Official Explanation
The problem provides all values in thousands (000s). As you solve each statement, first determine whether you can use the abbreviated numbers or whether you have to expand out the number. The first statement asks only whether there is a decrease; the second and third statements ask about a ratio. In all three cases, it’s fine to work with the abbreviated numbers as they appear in the table.
Statement 1: No.
First, identify which columns you need to answer the question: AV materials lent out (the second to last column) and registered users (the last column). You also need the rows 2002 and 2001.
Your first instinct might be to grab the calculator and starting to plug and chug. Hang on! Set up the math first. Note that you can also estimate, since the question just asks whether one value represents a decrease from another—you don’t need the exact numbers.
2001: AV lent = 7.2 and users = 50.3. So AV per user = 7.2 / 50.3.
2002: AV lent = 8.2 and users = 49.7. So AV per user = 8.2 / 49.7.
Think about what happened. In 2002, there were more AV items lent out. In other words, the numerator is larger—and when you increase the numerator of a fraction, the fraction gets larger. Also in 2002, there were fewer users, so the denominator got smaller—and when you decrease the denominator of a fraction, the fraction gets larger.
In other words, in 2002, the AV lent out per user figure got larger—it represents an increase, not a decrease. (If you’re not sure, you can plug those calculations into your calculator.)
Statement 2: Yes.
When comparing ratios, it’s often easier to write the ratios in fraction form. Since you just have to figure out which one is greater, it’s okay to estimate lightly in figuring this out.
There are a lot of categories here; be careful as you pull the data points. First, all of the categories are for the year 2005, so look only at that row in the table.
Ratio #1
Compare Total Vol in collection to AV lent out
Tot Vol: ~40
AV Lent: ~10
\(\frac{Tot Vol}{AV Lent}=\frac{40}{10}=\frac{4}{1}\)
Ratio #2
Compare AV lent out to AV in collection
AV Lent: ~10
AV in Coll: ~3.4
\(\frac{AV Lent}{AV in Coll}=\frac{10}{3.4}≈\frac{3}{1}\)
It is indeed the case that the first ratio, 4/1, is greater than the second ratio, 3/1.
Statement 3: Yes.
The statement asks you to compare books in the permanent collection to books lent out. Scan both columns.
The books in permanent collection column has very similar numbers all the way down, while the books lent out column changes much more significantly, so that second column is the one that’s going to matter. For that reason, sort by books lent out.
The top row, 2006, represents the lowest value for books lent out—and this is the year that they asked about. Good. Estimate the ratio.
\(\frac{Books Perm}{Books Lent}=\frac{36}{101}=\frac{36}{100}\)
Look at the next row, 2007. The books in permanent collection figure is still about 36. Books lent out, on the other hand, goes up by a lot so the ratio for 2007 is 36/107. The numerator stayed the same but the denominator got larger, so the ratio itself just got smaller. (If you’re not sure, check the value on your calculator.)
What can you conclude from that? The first column, books in permanent collection, is always roughly 36. If the second column, which represents the denominator, increases by more than 1, then you can conclude that the ratio for that year will be lower than for 2006.
Eyeball the rest of the data. In each case, the books lent out denominator figure is significantly higher than for either 2006 or 2007, so the ratio keeps decreasing. The ratio for 2006 is indeed the greatest ratio.