gmat1393
When Sarah visited the Canadian side of Niagara Falls, her cell phone plan charged a variable rate for data. After the first two megabytes of data, the rate per megabyte dropped by 10 cents. If the total data used while in Canada cost $7.95, how many megabytes of data did Sarah use?
(1) The rate for the first two megabytes is 30 cents per megabyte.
(2) If Sarah had used 8 more megabytes of data, the total data used would have cost $14.95.
Analyze the question stem first.
Let's say the rate for the first 2 megabytes is m dollars per megabyte. So, assuming that Sarah used at least 2 megabytes (and that's a big assumption), she definitely spends at least 2m dollars.
If she uses a total of x megabytes, then the remaining x-2 cost m-0.10 dollars per megabyte. As long as x is at least 2, her total cost is:
2m + (x-2)(m-0.10)
= 2m + mx - 0.1x - 2m + 0.2
= mx - 0.1x + 0.2
According to the question stem, the amount she spends is $7.95. So, we can create an equation.
mx - 0.1x + 0.2 = 7.95
mx - 0.1x = 7.75
We want to know the value of x (the total number of megabytes), so let's isolate it:
x(m-0.1) = 7.75
x = 7.75/(m-0.1)
However, this is only true if we assume that x is 2 or greater. It's also possible that Sarah only used one megabyte. In that case, m would have to equal 7.95, and x would equal 1. But we don't know whether that's the case or not yet.
Statement 1: This tells us that m = 0.3. So, we know that the second scenario (where she only used one megabyte) isn't true, because in that scenario, m would have to be 7.95. We must be in the first scenario, where x = 7.75/(m-0.1). So, we can calculate the exact value of x by plugging m = 0.3 into that equation. This statement is sufficient.
Statement 2: If Sarah had used 8 more megabytes, the total cost would have been $14.95. That is, using 8 more megabytes would have cost an additional $14.95-$7.95 = $7.00.
We can be certain that she used more than one megabyte originally, since if she had only used one megabyte, a second one would have cost $7.95, which is more than the additional $7 she actually spent. Therefore, she used at least two megabytes originally, and the remaining 8 megabytes cost $7.00/8 = $0.875 each. Therefore, m is $0.10 greater than this, so m = $0.975.
That's where things go off the rails. This is sufficient, since it gives us a value for m, just like the first statement. However, it gives us a
different value for m than the first statement did. This will never happen in a real Data Sufficiency problem, and if it seems to be happening as you solve an official problem, you've made a mistake. What is the source for this problem? Unless I've misread something or there's a typo in the problem text, the fact that this happens makes this an invalid DS problem.