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TheLostOne
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After receiving a 25% discount, Sue paid $180 for a lawnmowe 03 Aug 2014, 20:04
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Hello!

I was working on

After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?

And I was certain I had it. I figured if I multiplied $180 x 1.25 it would bring me back to the original price. How is that fundamentally different than .75x = 180 and then dividing 180 by .75?

Thanks!
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gautamodi
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After receiving a 25% discount, Sue paid $180 for a lawnmowe 04 Aug 2014, 04:56
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Let the price of the original be X
25% of x = .25X

therefore X-.25X = 180....75X=180

180 x1.25x is totally wrong as u cant multiply it this way or i did not understand how you came to this.

Kudos if i helped u!!!
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mikemcgarry
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After receiving a 25% discount, Sue paid $180 for a lawnmowe 06 Aug 2014, 11:50
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TheLostOne
Hello!

I was working on

After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?

And I was certain I had it. I figured if I multiplied $180 x 1.25 it would bring me back to the original price. How is that fundamentally different than .75x = 180 and then dividing 180 by .75?

Thanks!
Show more
Dear TheLostOne,
My friend, you have stumbled into one of the most fundamental math mistakes on the entire GMAT. This is a very common mistake, and therefore an extremely common trap, so it's crucial to understand this.

Suppose one number A is decreased to B. Whatever the percent decrease from A to B was, it will NEVER be the same numerical percent value as the percent increase from B back to A. Increase and decrease between the same two values NEVER are the same numerical value of the percent.

Think about it. Suppose price decreases from $100 to $75 --- obviously, that's a 25% decrease. Now, suppose we increase from $75 to $100. More than half the people who take the GMAT will fall into the trap of thinking that this is a 25% increase, and it is not. For that increase, we start with $75, and the increase amount, $25, is 1/3 of the starting value, so this is a 33 1/3% increase. That's the correct value, which most people will miss. The GMAT loves traps like this, because it can write the question, set up the trap, and scores of test takers will just run into it, as if they are running into a big butterfly net. What's more, most of the people who make this mistake are absolutely sure that they are doing the right thing! It's one of the easiest ways for the GMAT to write a question that separates the folks who understand from those who don't. If you understand this one fact, it will pay off huge dividends when you avoid these traps. See more here:
https://magoosh.com/gmat/2012/understand ... -the-gmat/

In this problem, we had some initial price X, which was decreased by 25%. Think about what that means: 1/4 of the price was removed, and 3/4 of the price remains. The part that remains, the 3/4 of the original price, is $180. Well, divide that by 3 --- $60 is the 1/4 part, the part that was removed in the decrease. Therefore, the initial price is $240. That's what you would get if you divided $180 by 0.75, but doing that division is a cumbersome way to think about it. It makes much more sense to think in terms of simple fractions.

You made the classic mistake of assume that, since from X to $180 was a 25% decrease, then $180 to X must be a 25% increase. Again, this is the big butterfly net that the GMAT simply sets up, and hordes of unsuspecting test takers run directly into this mistake, completely confident that they are doing something correct. You ran into this mistake in your thinking. I can't emphasize enough --- if you are able to understand and recognize this mistake, then you won't be caught be a trap that catches a huge number of test takers, and that alone will help to set you apart.

Does all this make sense?
Mike :-)
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TheLostOne
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After receiving a 25% discount, Sue paid $180 for a lawnmowe 06 Aug 2014, 11:56
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mikemcgarry
TheLostOne
Hello!

I was working on

After receiving a 25% discount, Sue paid $180 for a lawnmower. What is the original price of the lawnmower before the discount?

And I was certain I had it. I figured if I multiplied $180 x 1.25 it would bring me back to the original price. How is that fundamentally different than .75x = 180 and then dividing 180 by .75?

Thanks!
Dear TheLostOne,
My friend, you have stumbled into one of the most fundamental math mistakes on the entire GMAT. This is a very common mistake, and therefore an extremely common trap, so it's crucial to understand this.

Suppose one number A is decreased to B. Whatever the percent decrease from A to B was, it will NEVER be the same numerical percent value as the percent increase from B back to A. Increase and decrease between the same two values NEVER are the same numerical value of the percent.

Think about it. Suppose price decreases from $100 to $75 --- obviously, that's a 25% decrease. Now, suppose we increase from $75 to $100. More than half the people who take the GMAT will fall into the trap of thinking that this is a 25% increase, and it is not. For that increase, we start with $75, and the increase amount, $25, is 1/3 of the starting value, so this is a 33 1/3% increase. That's the correct value, which most people will miss. The GMAT loves traps like this, because it can write the question, set up the trap, and scores of test takers will just run into it, as if they are running into a big butterfly net. What's more, most of the people who make this mistake are absolutely sure that they are doing the right thing! It's one of the easiest ways for the GMAT to write a question that separates the folks who understand from those who don't. If you understand this one fact, it will pay off huge dividends when you avoid these traps. See more here:
https://magoosh.com/gmat/2012/understand ... -the-gmat/

In this problem, we had some initial price X, which was decreased by 25%. Think about what that means: 1/4 of the price was removed, and 3/4 of the price remains. The part that remains, the 3/4 of the original price, is $180. Well, divide that by 3 --- $60 is the 1/4 part, the part that was removed in the decrease. Therefore, the initial price is $240. That's what you would get if you divided $180 by 0.75, but doing that division is a cumbersome way to think about it. It makes much more sense to think in terms of simple fractions.

You made the classic mistake of assume that, since from X to $180 was a 25% decrease, then $180 to X must be a 25% increase. Again, this is the big butterfly net that the GMAT simply sets up, and hordes of unsuspecting test takers run directly into this mistake, completely confident that they are doing something correct. You ran into this mistake in your thinking. I can't emphasize enough --- if you are able to understand and recognize this mistake, then you won't be caught be a trap that catches a huge number of test takers, and that alone will help to set you apart.

Does all this make sense?
Mike :-)
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Beautiful post.

Ironically I am pretty good at these normally! At least the idea of consecutive percent changes, and yet I fell for this trap. Something to keep an eye out for.

Thanks again.
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duffy
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After receiving a 25% discount, Sue paid $180 for a lawnmowe 04 Sep 2014, 01:10
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The 1.25 is "Itself" and "0.25" or 180 times itself and another 25%
OR
180*1.25

Yes that is true BUT........

$100 increase 20% 100*1.2=120
Now decrease by 20% or you pay 0.8 120*0.8=96

You can see this with the 'itself' method
120*1.2=144 144-120=24 So 20% of the new number is 24 not 20 as before cause the new number is bigger.
120-24=96

So keep in mind that increasing by 25% then decreasing by 25% does not bring you back. 25% of the bigger number is bigger, than 25% of the smaller number.