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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
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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
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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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05 Oct 2011, 12:06
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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.
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 28061.6 is greater than 142
when you apply the same rule in Statement 2 them it should be 27059.4
this is also more than 142 so both are right
ANS D



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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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05 Oct 2011, 13:37
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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 MxM=C+2xC 2xC+xM=MC x(2C+M)=MC x=(MC)/(2C+M)1 Q: Is 2xC>0.4C OR Is x>0.2 Substitute 1: Is (MC)/(2C+M) > 0.2 MC>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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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 MxM=C+2xC 2xC+xM=MC x(2C+M)=MC x=(MC)/(2C+M)1 Q: Is 2xC>0.4C OR Is x>0.2 Substitute 1: Is (MC)/(2C+M) > 0.2 MC>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: 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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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)(1x/100)=(1+P/100) where M=markup X=discount P=profit.(given profit=2x%) (1+M/100)(1x/100)=(1+2X/100) (100+M)(100X)/100=(100+2X) 10^4100X+100MMX=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 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)(1x/100)=(1+P/100) where M=markup X=discount P=profit.(given profit=2x%) (1+M/100)(1x/100)=(1+2X/100) (100+M)(100X)/100=(100+2X) 10^4100X+100MMX=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)(1x/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?



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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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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 BunuelCan you please change the OA. It should be A.



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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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13 Nov 2017, 03:43
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OA is wrong. The answer would be D. Let the cost price be 100. Markup price = 100c Selling Price= 100(1x%) 100*(1+2x%) = 100c * (1x%) 100 + 2x = 100c  cx x (c+2) = 100 (c1) ..........eq1 Profit should be > 40% 100(1+2x%) > 40 100 + 2x > 40 x>20 Substitute value of x from above eq. 100(c1) > 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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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
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Abhishiek wrote: OA is wrong. The answer would be D.
Let the cost price be 100. Markup price = 100c
Selling Price= 100(1x%) 100*(1+2x%) = 100c * (1x%) 100 + 2x = 100c  cx x (c+2) = 100 (c1) ..........eq1
Profit should be > 40% 100(1+2x%) > 40 100 + 2x > 40 x>20
Substitute value of x from above eq. 100(c1) > 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



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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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13 Nov 2017, 23:20
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Mo2men wrote: Abhishiek wrote: OA is wrong. The answer would be D.
Let the cost price be 100. Markup price = 100c
Selling Price= 100(1x%) 100*(1+2x%) = 100c * (1x%) 100 + 2x = 100c  cx x (c+2) = 100 (c1) ..........eq1
Profit should be > 40% 100(1+2x%) > 40 100 + 2x > 40 x>20
Substitute value of x from above eq. 100(c1) > 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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