Hi, there. I'm happy to help with this.
This is a fascinating one.
Prompt: Each of some prices is rounded to the nearest integer. Is the difference between the sum of the real prices and the sum of the approximate prices greater than $6?
Typically, if you took a bunch of random items, and rounded the prices to the nearest integer, some would be rounded up, some would be rounded down, and on average, the sum of the rounded prices would be close to the sum of the real prices. In order to get a large discrepancy between sum of of the rounded prices and sum of the real prices, all the rounding would have to be in the same direction. For example, each and every price would have to be rounded up.
Statement #1: Number of the prices is less than 11
Suppose we are rounding each price up. For the maximum value, suppose each price is $XX.50, and we round up a full 50¢ to the next dollar. If we have fewer than 11, we could have as many as ten. If ten items are each rounded up 50¢, that's a full $5 of rounding --- in other words, the difference between the rounded and real prices would be $5. Thus, we can give a definitive answer to the prompt question: NO, the difference is not greater than $6. Whenever you can give an definitive answer, either YES or NO, that means you have sufficient information. Statement #1 is
sufficient.
Statement #2: All the approximate prices are $5.
Well, we now have no idea how many items we have. We could have 3 items, or we could have 700 items, or we could have the entire national inventory of $5 items at Walmart. If we have a large number of items, just by chance fluctuations, it's likely that there will be a difference between the sum of rounded prices and the sum of real prices, and if there's any pattern of rounding in the same direction, that difference will get big in a hurry. Therefore, with enough items, it certainly could be the case that the sums will differ by more than $6. This statement simply does not give us enough information. Statement #2 is
insufficient.
Answer =
A
Does that make sense? Please let me know if you have any questions on this.
Mike
