There were 36,000 hardback copies of a certain novel sold before the

From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold
Let x = number of hardback copies sold during this time
So 9x = number of paperback copies sold during this time
So, x + 9x = total number of copies sold DURING THIS TIME PERIOD

A total of 441,000 copies of the novel were sold in all
GIVEN: 36,000 hardback copies sold BEFORE the paperback version was issued.
So, we get: 36,000 + x + 9x = 441,000
Simplify: 36,000 + 10x = 441,000
We get: 10x = 405,000
Solve: x = 40,500
This also means 9x = 9(40,500) = 364,500

So, 364,500 paperback copies were

Answer: C

Cheers,
Brent

Say x was the # of hardback copies sold from the time the first paperback copy was sold.

Then the total # of paperback copies sold was 9x;
Hence the total # of copies sold was (hardback)+(paperback)=(36+x)+(9x)=441 --> x=40.5.

So, the total # of paperback copies sold was 9x=9*40.5=364.5 or 364,500.

Answer: C.
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36+9x+x=441

10x=405

x=40.5

9x=40.5*9=364.5

C

I used reverse plugging in to solve this problem.

I started with answer B:
*PB = paperback *HC = hardcopy
360000 PB/ 9 PB per HC = 40000 HC sold
360000+40000+36000 = 436000 copies sold
436000 < 441000 so I know the answer must be higher

Answer D:
Not even divisible by 9 so not a logical answer

Answer E:
396900 PB/ 9 PB per HC = 44100 HC
396900 + 44100 + 36000 > 441000

----> C is the correct answer

I will try to explain for the related question which says '9 times as many paperback copies as hardback copies were sold'

We will take hardback as x. So Paperback is 9 times as many as hardback, i.e, 9x.

Also, if you need help with translation, there is a superb video by GMATNINJA, https://www.youtube.com/watch?v=FIERkRCbi64

I have added the link for the same.

I hope it helps!
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There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?

Sold in all -> 441,000 = {36,000 hardback copies of a certain novel sold before the paperback version was issued} + {# of copies from the time the first paperback copy was sold until the last copy of the novel was sold}

{Total # of copies from the time the first paperback copy was sold until the last copy of the novel was sold}
= 441,000 — 36,000 = 405,000

Since “From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold.”, 405,000 copies are consisted of paper copies and hardback copies by 9:1.

Therefore, # of paper copies = \(405,000*\frac{9}{10}=364,500\)

Posted from my mobile device

Time period 1: before the paperback was even issued —> 36,000 H sold


Time Period 2: 9 times as many Paper as Hard were sold

P = 9 * H

For every 1 Hard sold———-> 9 Paper were sold

Given the Integer constraints of this physical item, the Ratio of Books Sold in Time Period 2 was:

Paper Sold : Hard Sold = 9g : 1g


Total Books Sold over the Two Time Periods:

441,000 = 36,000 + (9g + 1g)

405,000 = 10g

g = Unknown Ratio Multiplier = 40,500****

Total Paper Sold = 9g = 9 * (40,500) =


364,500

-C-

Posted from my mobile device

The obvious method to solve this question is making equations and solving them to get the answer. However, the alternate way is to use answer choices to get the answer which works the conditions given in the problem.

Start by trying option B as it is easier to work it as compared to option C (Ideally, we start with option C when we use this method).

If P = 360,000, then H = 360,000/9 = 40,000. P + H = 400,000. Not matching. Eliminate B.
We want a slightly bigger answer. So, the answer is C. Option D is too big.

Answer: C

Hope this helps!

"From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold"

Why can't we interpret the above to be saying 36000 + x + 9[36000 + x] = 441000 ??

In other words, why can't we interpret the statement as from the time the first paperback was sold, the number of paperbacks = the total number of hard copy sold?

The question tells us that 36,000 hardback copies of a certain novel sold BEFORE the paperback version was issued.

Later the question says "From the time the FIRST paperback copy was sold until the last copy of the novel was sold ....."
This time period doesn't include any sales of hardback copies because all of the hardback copies were sold BEFORE the first paperback copies were sold. \
Does that help?

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