If a price was increased by x% and then decreased by y%, is the new pr

Question

If a price was increased by  x\%  and then decreased by  y\% , where x and y are both non-zero, is the new price higher than the original?

(1)  x \gt y

(2)  x = 1.2y

M16-12

Bunuel · Accepted Answer

Official Solution:

If a price was increased by  x\%  and then decreased by  y\% , where x and y are both non-zero, is the new price higher than the original? 
 
Let  P  represent the original price.
 
(1)  x > y . 
 
If  x  is significantly larger than  y , the new price is higher than the original. However, if  x  is only slightly larger, the new price is lower. For example, if  x = 20  and  y = 19 , the new price is  P*1.20*0.81 < P .
 
(2)  x = 1.2y 
 
Similar reasoning applies here. If  y  is large, the new price is smaller (if  y = 100 , the new price is 0). If  y  is small, the new price is higher than the original (if  y = 10 , the new price is  P*1.12*0.9 = P*1.008 > P ).
 
(1)+(2) Combining Statement 1 with Statement 2 provides no additional information. For example, if  P = 100 ,  x = 120 , and  y = 100 , the new price becomes 0, which is lower than the original price of 100. However, if  P = 100 ,  x = 12 , and  y = 10 , the new price becomes  100 * 1.12 * 0.9 = 100 * 1.008 , which is higher than the original price of 100. Therefore, the given information is not sufficient to determine whether the new price is higher or lower than the original price.

Answer: E

chetan2u · Answer

The answer is not going to be B, as even statement II is also not sufficient..
Statement I is contained within statement II, so let us straight way check statement II..

Now x=1.2y..
The final price is 
 a(1+\frac{1.2y}{100})(1-\frac{y}{100})=a(1+\frac{1.2y}{100}-\frac{y}{100} +\frac{1.2y^2}{10000}=a(10000+2y-1.2y^2)/10000 ..
Now is this greater than initial a

If you take initial price as 100 and y a small %, say 10%..x=1.2y=12%..
So final price is 100*(1+0.12)(1-0.1)=100*(1.12)*0.9=112*0.9=100.8 , so greater than 100..

But let us take y slightly bigger % say 50% and x=1.2*50%=60%
So final price is 100*(1+0.6)(1-0.5)=100*1.6*0.5=160*0.5=80, which is less than 100..

So different answers..

E

Always be careful while solving % problems when everything is in variables.

gravy · Answer

Could someone evaluate from here? I am confused about distributing the a.

Do you first distribute the A to what is contained within the first set of parentheses, and then foil from there? Or do you distribute the a to every term immediately?

Thank you very much.

TestPrepUnlimited · Answer

Treat the price as 1, the new price would be  (1 + x\%) * (1 - y\%) = 1 + x\% - y\% - xy\%\% . We are comparing this with the original price 1, so the question is:

Is  x\% - y\% - xy\%\% > 0  ?
Is  x - y - xy/100 > 0  ?

As a note, we should treat x and y as positive (since we don't say increase by -20% etc).

Statement 1: 
 x > y  is true. However  y + xy/100  is greater than  y  so  x > y + xy/100  isn't necessaily true. Insufficient.

Statement 2: 
Note this statement already incorporates statement 1, and it is a stronger statement.

Plug in x = 1.2y into our new question:
  1.2y - y - \frac{1.2y^2}{100} > 0  ?
 0.2y > \frac{1.2y^2 }{ 100}  ?
 20 > 1.2y  ?
And we can see this is not necessarily true. So statement 2 is insufficient.

Combined: 
Since statement 2 already incorporates statement 1, combined we still have statement 2 so still insufficient.

Ans: E

TestPrepUnlimited · Answer

Hello  gravy  ,
We can only distribute  a  into one of the parenthesis, either of them. You can also foil first and then distribute the  a  into the final parenthesis.

If multiplying  a  into both parenthesis was allowed then we would be able to take out two multiples of  a  which doesn't make sense.

Varane · Answer

Answer is E

However if statement one was x<y then answer would have been A.

Posted from my mobile device

STanya · Answer

Hi ,I am not clear with the explanation, can someone please elaborate this?

Dream009 · Answer

Think this a 
Statement 1 - A number increases by 5/4 and then decreases 4/5 - number remains same
here x is 125% and y is 80%
now x> 125
and if Y was more than 80% number original number will decrease and if y was 70% orginal number will increase - so statement 1 is useless

trying option C - both statement 1 and 2 say x>y - so C option is out

You are left with B & E

Let see now - 1.2y-y - 1.2y^2/100 is successive % change
= 0.2y - 1.2y^2
this can be negative or positive basis value of Y. So B is not possible. Answer is E

GulfTube · Answer

If a price was increased by x% and then decreased by y%, where x and y are both non-zero, is the new price higher than the original?

(1) x>y 
Since we aim to get a Yes and a No, Use logical thinking:
To get a No is easier: take x=100 so if we start with the original price of 100, it will become 200 (200% of original price), and take y = 50 so reducing 200 by 50% means bringing it down back to 100. Hence we get a No b/c final price is same as original price.

Now to get a Yes, think along the lines that if we still double the price but reduce it a little less say y = 20, then 0.8*200 = 160, so final price is bigger than original.  Insufficient.

(2) x=1.2y 
use similar cases as used in first statement to get a No, x=120 so y = 100, starting with price of 100, 2.2*100=220. reducing this by 100% means bringing it down to 0. Hence we have got a No.

Using similar strategy of reducing by little %, we take y=10 so x=12. starting with price of 100, increase by 12% becomes 112. reduce by 10% = 90% of 112. 
easier way to do this calculation is to benchmark. 10% of 112 is 11.2, now multiply by 9, 11.2*9 = 100.8. so final price is 100.8 which is greater than original . we get a Yes as well.  Insfficient.

Since statement 2 already incorporates statement 1, combined statements are insufficient . answer E

If a price was increased by x% and then decreased by y%, is the new pr

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If a price was increased by x% and then decreased by y%, is the new pr

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