For each of the years 2012, 2013, 2014, and 2015, the table

Question

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 .

ID: 700254

chetan2u · Accepted Answer

You have to ensure that you do not end up calculating more than what is required, and compare the quantity asked.

We are to compare funds in the succeeding years to yr 2012 with year 2012 itself

2012:  Let it be y

2013:  Increase of 34*39k and a decrease of 33*38k...... 
34*39k>33*38k, so there was an increase over 2012. Do not waste time in calculationas that is not what has been asked.

2014: Increase of 28*30k and a decrease of 39*41k...Now, 41*39k>30*28k, so there was a decrease over 2013, and also this decrease was way greater than what ever increase would have been in 2013 from 2012.
Thus, this decrease results in the funds going lower than what were in 2012.

2015:  The decrease is more than increase in 2015 in comparison to 2014 , so surely a decreased amount in 2014 further reduces and will remain less than what was in 2012.

Solution: Increased, Not increased, Not increased

https://www.youtube.com/watch?v=lkGg3VziJQw

Edoua · Answer

Total value of all business in 2012
+(37501.22 *23) - 42998.33*44 = 862,528.06 -1,891,926.52 = -1,029,398.46

In. 2012 we have the value of all business -1,029,398.46 $

**In 2013
- (37985.15 *33) +( 38836.51*34) = 1,320,441.34 - 1,253,509.95 = 66,931.39

Increased 
 
**in 2014
+(30521.97*28) - (41697.34*39) = -1,626,196.26 + 854,615.16= -771,581.1

Increased

** in 2014

+(31777.43*32) - (36522.13*35) = -1,278,274.55 + 1,016,877.76 = -261,396.79

Increased

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chetan2u · Answer

Try to approximate the amounts to save time. You mave have to look into the solution. Did you mean decreased for the years 2014 and 2015

nikitathegreat · Answer

How is the decrease for the last 2 years?
for 2012, it was negative 10L. For 2014 it is negative 7L. Then for 2014 it has increased right since -7L> -10L?
Similary for the next year. Can you tell me where I am going wrong?

shyashyahs · Answer

they are not talking about the value of the holding whereas the data given is about the average increase and decrease values , it is different from the value itself

iamchinu97 · Answer

bb  Can you please help here why the ans is not increased for last two as well. according to calculation even though value is in negative its increased from 2012 for other 2 as mentioned in above comments.

cheshire · Answer

I think the confusion comes from mixing up the  year-to-year  net changes with the  cumulative  change since 2012. 
 
  2013 
 
 Net change in 2013 alone: 34(38,836.51) - 33(37,985.15) = +$66,931 
 Since that is positive, Jan 1 2013 holdings exceed Jan 1 2012.
 →  Increased from 2012   
 
  2014 
 
 Net change in 2014 alone: 28(30,521.97) - 39*(41,697.34) = –$771,581 
 Cumulative 2012→2014 = +$66,931 (from 2013) + (–$771,581) = –$704,650 
 Because that total is  negative , the Jan 1 2014 balance is  below  the Jan 1 2012 level.
 →  Did not increase from 2012   
 
  2015 
 
 Net change in 2015 alone: 32(31,777.43) - 35(36,522.13) = –$261,397 
 Cumulative 2012→2015 = –$704,650 + (–$261,397) = –$966,047 
 Still negative, so Jan 1 2015 is even further  below  the Jan 1 2012 total.
 →  Did not increase from 2012

Only 2013’s net effect turns the total positive. The negative cumulative sums for 2014 and 2015 mean the total holdings  fell  below the 2012 level, so those years “did not increase from 2012.”

steffe440 · Answer

The key to solving this quickly without a calculator is realizing that the question asks for the change relative to January 1, 2012. This means we are tracking the cumulative value over time, starting from zero at the beginning of 2012. 
 
The 2012 Row is Irrelevant: The table shows changes "from the previous year." The 2012 row tells us the change from 2011 to 2012. Since our baseline is Jan 1, 2012, we ignore the 2012 row entirely. We start counting from the moment 2012 ends and 2013 begins. 
 
2013 (Did it increase from 2012? YES): This one is straightforward. There were 34 businesses that increased (at a higher average of $38k) versus only 33 businesses that decreased (at a lower average of $37k). Since both the volume and the average value of increases are higher than the decreases, the net result for 2013 is positive. The total value definitely increased from the 2012 baseline. 
 
2014 (Did it increase from 2012? NO): This is where estimation beats calculation. We need to see if the gain from 2013 is still alive after 2014. The 2013 net gain was small (a difference of just 1 business and $1k average). However, the 2014 net loss is massive. In 2014, there were only 28 increases (at a low average of $30k) compared to a huge 39 decreases (at a high average of $41k). The loss in 2014 is overwhelming. There are far more businesses losing money, and they are losing much more per business than the winners are gaining. This massive deficit easily wipes out the tiny buffer we built in 2013. We are now well below the 2012 baseline.

2015 (Did it increase from 2012? NO): We are already deep in the hole from 2014. The 2015 row shows another net loss (more businesses decreasing than increasing, and the average decrease is higher than the average increase). Adding another loss to an existing deficit means we are definitely still below the 2012 start point.

Conclusion: 2013: Increased 2014: Did not increase 2015: Did not increase

For each of the years 2012, 2013, 2014, and 2015, the table

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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

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For each of the years 2012, 2013, 2014, and 2015, the table

Prep Toolkit

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