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Difficulty: 505-555 Level,    Inequalities,    Percent and Interest Problems,    Word Problems,                            
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?

(A) 45
(B) 67
(C) 75
(D) 83
(E) 150

Let the smallest amount the original price of sweater be X

So if we have 0.15*X>10
X> 10/0.15-----> 2/3*100= 66 Hence X is greater than 66.
Smallest possible value will be 67. Ans B

Difficulty level around 650 okay
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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Ans B

15/100 of x > 10

x>66.67 rounded off to 67.
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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15% of X = 10.
X = 1000/15 = 66.67% ~ 67%, (B).
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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I am seeing most of the solutions here were done with algebra. However, do you think it is just as efficient to think conceptually. Or did I happen to get lucky?

10% of 67 is 6.7

half of 6.7 is 3.35.

6.7+3.35 is 10.05.

is this an ok approach ?
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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militarytocorp wrote:
If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?

A. 45
B. 67
C. 75
D. 83
E. 150


Let's calculate what happens if she saves exactly $10.

Marked Price * (15/100) = 10

Marked Price = 200/3 = 66.67

The marked price must be greater than 66.67 since she saved more than $10. So the minimum amount of marked price = $67

Answer (B)
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
I have a question, I solved it by taking every value in the answer choice and multiplying it by 0.85 to see the difference.
For example,

75- 75*0.85> 10.

So the answer came to C as it has savings more than 10. B had savings equal to 10. Can someone explain me how to do it this way.
Have I done it correct? But the answer I got is wrong...

Posted from my mobile device
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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Shef08 wrote:
I have a question, I solved it by taking every value in the answer choice and multiplying it by 0.85 to see the difference.
For example,

75- 75*0.85> 10.

So the answer came to C as it has savings more than 10. B had savings equal to 10. Can someone explain me how to do it this way.
Have I done it correct? But the answer I got is wrong...

Posted from my mobile device


67 - 67*0.85 = 10.05 > 10, so the smallest amount the original price of the sweater could be, to the nearest dollar is $67.
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
Hi VeritasKarishma , Bunuel

I marked A- 45

Below is my approach, Please correct me

Discount can only be given on Marked Price. Hence I took Marked Price and solved the question.

Marked Price * (15/100) = 10

Marked Price = 200/3 = 66.67

The marked price must be greater than 66.67 since she saved more than $10. So the minimum amount of marked price is $67.

But the question is asking original price which should be Cost Price. Hence it should be lower than marked price i.e. 45 is the only option.


I am just a beginner. Please help me.

Thanks
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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a12bansal wrote:
Hi VeritasKarishma , Bunuel

I marked A- 45

Below is my approach, Please correct me

Discount can only be given on Marked Price. Hence I took Marked Price and solved the question.

Marked Price * (15/100) = 10

Marked Price = 200/3 = 66.67

The marked price must be greater than 66.67 since she saved more than $10. So the minimum amount of marked price is $67.

But the question is asking original price which should be Cost Price. Hence it should be lower than marked price i.e. 45 is the only option.


I am just a beginner. Please help me.

Thanks


Original price here means price before the discount. So what the question is asking is the marked price, not cost price. You cannot find the cost price here so there is no way you can say it must be $45.

Had the question been -
"Which of the following could be the cost price?"
- you would have been correct
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Re: If Mel saved more than $10 by purchasing a sweater at a 15 p [#permalink]
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