A charitable organization held an annual fundraising event in each of 5 consecutive years (Years 1 through 5). For each of Years 2 through 5, the organization’s goal was to raise at least 10 percent more through the event than was raised in the previous year. The graph shows the total amount raised in each of the 5 years.
Select from the drop-down menus the options that create the statements that most accurately reflect the information provided.The organization met its fundraising goal in Years __________.To answer this question, we can first confirm how the organization defines "met its fundraising goal." Reviewing the passage, we see the following:
For each of Years 2 through 5, the organization’s goal was to raise at least 10 percent more through the event than was raised in the previous year. So, we can determine whether the organization met its goal in years 2 through 5 by comparing the amount for each of those years with the amount for the previous year and then checking to see whether the difference is greater than 10 percent of the amount for the previous year.
Before we do so, however, it may help to look at the answer choices to get a sense of what we are looking for. Doing so, we see the following choices:
1 and 21 and 32 and 32 and 43 and 4We see that we need to look for just two years since each choice includes just two years.
Also, notice that we can eliminate the first two choices without doing any work because the goal can be met only in years 2 through 5. So,
1 and 2 and
1 and 3 cannot be correct.
Furthermore, year 5 is not included in the answer choices. So, we need to check only years 2, 3, and 4.
So, checking the answer choices was definitely helpful.
Now, we can use estimation to quickly determine in which of years 2, 3, and 4 the organization met its goal.
Comparing year 2 with year 1, we see that the amount for year 2, 40,457.xx, is more than 4,000 more than the amount for year 1, 36,275.xx.
Since 4,000 is 10 percent of 40,000, it must be more than 10 percent of 36,275. Thus, the amount for year 2 must be more than 10 percent greater than the amount for year 1.
So, the organization achieved its goal in year 2.
Checking year 3 against year 2 the same way, we see that the amount for year 3 is around 3,000 greater than the amount for year 2.
Since the amount for year 2 is over 40,000, to be more than 10 percent greater than the amount for year 2, the amount for year 3 would have had to be more than 4,000 greater than the amount for year 2.
So, the organization did not achieve its goal in year 3.
We can stop right there and choose
2 and 4, since 2, 3, and 4 are the only possible years, and we've eliminated 3.
Let's confirm that 4 works though.
Comparing the amounts for 4 and 3, we see that the amount for 4 is around 6,000 greater than the amount for 3. Thus, since the amount for 3 is less than 60,000, the amount for year 4 must be more than 10 percent more than the amount for 3.
So, 4 is correct.
For the first dropdown, select
2 and 4.
In Year 5, the organization failed to meet its fundraising goal, raising only __________ percent more than in the previous year, to the nearest percent.To answer this question, we can first check the answer choices to see how exact we need to be. Doing so, we see the following:
56789So, they aren't far apart, but at least they don't have decimals. So, we may be able to estimate for this one too. Let's see.
Looking at the amounts for year 4 and year 5, which are 50,063.xx and 54,000.xx, we see that the amount for year 5 is a little under 4,000 greater than the amount for year 4. In fact, the difference is sufficiently close to 4,000 and the amount for year 4 is sufficiently close to 50,000 that we'll be able to estimate the answer.
Now, we have to be careful not to choose 4 percent because the amount for year 4 is not 100,000. It's around 50,000. So, 4 percent will be too high.
Since 50,000 is half of 100,000, 4,000 will be twice 4 percent of 50,000, or 8 percent.
For the second dropdown, select
8.
Correct answer: 2 and 4,
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