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Expenditure and Income over 12 year period for Mr. A
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05 Mar 2018, 01:56
05 Mar 2018, 01:56
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1. Which of the following can be inferred from the graph? (Select ALL that apply)
A) The difference between Mr A's income and expenditure was less than five thousand dollars in more than half the years
B) Mr A's income was never less than 75 percent of his expenses in this 12-year period
C) Mr A's income rose uniformly throughout the 12-year period
2. From year 2 to year 4 Mr A's expenditure increased by what percent?
A) 75
B) 60
C) 50
D) 25
E) 20
3. Between which two years was the percent decrease in Mr A's expenditure greatest?
A) 4 and 5
B) 5 and 6
C) 6 and 7
D) 7 and 8
E) 9 and 10
4. If net income is defined as income minus expenditure, what is the best approximation to the difference in dollars between Mr A's net income in Year 4 and Year 9?
A) 12,500
B) 10,000
C) 7,500
D) 5,000
E) 2,500
A) The difference between Mr A's income and expenditure was less than five thousand dollars in more than half the years
B) Mr A's income was never less than 75 percent of his expenses in this 12-year period
C) Mr A's income rose uniformly throughout the 12-year period
Show: ::
A,B
2. From year 2 to year 4 Mr A's expenditure increased by what percent?
A) 75
B) 60
C) 50
D) 25
E) 20
Show: ::
D
3. Between which two years was the percent decrease in Mr A's expenditure greatest?
A) 4 and 5
B) 5 and 6
C) 6 and 7
D) 7 and 8
E) 9 and 10
Show: ::
B
4. If net income is defined as income minus expenditure, what is the best approximation to the difference in dollars between Mr A's net income in Year 4 and Year 9?
A) 12,500
B) 10,000
C) 7,500
D) 5,000
E) 2,500
Show: ::
A
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Re: Expenditure and Income over 12 year period for Mr. A
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05 Mar 2018, 19:07
05 Mar 2018, 19:07
1
Expert Reply
It's always important to invest whatever time is necessary to fully understand charts and graphs before answering the questions. This one is fairly straightforward though.
1.A. Notice that the scale in the vertical axis is measured in increments of $5000, so we can quickly check how many years have less than one increment between them. Years 1, 2, 4, 5, 11, and 12 clearly differ by less than $5000. That's half the years. The question is whether year 3 qualifies. If you look closely, you can see that the expenditure graph in year 3 is a little farther under the line above it than the income graph in year 3 is, indicating that there's less than $5000 difference between them. Thus, A is in.
1.B. Only in years 1, 2, 3, and 4 do the expenditures exceed the income. Since year 3 has the greatest difference, if we determine that the income is more than 75% of the expenditures, the other years won't either, and we'll be done. ETS will absolutely turn some of these charts and graphs problems into an eye test, so be very exacting when reading the graph. Be sure to read the middle of the triangles and squares, not the edges. Expenditures is above the halfway point between 20,000 and 25,000. But is it 23,000 or 24,000? To me 24,000 should be quite close to the top so this appears to be 23,000. 75% of 24,000 would be 18,000, so if income is above 18,000, it'll therefore be above 75% of 23,000. Income appears to me to be about 19,000. Thus, in no year is the income below 75% of expenditures and B is in.
1.C. Clearly, year 10's income is below that of year 9, so C is out.
So A and B only.
2. Expenditure in year 2 was 20,000, while in year 4 it was 25,000. When given a before and after picture and asked for a percent increase/decrease, you can use the "change/original" formula. The change is 5,000, while the original is 20,000. So:
5,000/20,000 = .25 or 25%. So D.
3. Options D and E are out since the expenditure actually increases. We can reuse the change/original formula from the last problem for options A, B, and C.
We should get decreases of 3,000/25,000 and 3,000/22,000 and 1,000/19,000 respectively. Comparing the first two, we know option B will be a larger decrease since we have the same numerator but B has a smaller denominator. Comparing B with C, we know B is larger, since the numerator is 3 times larger, but the denominator is only a bit smaller. So the answer is B.
4. In year 4, income appears to be 23,000, while expenditure appears to be 25,000. Subtracting them using the given formula gives us -2,000. His net income in year 9 appears to be 30,000 - 20,000 = 10,000. The difference between net incomes would thus be:
10,000 - (-2,000) = 10,000 + 2,000 = 12,000, which is pretty close to A. Note that since no other answer choice is anywhere near 12,000, we can safely conclude that it's A without going back to get a more exacting answer.
1.A. Notice that the scale in the vertical axis is measured in increments of $5000, so we can quickly check how many years have less than one increment between them. Years 1, 2, 4, 5, 11, and 12 clearly differ by less than $5000. That's half the years. The question is whether year 3 qualifies. If you look closely, you can see that the expenditure graph in year 3 is a little farther under the line above it than the income graph in year 3 is, indicating that there's less than $5000 difference between them. Thus, A is in.
1.B. Only in years 1, 2, 3, and 4 do the expenditures exceed the income. Since year 3 has the greatest difference, if we determine that the income is more than 75% of the expenditures, the other years won't either, and we'll be done. ETS will absolutely turn some of these charts and graphs problems into an eye test, so be very exacting when reading the graph. Be sure to read the middle of the triangles and squares, not the edges. Expenditures is above the halfway point between 20,000 and 25,000. But is it 23,000 or 24,000? To me 24,000 should be quite close to the top so this appears to be 23,000. 75% of 24,000 would be 18,000, so if income is above 18,000, it'll therefore be above 75% of 23,000. Income appears to me to be about 19,000. Thus, in no year is the income below 75% of expenditures and B is in.
1.C. Clearly, year 10's income is below that of year 9, so C is out.
So A and B only.
2. Expenditure in year 2 was 20,000, while in year 4 it was 25,000. When given a before and after picture and asked for a percent increase/decrease, you can use the "change/original" formula. The change is 5,000, while the original is 20,000. So:
5,000/20,000 = .25 or 25%. So D.
3. Options D and E are out since the expenditure actually increases. We can reuse the change/original formula from the last problem for options A, B, and C.
We should get decreases of 3,000/25,000 and 3,000/22,000 and 1,000/19,000 respectively. Comparing the first two, we know option B will be a larger decrease since we have the same numerator but B has a smaller denominator. Comparing B with C, we know B is larger, since the numerator is 3 times larger, but the denominator is only a bit smaller. So the answer is B.
4. In year 4, income appears to be 23,000, while expenditure appears to be 25,000. Subtracting them using the given formula gives us -2,000. His net income in year 9 appears to be 30,000 - 20,000 = 10,000. The difference between net incomes would thus be:
10,000 - (-2,000) = 10,000 + 2,000 = 12,000, which is pretty close to A. Note that since no other answer choice is anywhere near 12,000, we can safely conclude that it's A without going back to get a more exacting answer.
Re: Expenditure and Income over 12 year period for Mr. A
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09 Sep 2018, 17:59
09 Sep 2018, 17:59
Can we use a ruler on our computer screens on test day? Question 1 was very difficult without the exact values.
