This question can be attacked or upfront (for instance using back solve strategy) or in the smartest way possible: backsolving but without the using of the answer choices as anchor.

Pure reverse engineering.

The final cost of the coat is 95.6 and we need to find out the original price, from where we started.

\($ 95.6\) was discounted of \($50\). So, \(95.6 + 50 = $ 145.6\)

Next step is that the price was discounted of 20% which mean we have to add a 20%: \($ 145.6 * 1.2 = $ 174.72\).

Next, the coat at the beginning was charged of a 40% more the original starting price. Which means that we need now to cut off 40 %: \($ 174.72 * 0.6 =\)$ 104.83

The answer choice is C.

Regards

PS: without calculator........faster and convenient.

I do not understand this procedure.

We know a certain price is reduced by 20% to a final price of 145.6. Knowing this, we do

X - 0.2X = 145.6

X(1 - 0.2) = 145.6

X(0.8) = 145.6

X = 145.6/0.8 = 182

Further, we know this new price was obtained by increasing the original price by 40%, so

X + 0.4X = 182

X(1 + 0.4) = 182

X(1.4) = 182

X = 182/1.4 = 130


In particular, this line is why I think the solution doesn't make sense to me:



Discounting something by 20% does not work back in reverse directly. Example: I discount a price of 100 by 20% to obtain a new price of 80. However, this does not work in reverse like in your example: 80 x 1.2 = 96, not 100. Therefore, 145.6 * 1.2 = $ 174.72 is lower than the actual value you need.(<182)

This is the same principle behind why people say that a company which has a drop in share value will need to gain back more value to get back to the same spot as before. Losing 20% of the share price means you will have to get back 25% to get back to the same spot: 100 - 20% = 80. 80 x 1.25 = 100.

If the price was off of 20 %. usually, if a price is supposed 100 then is discounted of 20% we do have 100*0.8=80

However, we are working backward, we are going back, on the contrary so we must add 20%. So, 145.6*1.2= 174.72

Also, this is wrong \(X = \frac{145.6}{0.8} = 182\) because if you at the time had a discount of 20% BUT now you are working backward you do not have 20% off (minus) anymore (I.E divided for 0.8) but you must add up 20% so you have to multiply for 1.2. The result is NOT $ 182 but $174.72. of course, you do not reach C as the answer.

Hope is clear now.



Regards

PS: read carefully my explanation from the final price back to the original, I am sure it is easy to grasp

I cannot really explain my side of the calculations more than I already have so I will address



I am also working backward. I would like to clarify that the 20% we are adding back is not 20% of 145.6, but 20% of the original unknown price. To rephrase it:

Unknown price X is > 145.6

Decrease X by 20% first: we take 0.2*X, which is equal to 20% of unknown price X, and then subtract it from X to arrive at a new decreased price of 145.6

Here is a comparison to my simpler example for each step

X - 0.2(X) = 80
X - 0.2(X) = 145.6

X(0.8) = 80
X(0.8) = 145.6

X = 80/0.8 = 100
X = 145.6/0.8 = 182


Notice the error is in the 20% you take.

We all agree 80*1.2 =/= 100.
We all agree 80*1.25 = 100.

This means we KNOW we should not multiply by 1.2, but instead by 1.25.



If we are asked to find the original price, which at some point was modified by 20% off, then I will have to incorporate that 20% off to work backwards and find it. I don't know if we just don't agree on the phrasing used in the question but I will ask some people to double check this for me.

EDIT; I appreciate you taking the time to write out your explanations. I've asked some other people to double check this for what I'm having an issue understanding about the original prompt.

I think you also right.

Weirdly, I check the book and in the explanation pick E as answer and C in the answer choices.

Any explanation of calculations in book?

In the book is backsolving, picking before B and use it to assert if is more of this value or less and going ahead eliminating the answer choices. To cumbersome. Two pages more.

However, what I do not understand is you .25 value, honestly whe you have to calculate for the original value.

95.6+50= 145.6

145.6/0.8 (back 20%) = 182

182/1.4 (back of 40%) = 130

I edited the OA.

However, that value is unclear to me about the stock market in your example.

Thank you for the discussion, it was beneficial. kudos

It was just an example to illustrate percentage gains and losses and why it's harder get back to your previous value after negative shift.

Example:

I have 1 share of company that is worth $100.

If value of the share drops by 20%, my new value of the share is $80.

If I want to get back to the original value of the share ($100), the share price would have to increase by 25%.

80*1.25 = 100.

In the end, a loss of 20% has lost us $20, but to make up those SAME $20, we would have to gain 25%.

Difference in 5% to make up the same dollar value. Hence, easy to lose, hard to gain.

You are absolutely correct with your approach and the answer..

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