The fact that the statements need to be consistent means that, when using Statement 2 alone, there must be at least one solution for which Marta buys exactly 6 pencils. But that doesn't tell you anything useful: what you need to be sure of is that there is not some other solution where Marta buys 5 pencils, say, or 7 pencils. Now in the question above, using Statement 2 alone, it's easy to check that Marta can't have bought 7 pencils (since then she would spend at least 7*0.21 = $1.47) and can't have bought 5 pencils (since then she would have spent at most 5*0.23 = $1.15), so must have bought 6 pencils. But that won't always be the case. For example, if you had this question:Testtrainer wrote:Marta bought several pencils. If each pencil was either 23 cents or 21 cent, how many 23 cents pencil did Marta buy?
1) Marta bought a total of 6 pencils
2) The total value of pencil Marta bought was 130 cents.
I think the key to answering this very difficult question is to know two things: 1) Pencils are by definition positive integers and 2) The two statements will always be consistent with one another (at least on the actual GMAT, not necessarily from other material). So one can use statement (1) to see that the 23 cent and 21 cent pencils must be limited to: 0,6; 1,5; 2,4; or 3,3. Plug each of these values into statement (2) to see whether only one set of values works. As mentioned previously, only 2,4 work, so statement (2) is sufficient by itself.
This is very tricky because although we are using statement (1), we don't need the data from statement (1) to answer the question. We just use it because we know how this stupid test works!
Martin bought several DVDs, some for $3 each and the rest for $4 each. How many $3 DVDs did Martin buy?
1) Martin bought a total of 12 DVDs
2) The total cost of the DVDs Martin bought was $38
then yes, there will certainly be one solution using Statement 2 alone in which Martin buys precisely 12 DVDs, because the statements must be consistent. But there are other solutions as well; the answer is not B here. Using Statement 2 alone, Martin might have bought 10 DVDs for $3 and 2 DVDs for $4, or he might have bought 6 DVDs for $3 and 5 DVDs for $4, or he might have bought 2 DVDs for $3 and 8 DVDs for $4. So with Statement 2 alone, Martin could have bought 10, 11 or 12 DVDs in total, and could have bought 10, 6 or 2 DVDs costing $3 each. We need both statements here.
