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

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Intern
Joined: 22 Jun 2010
Posts: 15
On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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05 Oct 2011, 05:09
3
3
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Difficulty:

95% (hard)

Question Stats:

17% (03:06) correct 83% (02:44) wrong based on 120 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?

(1) The marked price is more than 1.8 times the cost price
(2) The marked price is more than 1.7 times the cost price
Intern
Joined: 04 Oct 2011
Posts: 10
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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05 Oct 2011, 12:06
1
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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Joined: 20 Dec 2010
Posts: 1828
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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05 Oct 2011, 13:37
2
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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Posts: 80
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GMAT Date: 12-07-2011
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Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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08 Oct 2011, 05:03
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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Joined: 20 Dec 2010
Posts: 1828
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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08 Oct 2011, 05:56
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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Joined: 05 Mar 2015
Posts: 1000
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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17 Jun 2016, 19:38
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
Manager
Joined: 23 Jun 2016
Posts: 108
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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11 Nov 2017, 18:41
rohit8865 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.

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

(1+M/100)(1-x/100)=(1+P/100)

I am not sure if we could do this here. I guess it would work if mark up, discounts and profits are all compared to Cost.

The question mentions discount on the "marked price" and profit on the "cost price"

Can someone confirm this understanding?
SVP
Joined: 26 Mar 2013
Posts: 1888
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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12 Nov 2017, 11:15
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.

Dear Bunuel

Can you please change the OA. It should be A.
Intern
Joined: 28 Dec 2010
Posts: 49
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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13 Nov 2017, 03:43
1
OA is wrong.

Let the cost price be 100.
Markup price = 100c

Selling Price= 100(1-x%)
100*(1+2x%) = 100c * (1-x%)
100 + 2x = 100c - cx
x (c+2) = 100 (c-1) ..........eq1

Profit should be > 40%
100(1+2x%) > 40
100 + 2x > 40
x>20

Substitute value of x from above eq.
100(c-1) > 20(c+2)
100c - 100 > 20c + 40
80c>140
c>1.75

Now when markup price is greater than 1.75, trader would make more than 40%.
1. Yes, he would make. Sufficient.
2. No, he wouldn't make. Sufficient.

D.
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SVP
Joined: 26 Mar 2013
Posts: 1888
On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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13 Nov 2017, 03:50
1
Abhishiek wrote:
OA is wrong.

Let the cost price be 100.
Markup price = 100c

Selling Price= 100(1-x%)
100*(1+2x%) = 100c * (1-x%)
100 + 2x = 100c - cx
x (c+2) = 100 (c-1) ..........eq1

Profit should be > 40%
100(1+2x%) > 40
100 + 2x > 40
x>20

Substitute value of x from above eq.
100(c-1) > 20(c+2)
100c - 100 > 20c + 40
80c>140
c>1.75

Now when markup price is greater than 1.75, trader would make more than 40%.
1. Yes, he would make. Sufficient.
2. No, he wouldn't make. Sufficient.

D.

In statement 2 if the price is 1.75 cost or less...Answer would be No

If the price greater than 1.75 cost..answer would yes...(take Any values from statement 1).

In both cases the value is grater than 1.7 as stated so you will have turning point at 1.75............so Insufficient
Intern
Joined: 28 Dec 2010
Posts: 49
Re: On a certain item, a discount of x% on the marked price gives a trader  [#permalink]

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13 Nov 2017, 23:20
1
Mo2men wrote:
Abhishiek wrote:
OA is wrong.

Let the cost price be 100.
Markup price = 100c

Selling Price= 100(1-x%)
100*(1+2x%) = 100c * (1-x%)
100 + 2x = 100c - cx
x (c+2) = 100 (c-1) ..........eq1

Profit should be > 40%
100(1+2x%) > 40
100 + 2x > 40
x>20

Substitute value of x from above eq.
100(c-1) > 20(c+2)
100c - 100 > 20c + 40
80c>140
c>1.75

Now when markup price is greater than 1.75, trader would make more than 40%.
1. Yes, he would make. Sufficient.
2. No, he wouldn't make. Sufficient.

D.

In statement 2 if the price is 1.75 cost or less...Answer would be No

If the price greater than 1.75 cost..answer would yes...(take Any values from statement 1).

In both cases the value is grater than 1.7 as stated so you will have turning point at 1.75............so Insufficient

Yeah, you are right. Thanks
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Re: On a certain item, a discount of x% on the marked price gives a trader &nbs [#permalink] 13 Nov 2017, 23:20
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