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For each of the following statements, select Yes if the statement can

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For each of the following statements, select Yes if the statement can [#permalink] New post   11 Jan 2021, 09:00
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IR Butler Competition 2021 - Participate and Win!
Question # 20, Date : 11-Jan-2021
This question is a part of IR Butler competition 2021. Click here for Details
­

State Population Size (persons )Income % of Income
from Wages 		% of Income
from Dividends
& Interest
Colorado 5,029,1962.4$60,83472.0%5.2%
Connecticut 3,574,0972.2$77,05972.3%6.1%
Georgia 9,687,6532.4$50,32076.0%4.5%
Idaho 1,567,5822.5$47,99969.6%5.3%
Maryland 5,773,5522.3$66,20675.1%4.6%
New Mexico 2,059,1792.4$44,12970.7%4.9%
Texas 25,145,5612.6$51,74776.8%4.4%
Vermont 625,7412.1$50,39469.1%6.6%
Wyoming 563,6262.3$62,07764.6%6.3%
(Sort ↕ the table by clicking on the headers)
 
For each of the following statements, select Yes if the statement can be shown to be true using the information provided. Otherwise, select No.

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Yes No
The percent of income derived from wages is negatively correlated with population.
The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.
The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico.
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The percent of income derived from wages is negatively correlated with population.: No The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.: Yes The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico.: Yes
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Re: For each of the following statements, select Yes if the statement can [#permalink] New post   12 Jan 2021, 09:30
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Statement 1: No. If two columns are positively correlated, then as the numbers in one column increase, the corresponding numbers in the other column trend in the same direction. A negative correlation is the opposite (as one increases, the other decreases). No correlation indicates that there is no trend: it can’t be said that the numbers trend up or down together. Sort by either Population or % of Income From Wages. Once one of the columns is in ascending order, take note of the direction of the other column. For example, when you sort by Population, the values in that column increase as you scan down. At the same time, the values in % of Income From Wages also increase as you scan down. The values are moving in the same direction, indicating a positive correlation, not a negative correlation. This statement is false.

Statement 2: Yes. The table provides the $ of income from wages and the % of income from dividends & interest. Therefore, the percent of income derived from sources other than those is 100% minus these given percentages. Because you are asked to maximize income derived from other sources, you need to find the state with the minimum percentage from the two given sources. Sort by % of Income From Wages. The smallest figure is 64.6% (Wyoming). Add the % from dividends & interest: 64.6% + 6.3% = 70.9%. Now, scan the other columns to see whether another state has a lower combined percentage.

Vermont and Idaho both start at about 69% and add 6.6% and 5.3%, respectively, so the final sum is greater than 70.9%. All of the other states start at a 70%+ value and add at least 4%, so no other state’s percent of income from wages, dividends, & interest is lower than Wyoming’s. Wyoming’s average household income is $62,077, which is over $60,000. This statement is true.

Statement 3: Yes. To find the dollar amount of income derived from dividends and interest in any given state, multiply the value from the Income column by the percent from % of Income from Dividends & Interest column. Do this for the two states in question: Georgia and New Mexico.

Georgia: $50,320 × 4.5% = $50,320 × 0.045 = $2,264

New Mexico: $44,129 × 4.9% = $44,129 × 0.049 = $2,162

The income from dividends and interest is greater in Georgia. This statement is true.

Answer: No, Yes and Yes
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Re: For each of the following statements, select Yes if the statement can [#permalink] New post   11 Jan 2021, 22:20
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For each of the following statements, select Yes if the statement can be shown to be true using the information provided. Otherwise, select No.

The percent of income derived from wages is negatively correlated with population.
% of income from wages Population
64.6 563,626
69.1 625,741
69.6 1567,528
70.7 2059,179
72 5029,196
72.3 3574,097
75.1 5733,572
76 9687,653
76.8 25145,561

From the above sorted data, we can see there is no correlation between % of income from wages and Population.

NO

The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.
The state with the highest percent of household income derived from sources other than wages, dividends, and interest = The state with the lowest percent of household income derived from wages + dividends, and interest i.e. Wyoming (64.6 + 6.3 = 70.9 %)
Wyoming has an average household income of $62,077.

YES

The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico.
Average household income from dividends and interest in
Georgia 4.5% of $50,320 = 2264.4
New Mexico 4.9% of $44,129 = 2162.3

YES
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Re: For each of the following statements, select Yes if the statement can [#permalink] New post   12 Jan 2021, 02:50
Yes....... No.......
The percent of income derived from wages is negatively correlated with population.
The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.
The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico.

1)The percent of income derived from wages is negatively correlated with population. : No

lets collate data points :

563k - 64.6%
625k -69%
1.5m -69.6%
2.05m - 70.7%
3.5m - 72.3 %
5.02m - 72%
5.7 m - 75%
9.6 m -76%
25 m - 76.8%

so we see that that as poulation increases the % of income from wages also increases on avg , so it cannot be negatively co-related to population

2 The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.- Yes


Lets compute the chart from table
% of household income derived from wages and interest /dividends % of household income derived from other sources

1 Co - 77.2% 22.8%

2 Conn 78.4% 21.6%

3 G 80.5% 19.5%

4 I 74.7% 25.3%

5 M 79.7% 20.3%

6 NM 75.6% 24.4%

7 T 81.2 % 18.8%

8 V 75.7% 24.3%

9W 70.7% 29.3%


SO CLEARLY Wyoming has highest % income from others and it has avg household income of 62,077$ which is >60K, SO answer to our q2 is yes

3 The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico: yes

avg household income from d and I in Georgia = 4.5% of 50320 =2264.4 $

avg household income from d and i in new mexico = 4.9% of 44129 =2162.32

so definitely georgia > new mexico , so answer to our statement is yes
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Re: For each of the following statements, select Yes if the statement can [#permalink] New post   12 Jan 2021, 03:44
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For each of the following statements, select Yes if the statement can be shown to be true using the information provided. Otherwise, select No.

The percent of income derived from wages is negatively correlated with population.....NO.
Case-1 - We can see that that Texas has highest population (25mn) and also the highest percent of income derived from wages (76.8%). Also Wyoming has the lowest population (.56mn) and the lowest percent of income derived from wages(64.6%).
Case-2 - We can see that that Georgia has the second highest population (9.6mn) and also the second highest percent of income derived from wages (76%). Also Vermont has the second lowest population (.62mn) and the second lowest percent of income derived from wages (69.1%).

The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.....YES. Kindly refer the image below:
The state with the highest percent of income other than wades, dividends and interests is Wyoming (29.1%), and its average household income id 62,077$.

The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico.....YES. Georgia has an income of ~2264$ from Dividends and interest, whereas New Mexico has an income of ~2162$ from dividends and interests.
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Re: For each of the following statements, select Yes if the statement can [#permalink] New post   12 Jan 2021, 09:02
1) The percent of income derived from wages is negatively correlated with population.- No.

negative correlation means, income of wages increases then Population decreases, but from Idaho to Connecticut, Population increases and so does % increase in wages.

2) The state with the highest percent of household income derived from sources other than wages, dividends, and interest has an average household income of more than $60,000.- Yes.

For calculation of other than means: 100- % from wages- % from other sources.

3) The average household income, in dollars, derived from dividends and interest is greater in Georgia than in New Mexico.- No.
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Re: For each of the following statements, select Yes if the statement can [#permalink] New post   12 Jan 2021, 09:18
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This is a Medium level question, OA is posted, It is No, Yes and Yes. Everyone did a wonderful job here. OE will be posted within 10-15 minutes so you can match your reasoning.
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Re: For each of the following statements, select Yes if the statement can [#permalink]
12 Jan 2021, 09:18
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