Dear
mathewmithun
Hi, there. I'm happy to help with this.
This is a particularly challenging question! I also think: it's not the best written DS question. What is the source? I would consider it questionable.
Prompt:
If each customer purchases exactly one copy of the book, did the book sell at least 500 copies overall on the online book selling portal?
Other than specifying (one customer) = (one book) ---- which would be exceedingly difficult if it weren't the case! --- this is a straightforward prompt.
Statement #1:
The portal found that after selling 5 copies on a particular day, the percentage of customers who ultimately buy the book after viewing it increased from 46% to 47%.
Let P = The percent of customers who ultimately buy the book after viewing it
P = (# who buy)/(# who view) * 100
Before the day they sell 5 books, let's say Y people have looked at the book, and X of them have bought it, and X/Y = 0.46 (the percent as a decimal). ===> (a) X= 0.46*Y
Then, that day, five people both look at it, and buy it, so both X and Y increase by five, and the new ratio is (X + 5)/(Y +5) = 0.47 ==> (X + 5) = (Y + 5)*0.47 ===> (b) X + 5 = 0.47*Y + 2.35
Plug (a) into (b):
0.46*Y + 5 = 0.47*Y + 2.35
5 - 2.35 = 0.47*Y - 0.46*x
2.65 = 0.01*Y
265 = Y
This tells us --- 265 people looked at the book, and 47% bought it, on that particular day we know 500 copies had not been sold. But the prompt question is not clear --- is it asking about sales up to this particular day, or sales in general? The fact that the prompt is wildly unclear makes this a totally unsuitable DS question, despite the sophisticated mathematics.
Statement #2:
On a particular day the portal found that 10 consecutive customers who viewed the items purchase some other book and the percentage dipped from 47% to 46%.
This statement will share the same ambiguity problem with the first, but I'll show the math just so you understand what you would do.
Before that day, X/Y = 0.47 ===> (c) X = Y*47
After that day, X/[Y + 10] = 0.46 ===> (d) X = 0.46*Y + 4.6
Set (c) and (d) equal.
Y*47 = 0.46*Y + 4.6
0.01*Y = 4.6
Y = 460
Up to that particular day, 460 had viewed it before that day, and 470 had viewed it by days's end, and 46% of 470 have bought it --- less than 500.
Again, though -- are we being asked about sales on this particular day, or in general.
My friend, there are many sources of GMAT test prep questions -- some of them are excellent, just as good as the OG, and some of them are pig's slop. I think this question is in the latter category.
Here's a rigorous DS question about percents:
https://gmat.magoosh.com/questions/31
When you submit your answer, the following page will have the video explanation. Each of our 800+ questions has its own video explanation.
Does all this make sense? Please let me know if you have any further questions.
Mike
