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

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Math Expert
Joined: 02 Sep 2009
Posts: 58335
If a price was increased by x% and then decreased by y%, is the new pr  [#permalink]

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05 Feb 2019, 23:59
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Difficulty:

95% (hard)

Question Stats:

33% (02:17) correct 67% (01:48) wrong based on 78 sessions

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If a price was increased by $$x$$% and then decreased by $$y$$%, is the new price higher than the original?

(1) $$x \gt y$$

(2) $$x = 1.2y$$

M16-12

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Math Expert
Joined: 02 Aug 2009
Posts: 7949
If a price was increased by x% and then decreased by y%, is the new pr  [#permalink]

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06 Feb 2019, 11:41
Bunuel wrote:
If a price was increased by $$x$$% and then decreased by $$y$$%, is the new price higher than the original?

(1) $$x \gt y$$

(2) $$x = 1.2y$$

M16-12

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..

E

Always be careful while solving % problems when everything is in variables.
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##### General Discussion
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Joined: 07 Dec 2017
Posts: 1129
If a price was increased by x% and then decreased by y%, is the new pr  [#permalink]

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06 Feb 2019, 01:23
Here's the logic: if a product increases and then decreases by the same percent, it's overall value will decrease - because the decrease % is being taken from a larger base. for example, if 30 is increased by 100% - that's 60, and if that's decreased by 100 we get 0 - less than the original!
Looking at the answers, 1) is inconclusive. it depends what the base is and how much larger x is than y.
ex' where the answer is yes: base=100, x=100, y=10 ==> new number 180>100. ex' where its no: x=100,y=90 ==> new number = 20< 100.
2) tells is y>x which means that the new number is definitely smaller than the original. B is the answer
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If a price was increased by x% and then decreased by y%, is the new pr  [#permalink]

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06 Feb 2019, 11:12
1
A price marked up by 25% and subsequently marked down 20% will result in original price.

i.e. If mark up= 1.2*mark down, final price = original price

Eg.
Original price: \$100
Mark up 25%: 25
Price after mark up: 125
Mark down 20%: 125/5= 25
Price after mark down: 100

St.1 is Insufficient.
X= 25%, Y >20% No
X= 25%, Y= < 20% Yes

St.2 is sufficient as calculated above. Final price will be equal to original price.

Ans B

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If a price was increased by x% and then decreased by y%, is the new pr   [#permalink] 06 Feb 2019, 11:12
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