In the period 1989 through 1991, the average prices of country

Question

https://gmatclub.com/forum/download/file.php?id=88709 Use the drop-down menus to create the most accurate statements based on the information provided. In the period 1989 through 1991, the average prices of country homes GRAPH_1_PLACEHOLDER than the average prices of city homes. For city homes, the overall percent increase in average prices (compounded, and rounded to the nearest 1 percent) in the period 1989 through 1993 was GRAPH_2_PLACEHOLDER GMAT-Club-Forum-qez82xei.png

FrozenDragon · Answer

OFFICIAL EXPLANATION

The graph only shows annual percent changes in average prices of city homes and of country homes. It doesn’t show whether country homes cost more or less than city homes on average in any year. But it does show that in each of the years 1989, 1990, and 1991, the average prices of country homes increased by a larger percentage than the average prices of city homes.

To find the overall compounded percent increase in average prices for city homes in the period 1989 through 1993, first find the average price at the end of each year as a percentage of the average price at the beginning of that year. The blue bars in the graph show that these five percentages are 98% for 1989, 99% for 1990, 106% for 1991, 105% for 1992, and 108% for 1993. Next, multiply these five percentages as decimal amounts and round to the nearest 1 percent: 0.98 × 0.99 × 1.06 × 1.05 × 1.08 ≈ 1.17 = 117%. This means that rounded to the nearest 1 percent, the overall percent increase in average prices of city homes in the period 1989 through 1993 was 17%.

The correct answers are “increased by a larger percentage” in the first drop-down menu and 17 in the second drop-down menu.

sydneyxinning · Answer

FrozenDragon

Sorry, where do you get these "the blue bars in the graph show that these five percentages are 98% for 1989, 99% for 1990, 106% for 1991, 105% for 1992, and 108% for 1993."?

FrozenDragon · Answer

Hey there, blue bar shows the percentage difference here; so if blue bar indicate 1% difference, it means that --- now original value is 99% instead of 100%. I hope this helps.

egmat · Answer

Hi sydneyxinning,

Good question. Those five percentages come straight from the  blue bars , but with one translation step that the official explanation skipped over.

Read the height of each blue (city home) bar first. On the graph they are:

- 1989:  -2 
- 1990:  -1 
- 1991:  +6 
- 1992:  +5 
- 1993:  +8

Those are  percent changes  - how much the price went up or down that year, not the price itself.

Turning a change into a multiplier

To compound prices, you need each year's ending price as a percent of its starting price. That is just  100%  plus the change:

-  -2%  change -  100%  -  2%  =  98% 
-  -1%  change -  100%  -  1%  =  99% 
-  +6%  change -  100%  +  6%  =  106% 
-  +5%  change -  100%  +  5%  =  105% 
-  +8%  change -  100%  +  8%  =  108%

That's where  98% ,  99% ,  106% ,  105% ,  108%  come from - each is "the whole price ( 100% ) after the bar's change is applied." Written as decimals, they become  0.98 ,  0.99 ,  1.06 ,  1.05 ,  1.08 , which is what you multiply together.

Quick rehearsal with easy numbers:  if a price rises  +10%  in a year, it ends at  110%  of where it started, i.e. a multiplier of  1.10 . If it falls  -10% , it ends at  90% , i.e.  0.90 . Same rule for every bar: start from  100% , add the bar's percent change.

So the graph never gives you the multipliers directly - you build each one by adding the bar's percent change to  100% .

Answer: increased by a larger percentage

VenkataSai · Answer

FrozenDragon

The second question is asking about the change of prices for the period 1989 ~ 1993. which means if the price of house was 100 in 1989 what is its price difference from that of in 1993. So I think the first 0.98 that you multiplied should not be considered because that 2% reduction is from 1988 to 89 and the second question doesn't ask about 1988.

FrozenDragon · Answer

Hey there , you are treating the 1989 bar as a change that happened before the period, whereas it actually represents the change during 1989. Therefore, the period 1989 through 1993 includes all five annual changes (1989, 1990, 1991, 1992, and 1993), so the 1989 −2% must be included in the compounding.

In the period 1989 through 1991, the average prices of country

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In the period 1989 through 1991, the average prices of country

Prep Toolkit

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