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A seller increased the price of an item by X% and then decreased it by

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Manager
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Joined: 28 May 2018
Posts: 87
Location: India
Schools: Tuck '21, ISB '20, NTU '20
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
A seller increased the price of an item by X% and then decreased it by  [#permalink]

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New post 24 Mar 2019, 08:53
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E

Difficulty:

  75% (hard)

Question Stats:

25% (01:29) correct 75% (02:00) wrong based on 20 sessions

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A seller increased the price of an item by X% and then decreased it by Y%. What is the original price of the item, if X is an odd perfect square less than 10?

1) The price of the item after X% increase and Y% decrease is $2475
2) Y = 2X

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Joined: 12 Apr 2011
Posts: 148
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: A seller increased the price of an item by X% and then decreased it by  [#permalink]

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New post 24 Mar 2019, 10:32
PriyankaPalit7 wrote:
A seller increased the price of an item by X% and then decreased it by Y%. What is the original price of the item, if X is an odd perfect square less than 10?

1) The price of the item after X% increase and Y% decrease is $2475
2) Y = 2X


From the question stem we are told X is an odd perfect square below 10, hence X can have 2 values either 1 or 9.

If we solve further we will see neither statement A nor B can help us to get the answer.

Hence E is the correct answer.
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Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
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Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A seller increased the price of an item by X% and then decreased it by  [#permalink]

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New post 24 Mar 2019, 11:08
PriyankaPalit7 wrote:
A seller increased the price of an item by X% and then decreased it by Y%. What is the original price of the item, if X is an odd perfect square less than 10?

1) The price of the item after X% increase and Y% decrease is $2475
2) Y = 2X


Let the original price of the item be P.
So after increasing price by x%. Price becomes P(1+x/100)
after decreasing the price by y%. Price becomes P(1+x/100)(1-y/100)

Since x is an odd perfect square less than 10. So either x = 1 or 9

Statement 1: The price of the item after X% increase and Y% decrease is $2475
i.e. P(1+x/100)(1-y/100) = 2475 where x = 1 or 9
even if we put value of x we can't find P or y uniquely.
P*1.01*(1-y/100) = 2475 or P*1.09*(1-y/100) = 2475

NOT SUFFICIENT

Statement 2: Y = 2X
So, (x,y) = (1,2) or (9,18)
NOT SUFFICIENT

Combined:
P*1.01*0.98 = 2475 or P*1.09*0.82 = 2475
again P has two values. So we can't determine unique values of P.

NOT SUFFICIENT
Answer E...
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Re: A seller increased the price of an item by X% and then decreased it by   [#permalink] 24 Mar 2019, 11:08
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A seller increased the price of an item by X% and then decreased it by

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