Lesson: How Many Variables to Assign

Comment on How Many Variables to Assign

How can we solve this using only one variable: The original price of an item was increased by 24 percent. The new price was then increased by p percent, resulting in a final price. If the final price was 55 percent greater than the original price, what is the value of p?
gmat-admin's picture

Nice question.

First off, an increase of p percent is the same a multiplying the original value by (1 + p/100)

Let's say the ORIGINAL price = $100

GIVEN: The original price ($100) of an item was increased by 24 percent
So, the new price = (1 + 24/100)($100)
= (1.24)($100)
= $124

GIVEN: The new price was then increased by p percent, resulting in a final price.
So, the final price = (1 + p/100)(124)
= 124 + 124p/100

GIVEN: The final price was 55 percent greater than the original price ($100)
So, the final price = (1 + 55/100)($100)
= (1.55)(100)
= 155

Since we have two different expressions for the final price, those two expressions must be equal.

That is: 124 + 124p/100 = 155
Subtract 124 from both sides to get: 124p/100 = 31
Multiply both sides by 100 to get: 124p = 3100
Solve: p = 3100/124 = 25

So, p = 25%

How's that?


Hi Brent!

Not sure how to solve this one: https://gmatclub.com/forum/a-certain-purse-contains-30-coins-each-coin-is-either-a-nickel-or-188659.html (There's no mention of the values of the nickel or quarter, how do we figure it out?)
gmat-admin's picture

Hi Swatato,

The GMAT will never require you to know the value of quarters, dimes, pennies and nickels.
If this were an OFFICIAL question, it would be sure to also mention the values.

For this reason, I have added the values of nickels and quarters to my solution here: https://gmatclub.com/forum/a-certain-purse-contains-30-coins-each-coin-i...


Could you please summarise the guidelines among the *assigning number of variables*, *testing answer choices*, and *solving using algebraic equation(s)*?

I'd like to better understand which technique to use based on the question. Also, (when) is it a good idea to start with *testing answer choices* first?

gmat-admin's picture

Hi Victoriano,

Those concepts are already covered (and somewhat summarized) in videos #2, #3, #4, and #7 in this module.

In most cases, testing the answer choices will be the longer approach. That said, if you aren't sure about how to create corresponding equations from the given information, a good back-up plan is testing the answer choices.

As you're answering practice questions throughout this module, I suggest that you try solving the question in a variety of ways (assigning one variable, assigning two variables, and testing the choices). During that process, you will gain valuable insights into which approaches work best for YOU.

I hope that helps.

I feel like as long as I understand what the question is asking and formulate my equations im more than sufficient to solve stuff, unfortunately there are many questions that I'm struggled on by their wording LOL
gmat-admin's picture

That's very common hurdle. Keep at it!

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