idiot proof sales tax formula?

[jzw]

Sarah paid a sales tax of 8% on her purchase. If the sales tax had only been 5%, she would have paid $12 less on her purchase. What was the total amount Sarah paid for her purcahse, including sales tax?

A. 368
B. $380
C. $400
D. $420
E. $432

Ok. So I know the answer is E, but only because I kinda got lucky when I looked @ the answer choices and kind of intuitively guessed that $400 was the starting price that $420 was the price @ 5% (which I knew right away) and that @ 8% it's $432, and I was right. I double checked it by doing the math just to be sure. But what if the numbers hadn't been so "obvious"? Is there an idiot proof formula for figuring this out? Thanks.

[Mike@Magoosh]

Hi, there. I happy to help with this.

Sarah paid a sales tax of 8% on her purchase. If the sales tax had only been 5%, she would have paid $12 less on her purchase.

The difference of those two percents is 8 - 5 = 3%, so this is saying 3% of her purchase is $12. If 3% is $12, then 1% is $4, and 100% is $400.

That's a method you can always use when given two different percent values and the difference between them.

For more general strategies on percent, we have a whole set of video lessons at Magoosh that explain everything you'll need to know about percents for the GMAT.

Here's a sample lesson:
https://gmat.magoosh.com/lessons/209-wor ... h-percents

Here's another percent problem you can practice.
https://gmat.magoosh.com/questions/30
After you submit your answer to that question, the next page will have a full video explanation. Each one of our 800+ of our practice questions has its own video explanation.

Let me know if you have any questions.

Mike

[sam2304]

108% - 105% = 12$
3% = 12$
1% = 4$

We are asked to find 108% = 432.