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# A retail item is offered at a discount of p percent (where p

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A retail item is offered at a discount of p percent (where p [#permalink]

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27 Mar 2013, 15:41
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A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

A. p+5/1.05
B. p/1.05 +5
C. 1.05p-5
D. p-5/1.05
E. 1.05(p – 5)
[Reveal] Spoiler: OA

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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27 Mar 2013, 22:51
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Let x be the price of the item.
Final price after discount and sales tax = x * (1 - p/100) * 1.05

Let q be the percent discount which would result in the same final price.
Then,
x * (1 - p/100) * 1.05 = x * (1 - q/100)
=> 1.05 - 1.05p/100 = 1 - q/100
=> q/100 = 1.05p/100 - .05
=> q = 1.05p - 5

Hence , option C is correct.
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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27 Mar 2013, 21:23
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manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

p+5/1.05
p/1.05 +5
1.05p-5
p-5/1.05
1.05(p – 5)

Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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28 Mar 2013, 05:24
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So I initially approached it the way you all did but messed up the math as I tried to convert the 1.05 into a fraction over 100 on both sides.

Instead to stay within 2:30 I plugged and chugged
Original Price: 100
Discount: 10
Discounted Price: 90

Sales tax on 90 is 4.5. Final price is 94.5

To achieve this price without tax you need a discount of 5.5

The answer choices are nice too for plugging and chugging

p+5/1.05 too big approximately 15/1
p/1.05 +5 too big again
1.05p-5 10.5-5=4.5 exactly
p-5/1.05 5/1.05...slightly smaller than 5 but not by much. Not nearly as big as the denominator bring the value to half way between 4 and 5
1.05(p – 5) More than 5. In fact 5.25

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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23 Sep 2013, 02:50
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rrsnathan wrote:
mau5 wrote:
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

p+5/1.05
p/1.05 +5
1.05p-5
p-5/1.05
1.05(p – 5)

Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.

Hi,

.
What does the second part of the question states " If the state sales tax were not assessed......"

My understanding is that for text ''if the sales tax were not assessed" mean tax is not charged that means the discounted purchase price would be

Discounted purchase price = 80 i.e. with out the 5% of tax in the discounted purchase price

Rrsnathan.

Original price = \$100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = \$84.

The question asks: if the tax were not assessed, what percent discount from the original price (\$100) would result in the same final price of \$84. The answer is 16%.

Does this make sense?
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A retail item is offered at a discount of p percent (where p [#permalink]

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23 Sep 2013, 05:14
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manimgoindowndown wrote:
So I initially approached it the way you all did but messed up the math as I tried to convert the 1.05 into a fraction over 100 on both sides.

Instead to stay within 2:30 I plugged and chugged
Original Price: 100
Discount: 10
Discounted Price: 90

Sales tax on 90 is 4.5. Final price is 94.5

To achieve this price without tax you need a discount of 5.5

The answer choices are nice too for plugging and chugging

p+5/1.05 too big approximately 15/1
p/1.05 +5 too big again
1.05p-5 10.5-5=4.5 exactly
p-5/1.05 5/1.05...slightly smaller than 5 but not by much. Not nearly as big as the denominator bring the value to half way between 4 and 5
1.05(p – 5) More than 5. In fact 5.25

Just a small tip...When plugging in always try the easier option first. A,B and D involve divsion whereas C and E involve only multiplication.

Last edited by b2bt on 03 Oct 2014, 00:35, edited 1 time in total.

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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21 Sep 2013, 22:43
mau5 wrote:
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

p+5/1.05
p/1.05 +5
1.05p-5
p-5/1.05
1.05(p – 5)

Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.

Hi,

.
What does the second part of the question states " If the state sales tax were not assessed......"

My understanding is that for text ''if the sales tax were not assessed" mean tax is not charged that means the discounted purchase price would be

Discounted purchase price = 80 i.e. with out the 5% of tax in the discounted purchase price

Rrsnathan.

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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28 Oct 2013, 15:53
Original price = \$100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = \$84.

The question asks: if the tax were not assessed, what percent discount from the original price (\$100) would result in the same final price of \$84. The answer is 16%.

Does this make sense?

Bunuel,

How have you arrived at this-
Discount = p = 20%.
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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30 Oct 2013, 00:53
honchos wrote:
Original price = \$100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = \$84.

The question asks: if the tax were not assessed, what percent discount from the original price (\$100) would result in the same final price of \$84. The answer is 16%.

Does this make sense?

Bunuel,

How have you arrived at this-
Discount = p = 20%.

I assumed it, plugged smart numbers.
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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24 Dec 2013, 12:20
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

A. p+5/1.05
B. p/1.05 +5
C. 1.05p-5
D. p-5/1.05
E. 1.05(p – 5)

Backsolving would be the best approach here using Smart Numbers
Original price = 100
p = 20%
Tax = 5%

Then reduced price after tax \$84
So then we need 16% before taxes

Therefore,
Target 16
Input P = 20

Now, it would help if the answer choices are stated clearly as fractions but anyway the approach is clear

Hope it helps
Cheers!
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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21 Jul 2014, 12:31
Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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21 Jul 2014, 12:42
maggie27 wrote:
Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !

Original price = \$100.
Final price = \$84.

The question basically asks about the actual discount on the item, which is 16%.
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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21 Jul 2014, 12:53
Bunuel wrote:
maggie27 wrote:
Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !

Original price = \$100.
Final price = \$84.

The question basically asks about the actual discount on the item, which is 16%.

But my doubt is how do we decide that "final price" is 84 which with the applied sales tax or jus 80 which is without sales tax?
What if the "If the state sales tax were not assessed" part is omitted?

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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18 Jun 2015, 02:47
Bunuel wrote:
honchos wrote:
Original price = \$100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = \$84.

The question asks: if the tax were not assessed, what percent discount from the original price (\$100) would result in the same final price of \$84. The answer is 16%.

Does this make sense?

Bunuel,

How have you arrived at this-
Discount = p = 20%.

I assumed it, plugged smart numbers.

Hi Bunnuel,

if 5% on 80 is assessed as sales tax then it should be 80-4 right?

why is it 80+4?

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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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18 Jun 2015, 03:28
SunthoshiTejaswi wrote:
Hi Bunnuel,

if 5% on 80 is assessed as sales tax then it should be 80-4 right?

why is it 80+4?

5% state sales tax is assessed on the discounted purchase price, so (final price) = (discounted purchase price)*1.05. How else?
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A retail item is offered at a discount of p percent (where p [#permalink]

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11 Jul 2016, 06:19
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

A. p+5/1.05
B. p/1.05 +5
C. 1.05p-5
D. p-5/1.05
E. 1.05(p – 5)

When we usually talk about taxes being applicable..they are applicable on both the Marked Price and the Discounted Price. The question should state that state sales tax is assessed on what and on what its not...ambiguous wording..
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Re: A retail item is offered at a discount of p percent (where p [#permalink]

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23 Nov 2016, 20:41
Understand the right answer is to plug in smart numbers. But could someone please show step by step on how to solve this algebraically? I can't seem to be able to get the right answer. Any help much appreciated ! Bunuel

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Re: A retail item is offered at a discount of p percent (where p   [#permalink] 23 Nov 2016, 20:41
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