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Updated on: 09 Aug 2025, 06:26
Originally posted by Sajjad1994 on 03 Dec 2019, 03:58.
Last edited by Sajjad1994 on 09 Aug 2025, 06:26, edited 11 times in total.
Last edited by Sajjad1994 on 09 Aug 2025, 06:26, edited 11 times in total.
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The number of AV materials per registered user lent out in 2002 represented a decrease from 2001.: No
The ratio of total volumes in the permanent collection to AV materials lent out in 2005 is greater than the ratio of AV materials lent out to AV materials in the permanent collection in the same year.: Yes
The ratio of books in the permanent collection to books lent out was greatest in 2006.: Yes
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
65% (03:40) correct
35%
(03:22)
wrong
based on 294
sessions
History
Date
Time
Result
Not Attempted Yet
| In permanent collection (000s) | Lent out (000s) | Users (000s) | ||||||
| Year | Total Volumes | Books | AV materials | Total Volumes | Books | AV materials | Registered | |
|---|---|---|---|---|---|---|---|---|
| 2001 | 42.8 | 36.9 | 2.4 | 156.5 | 147.9 | 7.2 | 50.3 | |
| 2002 | 40.1 | 36.4 | 2.9 | 155 | 144.8 | 8.2 | 49.7 | |
| 2003 | 41.5 | 36.9 | 3 | 154 | 142.8 | 7.9 | 50.4 | |
| 2004 | 39.7 | 35.8 | 3.2 | 154 | 133.6 | 9 | 51.5 | |
| 2005 | 40.2 | 36 | 3.4 | 153.8 | 121.7 | 10.1 | 51.8 | |
| 2006 | 40.8 | 36 | 4.1 | 154.2 | 101 | 11.3 | 52.6 | |
| 2007 | 41.7 | 36.3 | 4.5 | 155.1 | 107.5 | 11.9 | 52.9 | |
Between 2001 and 2007, a university library reported the total number of volumes included in its permanent collection at the end of each year, as well as the figures for the two largest sub-categories, books and audiovisual (AV) materials. The "lent out" figures represent the total number of times that materials of that type were lent out to library users during that year. All figures are in thousands.
For each of the following statements, select Yes if the statement can be shown to be true with the information provided. Otherwise, select No.
Attachment:
2.jpg [ 77.2 KiB | Viewed 8676 times ]
| Yes | No | |
| The number of AV materials per registered user lent out in 2002 represented a decrease from 2001. | ||
| The ratio of total volumes in the permanent collection to AV materials lent out in 2005 is greater than the ratio of AV materials lent out to AV materials in the permanent collection in the same year. | ||
| The ratio of books in the permanent collection to books lent out was greatest in 2006. |
ShowHide Answer
Official Answer
The number of AV materials per registered user lent out in 2002 represented a decrease from 2001.: No
The ratio of total volumes in the permanent collection to AV materials lent out in 2005 is greater than the ratio of AV materials lent out to AV materials in the permanent collection in the same year.: Yes
The ratio of books in the permanent collection to books lent out was greatest in 2006.: Yes
31 Mar 2021, 23:37
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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.
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.
General Discussion
03 Dec 2019, 04:22
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1) No ,since the ratio in 2002 was nearly ~.058 and in 2001 was ~ .04
2) Yes, since 40.2/3.4 > 10.1/3.4
3) Yes, since the books in permanent collection was roughly around 36 in all years but the lent out number was lowest in 2006, hence making the ratio highest in 2006
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2) Yes, since 40.2/3.4 > 10.1/3.4
3) Yes, since the books in permanent collection was roughly around 36 in all years but the lent out number was lowest in 2006, hence making the ratio highest in 2006
Posted from my mobile device
