Question

When a certain number is increased by 25% its value becomes 388. What will the value be if the original number is decreased by 30%?

Answer 1

Please NAME the "certain number".

Answer 2

They didn't say

Answer 3

But I think it's 291

Answer 4

Seriously? I did not ask what name was given in the problem statement. I asked YOU to name it. Go ahead. Just give it a name.

Answer 5

x

Answer 6

Perfect.

Can you write an expression for 25% of x?

Answer 7

0.25x?

Answer 8

Excellent.

Can you now write an expression for x increased by 25% of x?

Answer 9

x+0.25x

Answer 10

Superb.

And this is the same as x(1 + 0.25) = x(1.25)

Do you agree with this assessment?

Answer 11

Yes

Answer 12

Okay, now we have

x + 0.25x = 388

or

x*(1 + 0.25) = 388

or

x*(1.25) = 388

If you agree, can you now solve for x?

Answer 13

x = 310.40

Answer 14

You are awesome. Where does that leave us?

What is that number increased by 30% of itself?

Answer 15

I have no idea

Answer 16

Can you write an expression that represents 30% of the value we are calling 'x'?

Answer 17

Would it be 0.30x ?

Answer 18

Perfect. Just like the 25% we did earlier.

Now, how about the value, x increased by 30% of itself?

Answer 19

x+0.30x

Answer 20

You have it.

x + 0.30x = x(1 + 0.30) = x(1.30)

We know the value of x. x = 310.40

What is 310.40 * 1.30?

Answer 21

403.52

Answer 22

That's what I get.

Answer 23

Hmmm, it's saying that's incorrect

Answer 24

Whoops! Another reading of the problem says we DECREASE by 30%, not INCREASE.

Answer 25

Start back here... Can you write an expression representing a number we are calling 'x' DECREASED by 30% of its value? Keep in mind that 30% of the value is 0.30x.

Answer 26

x-0.30x

Answer 27

That's it. Can you now solve the problem?

Answer 28

217.28

Answer 29

Thanks!

Answer 30

NOW we have it.

Lesson learned? ALWAYS reread the problem statement before you think you are done. Let's just make sure we are answering the right question!

Answer 31

Good practice to always reread the problem before checking your answer. Many times you'll discover that you've actually answered some other question. And always check the answer!

Answer 32

While we're beating the dead horse of philosophy, this is not ALWAYS a good rule. If you are under extreme time pressure, such as GRE, LSAT, GMAT or various competitions and important exams, you simply don't have time to do that. Do the best you can and move on! Under normal circumstances, it IS a GREAT rule to follow.