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# Problem Solving Territory: 700+ questions only..............

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Senior Manager
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Problem Solving Territory: 700+ questions only.............. [#permalink]

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22 Sep 2006, 21:53
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Folks, I will be posting questions from Problem Solving section regularly in this thread.............

Here comes our first question

1. A shopkeeper increases the price of the article by X% and then decreases the resulting price by X%. As a result the price of the article is reduced by 180 \$. Ater one more such cycle the price is further reduced by 153\$. Find the oriiginal price of the article.
_________________

Last edited by cicerone on 25 Sep 2008, 00:58, edited 1 time in total.

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Director
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23 Sep 2006, 00:10
CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

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Senior Manager
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23 Sep 2006, 02:19
CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)

u r missing something........
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Last edited by cicerone on 25 Sep 2008, 00:57, edited 1 time in total.

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SVP
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23 Sep 2006, 02:28
He definied x = X / 100 It makes sens as x < X

Actually, he could set y=(1+X/100)(1-X/100)

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Senior Manager
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23 Sep 2006, 02:50
Fig wrote:
He definied x = X / 100 It makes sens as x < X

Actually, he could set y=(1+X/100)(1-X/100)

Hey fig, that's fine.
But i said the price is decreased by 180 and not that the decreased price is 180.

So how can he write cp(1+x)(1-x) =180
CP(1+x)(1-x) is the reduced price where as 180 is the reduction in the prize.

The correct expression would be
CP(1+x)(1-x) = P-180, where P= initial price and x=X/100.
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Last edited by cicerone on 25 Sep 2008, 00:57, edited 1 time in total.

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23 Sep 2006, 02:55
Absolutly

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Director
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23 Sep 2006, 04:45
CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)

DAMN! 2 days to go and I'm crapping up!!!

Okay.. here goes.

CP - CP(1-x^2) = 180
=> CP*x^2 = 180 --(1)

CP(1-x^2) - CP(1-x^2)(1-x^2) = 153
=> CP(1-x^2)x^2 = 153 --(2)

Using (2)/(1), we get
(1-x^2) = 153/180
=> x^2 = 1 - 153/180 = 27/180 = 3/20 --(3)

From (1) and (3) we get,

CP(3/20) = 180 => CP = 1200.

Howzzat? Don't tell me I'm wrong again
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Kudos [?]: 37 [0], given: 2

SVP
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23 Sep 2006, 04:55
CP (1+x)(1-x) = 180
180 (1+x)(1-x) = 153 => (1-x^2) = 153/180

=> CP/180 = 180/153
=> CP = 210.60 (approx)

Oops! 2 days to go and I'm crapping up!!!

Okay.. here goes.

CP - CP(1-x^2) = 180
=> CP*x^2 = 180 --(1)

CP(1-x^2) - CP(1-x^2)(1-x^2) = 153
=> CP(1-x^2)x^2 = 153 --(2)

Using (2)/(1), we get
(1-x^2) = 153/180
=> x^2 = 1 - 153/180 = 27/180 = 3/20 --(3)

From (1) and (3) we get,

CP(3/20) = 180 => CP = 1200.

Howzzat? Don't tell me I'm wrong again

paddyboy, will u go on this monday for the GMAT?

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Director
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23 Sep 2006, 04:59
Tuesday actually, but I'm not counting it...
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Kudos [?]: 37 [0], given: 2

SVP
Joined: 01 May 2006
Posts: 1794

Kudos [?]: 165 [0], given: 0

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23 Sep 2006, 05:04
I c Best of luck for it :D U are on the right track for it

Next week seems to be the week for at least 3 of us

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Director
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23 Sep 2006, 05:08
Who's the third?

And dude, Best of luck! I'm sure we'll maul the GMAT

Or as Futuristic put it, "Spread it out on the lawn and jump on it with hob-nailed boots!"
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

Kudos [?]: 37 [0], given: 2

SVP
Joined: 01 May 2006
Posts: 1794

Kudos [?]: 165 [0], given: 0

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23 Sep 2006, 05:31
I prefer to PM u it

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Senior Manager
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Re: Problem Solving Territory: 700+ questions only.......... [#permalink]

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25 Sep 2006, 15:37
cicerone wrote:
Folks, I will be posting questions from Problem Solving section regularly in this thread.............

Here comes our first question

1. A shopkeeper increases the price of the article by X% and then decreases the resulting price by X%. As a result the price of the article is reduced by 180 \$. Ater one more such cycle the price is further reduced by 153\$. Find the oriiginal price of the article.

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Senior Manager
Joined: 28 Aug 2006
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27 Sep 2006, 20:58
Folks, this is again based on the basic funda of Percentages.

If a number is increased by x% and then decreased by x% there always will be a decrease.

It is given that the price (P)of the article is increased by x% and then decreased by x%. So the price will definitely decrease. Let the price decrease by y%

So clearly it is given that the price is decreased by 180 \$.
Hence y%(P) = 180.............................(1)
Now the price of the artice is P-180. Since that same change is applied again on the present price this also will decrease by the same y%
Clearly it is given that the present price is decreased by 153\$
Hence y%(P-180) = 153.....................(2)

From (1) and (2)
y%(180) = 27

ie y = 15.

Substituting the value of y in (1) we get
15%(P) = 180
Hence P=1200.

Now since u know the concept , u can use the options given in the exam to solve the questions like these.

Let's take 1200 as our first option
Initially the price is reduced by 180.

So the present price is 1020.

Now if 180 is the decrease on 1200, calculate the proportinate decrease on 1020.....

So i mean 1200------180
1020------??
ie (1020/1200)180 = (102/120)180 =153 which is exactly the second decrease in the given question..

Hence 1200 must be the answer........

I think i am lucid

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Senior Manager
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27 Sep 2006, 21:34
Ok folks, let's get into the next question.........

2.
Attachments

q2.doc [24.5 KiB]

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Senior Manager
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28 Sep 2006, 23:44
Hey, what happened?

Kevin, yezz, paddyboy,......... where r u?

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Senior Manager
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29 Sep 2006, 18:54
cicerone all of them are drinking beer !!!

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Manager
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29 Sep 2006, 19:46
CE=1, not sure on how to calculate CD
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"Success is 99 percent failure" - Soichiro Honda

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VP
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29 Sep 2006, 23:31
hey, I know this problem has to be solved based on similarity of triangles. But finding it difficult to identify which triangles need to be compared.

Cicerone, great initiative. Please keep posting questions.
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The path is long, but self-surrender makes it short;
the way is difficult, but perfect trust makes it easy.

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Senior Manager
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04 Oct 2006, 08:57

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04 Oct 2006, 08:57

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