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# On a certain item, a discount of x% on the marked price

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Intern
Joined: 22 Jun 2010
Posts: 18

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On a certain item, a discount of x% on the marked price [#permalink]

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05 Oct 2011, 06:09
3
This post was
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Difficulty:

95% (hard)

Question Stats:

41% (01:52) correct 59% (02:33) wrong based on 66 sessions

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On a certain item, a discount of x% on the marked price gives a trader a profit of 2x% on the cost price. Is his profit more than 40% of the cost price?

A. The marked price is more than 1.8 times the cost price
B. The marked price is more than 1.7 times the cost price

Please explain the solution. I am unable to solve this.
[Reveal] Spoiler: OA

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Intern
Joined: 04 Oct 2011
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Re: Hard DS question. Help needed [#permalink]

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05 Oct 2011, 13:06
1
KUDOS
On a certain item, a discount of x% on the marked price gives a trader a profit of 2x% on the cost price. Is his profit more than 40% of the cost price?

A. The marked price is more than 1.8 times the cost price
B. The marked price is more than 1.7 times the cost price

Please explain the solution. I am unable to solve this.

discount = x % of marked price
profit 2x % of the cost

take A

marked price more than 1.8 times
so if the Cost price is 100 then marked price = 280

to get more than 40 % profit x should be (41/2) will take it as 42/2 = 21

if x is equal to 42 then the sell price should be more than 142 so that the merchant will get more than 40%
21% of 280 is 61.6
280-61.6 is greater than 142

when you apply the same rule in Statement 2 them it should be 270-59.4

this is also more than 142 so both are right

ANS D

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Intern
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Re: Hard DS question. Help needed [#permalink]

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05 Oct 2011, 13:53
looks like A to me........ even though OA=D

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Math Forum Moderator
Joined: 20 Dec 2010
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Re: Hard DS question. Help needed [#permalink]

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05 Oct 2011, 14:37
1
KUDOS
gmatblues wrote:
On a certain item, a discount of x% on the marked price gives a trader a profit of 2x% on the cost price. Is his profit more than 40% of the cost price?

A. The marked price is more than 1.8 times the cost price
B. The marked price is more than 1.7 times the cost price

Please explain the solution. I am unable to solve this.

Marked Price: M
Cost Price: C

M-xM=C+2xC
2xC+xM=M-C
x(2C+M)=M-C
x=(M-C)/(2C+M)------------1

Q: Is 2xC>0.4C
OR
Is x>0.2

Substitute 1:
Is (M-C)/(2C+M) > 0.2
M-C>0.4C+0.2M
0.8M>1.4C
M>1.75C

Rephrase: Is M>1.75C?

1. M>1.8C
Sufficient.

2. M>1.7C
Not Sufficient.

Ans: "A"
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Manager
Joined: 31 May 2011
Posts: 85

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Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Re: Hard DS question. Help needed [#permalink]

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08 Oct 2011, 06:03
fluke wrote:
gmatblues wrote:
On a certain item, a discount of x% on the marked price gives a trader a profit of 2x% on the cost price. Is his profit more than 40% of the cost price?

A. The marked price is more than 1.8 times the cost price
B. The marked price is more than 1.7 times the cost price

Please explain the solution. I am unable to solve this.

Marked Price: M
Cost Price: C

M-xM=C+2xC
2xC+xM=M-C
x(2C+M)=M-C
x=(M-C)/(2C+M)------------1

Q: Is 2xC>0.4C
OR
Is x>0.2

Substitute 1:
Is (M-C)/(2C+M) > 0.2
M-C>0.4C+0.2M
0.8M>1.4C
M>1.75C

Rephrase: Is M>1.75C?

1. M>1.8C
Sufficient.

2. M>1.7C
Not Sufficient.

Ans: "A"

Fluke i guess the answer should be D.
The question asks whether profit is more than 40% of CP or not. As you have explained from statement 1 we get the answer as Yes and from statement 2 we get the answer as NO. Hence in both the cases we are getting a unique answer and hence sufficient. As here No is also considered as sufficient to answer the question

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Re: Hard DS question. Help needed [#permalink]

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08 Oct 2011, 06:56
Sudhanshuacharya wrote:
Rephrase: Is M>1.75C?

1. M>1.8C
Sufficient.

2. M>1.7C
Not Sufficient.

Ans: "A"

Fluke i guess the answer should be D.
The question asks whether profit is more than 40% of CP or not. As you have explained from statement 1 we get the answer as Yes and from statement 2 we get the answer as NO. Hence in both the cases we are getting a unique answer and hence sufficient. As here No is also considered as sufficient to answer the question

Question is:

Is M>1.75C?

1. M>1.8C
Sufficient because 1.8C>1.75C. The answer will always be YES.

2. M>1.7C
Because we just know that M>1.7C, now M can be 1.8C(of course greater than 1.7C), in which case the answer to the question would be Yes OR 1.72C(of course greater than 1.7C), in which case the answer to the question would be No.
So, Not Sufficient.

Unless there is something wrong with my rephrasing, A seems logical.
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Re: On a certain item, a discount of x% on the marked price [#permalink]

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17 Jun 2016, 20:38
gmatblues wrote:
On a certain item, a discount of x% on the marked price gives a trader a profit of 2x% on the cost price. Is his profit more than 40% of the cost price?

A. The marked price is more than 1.8 times the cost price
B. The marked price is more than 1.7 times the cost price

Please explain the solution. I am unable to solve this.

relationship in markup ,discount & profit is given as
(1+M/100)(1-x/100)=(1+P/100)
where M=markup
X=discount
P=profit.(given profit=2x%)

(1+M/100)(1-x/100)=(1+2X/100)
(100+M)(100-X)/100=(100+2X)
10^4-100X+100M-MX=10^4+200X
100M=200X+MX
100M=X(200+M)
X=100M/(200+M)------(a)
statement(1)
M=1.8CP(cP=cost price)
substituting in (a)
X=180CP/(200+1.8CP)
Let CP=1 then X= 89%
we will get X profit in terms of CP....suff...
similarly Statement(2) also suff..

Ans D

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Re: On a certain item, a discount of x% on the marked price [#permalink]

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07 Sep 2017, 02:28
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Re: On a certain item, a discount of x% on the marked price   [#permalink] 07 Sep 2017, 02:28
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