M16-12

Well E is correct.

Lets assume principal is P

P(1+x/100)(1-y/100) is the final price.

Now if we have x=1.2y

P(1+x/100)(1-x/120)
To find out if this will be <P

P(1+x/100)(1-x/120)<P

or (100+x)(120-x)<120*100
or 20x-x^2< 0

or x>20

So lets take Y = 30
X =42

So 100 becomes 142 and multiply 142 by 0.7 =99.4

So X=12, Y =10.. The final value is greater than P
but in X =42, Y=30.. the final value is less than P

lastminutemba 1.2x/100 is not equal to x/120

Great question, almost got tricked into selecting C, but then decided to continue solving and plugging in values to test.

My solution below (a bit too time-consuming for GMAT, but helps me with understanding).
Let P = original price.
New price = P(1+ x/100)(1- y/100) = P(1+ x/100 - y/100 -xy/1000)
Test if (1+ x/100 - y/100 -xy/1000) > 1
x-y- xy/100 > 0
100x - 100y - xy > 0 --- (1)

Statement (1) gives the same information as statement (2), which has more details.

Sub x = 1.2y into (1),
120y - 100y - (1.2y)*y > 0
20y - 1.2y^2 > 0
y (20 - 1.2y) > 0

Since y is a %, it has to be > 0
20 - 1.2y > 0
1.2y < 20
y < 20/1.2 = 16

The new price is only higher for y < 16

Hi all / Bunuel

My two-cents' worth here, pardon my approach - I was looking at the problem by seeing the issue in a certain way under time pressure, not sure if this is right.

I do not intend to go the lazy route by any means - please feel free to give me your suggestions and feedback.

My reasoning:

The stem does not mention if P = price can only be a positive number. Suppose P is:
a) Positive
- Without calculating, we know we can have a certain combination of x, y such that the new price is either bigger or smaller than the original price.
- We know that this is definitely possible with some smart numbers plugged in (see Bunuel's example)

b) P=0
- If P=0, then new price will DEFINITELY not be higher than the original price (since new = old price = $0).

Knowing that P=0 potentially (not stated by stem specifically to be positive P), we know that we would always end up with the case of YES/NO and NO when P=0.

Hence, Answer = E.

PS: This is the only way I could solve under 90 secs .

We can potentially make an adjustment to the question stem to say that P = some positive number to be absolutely sure that we force the thinking in the way the various authors have expounded previously.

Can someone provide an example where x=1.2y and the original value is higher than the new price


Thanks
Nikita

Sure. Say p = 100, x = 60 and y = 50.

Then the new price = 100*1.6*0.5 = 80.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

I think this is a high-quality question and I agree with explanation.