AustinKL wrote:
If you are buying a product by rounding up to a $1 digit, is the sum of the differences between buying a product as its actual price and buying a product by rounding up to a $1 digit less than $12?
1) The sum of the differences in the total of 80% of the products bought is less than $10.
2) A total of 20 products were bought
Dear
AustinKL,
I'm happy to respond.
My friend, the wording on this problem is truly atrocious. If the author was trying to write a GMAT Quant problem, then I would give the author a grade of an
F for his efforts. It may well be that the author is a non-native speaker who doesn't understand the implications of different phrasing and how they impact the clarity and precision of the problem. The wording is exceptionally unclear.
Also, absolutely no official GMAT Quant question is addressed to "
you." There are many ways this question gives evidence of absolutely no careful knowledge of the GMAT.
Here is a complete re-writing of the prompt, in an attempt to make clear what this flawed question is trying to ask
Samantha bought N of the same product, each at the same price. She estimated the total price of the set of N products by rounding the price of the individual product up to the nearest dollar, and multiplying this rounded price by N: call this estimate E. The actual total price of the set N products is the real unrounded price of each product times N: call this actual total price T. Is E - T < $12?
Statement #1: If Samantha had bought only 80% of N products, the difference between the same estimate and true price would be less than $10.
Statement #2: N = 20 Now, to solve this:
Statement #1: Everything is proportional, so if Samantha bought 80% of N, the difference in that case would be 80% of the total difference, E - T
.80(E - T) < 10
(4/5)(E - T) < 10
E - T < 10(5/4)
E - T < 5(5/2)
E - T < 25/2
E - T < 12.5
If something is less than 12.5, it could be less than 12, or it could be greater, that is, between 12 and 12.5. We cannot draw a conclusion for this statement. This statement is insufficient.
Statement #2: N = 20
Well, if the price of an individual item is $0.95, so the different for an individual item is $.05, so for twenty, the difference would be (0.05)*20 = $1, which of course is less than $12. This produces a "yes" answer to the prompt.
The prompt very specifically says that we are going to round UP, regardless of the actual price. Thus, the price could be, say $.20, and we would round up to $1, a different of $0.80. The difference for N = 20 would be 20*$0.80) = $16, which is more than $12.
Two different choices produce two different answers to the prompt. This statement is not sufficient.
I will not continue with the solution. Clearly, even my rewrite is not what the author of the question had it mind. I suspect that the problem is in the rounding. I think what the author was trying to say was that the individual item had such a price that would be rounded up rather than down. That is very different from what he actually said in the problem. There are a few more elegant ways to express this information, but clearly the language problems in the original question are many. This is a truly atrocious question.
Does all this make sense?
Mike
I guess, to know whether E-T is less than $12 or not we only require the number of products purchased.
For 1 product maximum value of E-T can be $0.50 (more than 0.50 it will round off to next dollar value). Therefore for 20 products maximum value of E-T can be 20x0.50= 10, which is less than 12. Thus IMO statement B is sufficient.