Loading...
For each of the years 2012, 2013, 2014, and 2015, the table gives the total number of businesses that had an increase in the total value of their holdings with a certain community bank from January 1 of the previous year to January 1 of that year, the average (arithmetic mean) value by which holdings increased among businesses that had an increase during that time, and similar data for holdings decreases. For each year, all businesses with holdings at the bank had the value of their holdings either increase or decrease from the previous year.
| Year | Businesses with increased holdings | Average holding increase | Businesses with decreased holdings | Average holding decrease |
|---|---|---|---|---|
| 2012 | 23 | $37,501.22 | 44 | $42,998.33 |
| 2013 | 34 | $38,836.51 | 33 | $37,985.15 |
| 2014 | 28 | $30,521.97 | 39 | $41,697.34 |
| 2015 | 32 | $31,777.43 | 35 | $36,522.13 |
Based on the information provided, for each of the following years, select Increased from 2012, if, on January 1 of that year, the total value of all business holdings at the bank (the sum of all individual business holdings) had increased from January 1 of 2012. Otherwise, select Did not increase from 2012.
2013
2014
2015
Let's start by understanding what we're working with. This table shows business holdings data across several years (2013-2015), comparing them to a baseline of January 1, 2012. For each year, we can see:
Key insight: The table doesn't directly tell us the total value change - it gives us the components we need to determine direction of change. This means we can potentially avoid detailed calculations if we spot clear patterns.
For example, looking at 2014's row, we can immediately notice that more businesses decreased (39) than increased (28), AND the average decrease ($41,742.33) is significantly higher than the average increase ($30,517.86). This visual pattern suggests a net decrease without needing exact calculations.
Statement 1 Translation:
Original: "As of December 31, 2013, the value of holdings had increased compared to January 1, 2012."
What we're looking for:
In other words: Were the gains in 2013 greater than the losses?
To determine this efficiently, let's estimate the total increases and decreases:
For increases:
For decreases:
Comparing these estimates:
The increases slightly outweigh the decreases, indicating a positive net change from the 2012 baseline.
Statement 1 INCREASED FROM 2012.
Note how we used rounded numbers for quicker mental math rather than calculating to the penny. When we only need to know if a value increased or decreased, approximation is much more efficient than precise calculation.
Statement 2 Translation:
Original: "As of December 31, 2014, the value of holdings had increased compared to January 1, 2012."
What we're looking for:
In other words: Were holdings worth more at the end of 2014 than they were at the start of 2012?
Here's where pattern recognition becomes powerful. Looking at the 2014 data, we can spot two critical patterns:
When both factors (quantity and magnitude) point toward decreases, we can be certain that the overall change is negative without performing detailed calculations. This is a key pattern to recognize for efficiency!
Let's verify with a quick magnitude check:
This negative change clearly exceeds 2013's modest positive change, meaning that holdings have fallen below the 2012 baseline.
Statement 2 DID NOT INCREASE FROM 2012.
Teaching callout: Notice how recognizing the double-negative pattern (more businesses decreasing AND higher average decrease) allowed us to quickly determine the direction of change without precise calculations.
Statement 3 Translation:
Original: "As of December 31, 2015, the value of holdings had increased compared to January 1, 2012."
What we're looking for:
In other words: Were the cumulative changes across 2013-2015 positive overall?
Here we can leverage a powerful inference chain from our previous finding. Since we already know that holdings were below 2012 levels at the end of 2014, we only need to determine if 2015 showed enough positive change to overcome that deficit.
Looking at the 2015 data, we see the same pattern as 2014:
With both factors again pointing toward a negative change within 2015 itself, it's impossible for holdings to have recovered back above 2012 levels. In fact, the gap would have widened further.
Quick verification:
Since 2014 already put us below the 2012 baseline, and 2015 shows another negative change, holdings remain below 2012 levels.
Statement 3 DID NOT INCREASE FROM 2012.
Here's where strategic thinking saves time: Once we know we're below the baseline after 2014, we only need to confirm 2015 doesn't show a massive recovery to answer the question.
After analyzing all three statements:
The correct answer pattern is: INCREASED FROM 2012, DID NOT INCREASE FROM 2012, DID NOT INCREASE FROM 2012
Remember: On data questions, always ask yourself "What's the minimum I need to determine to answer this question?" Often, it's much less than you think!
2013
2014
2015