x
I reached y = 37.5 * x and chose answer B = 37.5%
How do we get to y=37500?
gmat-admin's picture

The question asks: "y is what percent of x?"

You're correct to say that y = (37.5)(x)
This, however, this does not mean that y is 37.5% of x.

Here are two different ways to look at it:
1) If y is 37.5% of x, then y = 37.5/100 of x
In other words, y = 0.375x (not y = 37.5x)

2) If y = x, then y = 100% of x
If y = 2x, then y = 200% of x
If y = 3x, then y = 300% of x
If y = 10x, then y = 1000% of x
If y = 20x, then y = 2000% of x
If y = 37.5x, then y = 3750% of x

Does that help?

Hi Brent.


In the above question, I do not understand. How does 12x = 2y turn into x/y = 2/12 ?
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-12x-2y-is-80-of-5y-what-is-the-value-of-26...

Start with: 12x = 2y
Divide both sides of the equation by y to get: 12x/y = 2
Divide both sides of the equation by 12 to get: x/y = 2/12

Does that help?

ASIDE: You might want to review this video on solving equations: https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...


Of the 14,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?

Would this count as faster way to do it?

1/2 x 2/7 = 1/7 (remaining journeymen)
Total remaining employees 1 - 1/7 (who left) = 6/7
New percent of journeymen employees 1/7 divided by 6/7 = 1/6

gmat-admin's picture

Question link: https://gmatclub.com/forum/of-the-14-210-employees-of-the-anvil-factory-...

That's perfectly sound logic!


Hi Brett,

Hope you can clarify this problem for me.

In an election, 68% of the voters exercised their franchise. Of these, 48% were women. The number of males exercising their franchise was 53,040. How many eligible voters were there in all?

The wording again put me off here.

The question stem says 48% OF THESE voters. So naturally, I took .48 x .68 to get the actual percentage of female voters. Apparently this is not right. The question stem means that 48% of women were voters and 52% were male. What's going on here?
gmat-admin's picture

Question link: https://gmatclub.com/forum/in-an-election-68-of-the-voters-exercised-the...

One of the issues with your approach is that you're mixing up the total number of ELIGIBLE voters with the total number of people who ACTUALLY VOTED. Also, notice that the value we derive from 0.48 x 0.68 doesn't tell us anything.

To show the error of your conclusion, consider this analogous question:

In an election, only 1% of the voters exercised their franchise. Of these (actual voters), 50% were women.
Applying your approach, 0.01 x 0.50 = 0.005 = 0.5%

So, does this mean only 0.5% of the ELIGIBLE voters were women? No. We have no information about the male/female breakdown of the eligible voters who did NOT vote.

Does this mean only 0.5% of the ACTUAL voters were women? No. We are already told that 50% of the ACTUAL voters are women.

That said, you're right about the wording. The question basically says 68% of the VOTERS voted.
That makes about as much sense as saying "68% of the dogs are dogs"

The question should read:
"In an election, 68% of the ELIGIBLE voters exercised their franchise."
In other words, "In an election, 68% of the ELIGIBLE voters actually voted."

Does that help?


Thanks Brent. That makes sense now.

Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?

A. x=y=z
B. x=y<z
C. x<y<z
D. x<z<y
E. y<z<x

Can you please give your solution for this problem

I kept X Y Z to be 100 for all three and respectively adding and subtracting as told i got

Z = 100 ( original price no disc no tax)
X = 99.75
Y = 110.25

for that reason i chose answer X<Z<Y

gmat-admin's picture

For Store Y, you didn't apply the 5% discount.

Here's my solution: https://gmatclub.com/forum/stores-x-y-and-z-each-sell-a-certain-item-tha...


Hi Brent,

question link https://www.beatthegmat.com/if-x-is-8-3-percent-of-y-y-is-what-percent-of-x-t292760.html

Can you, please, show more of an algebraic approach to this problem. I do not feel I understand your approach very well. This is what I am doing algebraically, but I cannot get to the correct answer and for the life of me, I cannot understand what am I doing wrong.
divide both sides by x and get 1=8y/3x ==>(8/3)*(y/x)=1 ==>y/x=3/8 ==> y/x=0.375 to transfer back to percent multiply result by 100 ==> y/x=37,5% What am i doing wrong here?
gmat-admin's picture

The problem is right here, where you wrote: x = (8/3)*y
We're told that "x is 8/3 PERCENT OF y"
You have read the information as "x is 8/3 of x"

Here's my solution: https://www.beatthegmat.com/if-x-is-8-3-percent-of-y-y-is-what-percent-o...


Question link: https://gmatclub.com/forum/a-certain-city-with-population-of-132-000-is-to-be-divided-into-76217-20.html

I tried to test if the answer could be 10,700 (least among the given options). First i calculated the average population (12000) then checked that if one district has 10700 as population, balance 1300 (deviation from average) could be borne by remaining 10 districts, leaving remaining districts with a population of 12,130. This way, no other district exceeds the population by more than 10%.
Your thoughts, Brent?
gmat-admin's picture

Question link: https://gmatclub.com/forum/a-certain-city-with-population-of-132-000-is-...

10% of 10,700 = 1,070
10,700 + 1,070 = 11,770
So, a population of 11,770 is 10% greater than a population of 10,700

So, if the other districts have populations of 12,130, then we've broken the condition that no other district exceeds the population by more than 10%.



Please let me understand how is 57=1/3 here.

Thank you.
gmat-admin's picture

Solution link: https://gmatclub.com/forum/at-the-end-of-year-x-automobile-installment-c...

Since 57 doesn't equal 1/3, I think you're missing a piece of information.

The question tells us that "automobile finance companies extended $57 billion of credit, or 1/3 of the automobile installment credit."
In other words, $57 billion = 1/3 of the automobile installment credit.
If x = the automobile installment credit, then: $57 billion = (1/3)(x)

Does that help?

Yes, thank you.

At the end of year X, automobile installment credit accounted for 36% of all outstanding consumer installment credit. At that time automobile finance companies extended$57 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?

A. 62
B. 171
C. 475
D. 513
E. 684
For this you mentioned C as answer but wrote 513 ..so which one is correct
gmat-admin's picture

My solution: https://gmatclub.com/forum/at-the-end-of-year-x-automobile-installment-c...

In my explanation about how to approximate the answer, I say that the correct answer is a little less than $513 billion.
Since C (475) is little less than $513 billion, C is correct.

Thank you for the explanation that helps a lot

Hey Brent, I read through quite a few solutions and still having a hard time understanding this questions:
gmat-admin's picture

It's a very tricky question. If you haven't already seen it, my solution appears on page 2: https://gmatclub.com/forum/a-certain-city-with-population-of-132-000-is-...

I saw a little ambiguity in this question https://gmatclub.com/forum/exactly-how-many-bonds-does-bob-have-282720.html.

I thought bonds are money, if the target question is asking money then the answer would have been E
gmat-admin's picture

Question link: https://gmatclub.com/forum/exactly-how-many-bonds-does-bob-have-282720.html

That's correct. If the question had asked "What is the VALUE of Bob's bonds?", then E would have been the correct answer.


I didn't do the way like you did, instead I just wrote x = (2/75)y, and then I wrote, y = (?/100)x, for the first equation I get y = (75/2)x, this must equal to the second equation, so noticed that 100 is 50 times 2, so 75*50 = Answer D
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-x-is-8-3-percent-of-y-y-is-what-percent-of...

That approach works perfectly! One of the great things about GMAT math questions is that they can (almost always) be solved using more than one approach.

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