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505-555 (Easy)|   Inequalities|   Percent and Interest Problems|   Word Problems|                           
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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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Ans B

15/100 of x > 10

x>66.67 rounded off to 67.
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15% of X = 10.
X = 1000/15 = 66.67% ~ 67%, (B).
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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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militarytocorp
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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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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Shef08
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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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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a12bansal
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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As per the question: Let's assume the OG price be "x".

Now,

x-x(0.85) > 10
x(1-0.85) > 10
x > 10/0.15
x > 66.66

Just greater is 67, option B.

Cheers
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Bunuel
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





Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

[email protected]
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