Which of the following statements can be inferred from the

[askhoman4]

[Two dimensional chart - see screenshot in link below. Heading: The Klein Family's Annual Income, 1985-1995. X-axis: year, from 1985 to 1995. Y-axis: income, from 20,000 to 70,000 with lines at 5,000 increments]
http://www.postimage.org/image.php?v=gx1m4OW9

Which of the following statements can be inferred from the data above?
I. The Klein family's annual income more than doubled from 1985 to 1995.
II. The Klein family's annual income increased by a greater amount from 1985 to 1990 than from 1990 to 1995.
III. The Klein family's average (arithmetic mean) annual income for the period shown was greater than $40,000.

a. I only
b. II only
c. I and III only
d. II and III only
e. I, II, and III

Original Answer is C.
Could anyone help explain why?

[RonPurewal]

[Two dimensional chart - see screenshot in link below. Heading: The Klein Family's Annual Income, 1985-1995. X-axis: year, from 1985 to 1995. Y-axis: income, from 20,000 to 70,000 with lines at 5,000 increments]
http://www.postimage.org/image.php?v=gx1m4OW9

Which of the following statements can be inferred from the data above?
I. The Klein family's annual income more than doubled from 1985 to 1995.
II. The Klein family's annual income increased by a greater amount from 1985 to 1990 than from 1990 to 1995.
III. The Klein family's average (arithmetic mean) annual income for the period shown was greater than $40,000.

a. I only
b. II only
c. I and III only
d. II and III only
e. I, II, and III

Original Answer is C.
Could anyone help explain why?

you can solve these by reading the incomes off the graph. for each year, the income is the y-value for that year.

(i)
the income for 1985 is about $25,000.
the income for 1995 is over $60,000, which is well over twice $25,000.
so, this statement is true.

(ii)
the income for 1985 is about $25,000.
the income for 1990 is between $35,000 and $40,000, closer to $40,000. let's say $38,000.
the income for 1995 is between $60,000 and $65,000, closer to $65,000. let's say $63,000.
the increase from '85 to '90 is about $13,000; the increase from '90 to '95 is about $25,000. there is no question that the second is greater.
thus, statement (ii) is false.

(iii)
this problem is the time-suck; the easiest way to do it is to add all the incomes together and divide by eleven (the total number of years for which income is shown).
let's estimate (in thousands - i'm not going to type all the ",000"s, and you shouldn't write them on test day either):
(25 + 26 + 26 + 35 + 36 + 38 + 38 + 57 + 63 + 63 + 63) / 11
= 470/11
= comfortably greater than 40 (it's 42 and change)
so, this statement is true.

unfortunately, not a lot of shortcuts here.

[askhoman4]

Thanks! I approached it the same way you did, and just realised I made a calculation error.

[RonPurewal]

Thanks! I approached it the same way you did, and just realised I made a calculation error.

if you made a calculation error, be sure to take inventory of whatever error(s) you made, so that you can be on "extra lookout" for the same type of error in the future.

usually, the arithmetic errors you make will fit some sort of narrow pattern or description - i.e., it's rare for your errors to be completely random - so, if you take inventory, you'll become aware of the particular types of errors that you tend to commit most often.

[AnjaliS420]

Since the question asks, which of the statements can be inferred then why isn't statement 2 included in the answer? I agree that the information it provides is false but the point is that we can infer from the table that it is incorrect.

[RonPurewal]

Since the question asks, which of the statements can be inferred then why isn't statement 2 included in the answer? I agree that the information it provides is false but the point is that we can infer from the table that it is incorrect.

"I can infer ____" means that "____" must be true.

[NinaP494]

Ron:
Any shortcuts to solving III quickly? Thanks

[RonPurewal]

Ron:
Any shortcuts to solving III quickly? Thanks

well, you could add/subtract together all the distances from 40,000.

i.e., you could add all the amounts by which the last 4 dots exceed 40,000, and subtract the amounts by which the first 7 dots fall short of it.

*IF* the average were actually 40,000, then you'd get exactly zero from doing this. so, if you get a positive result, that means the average is actually higher than 40,000; if the result is negative, the average is less than 40,000.

i doubt whether this method will give any significant time savings over just finding the average... but, it's a thing.

[RonPurewal]

more importantly, though, DO NOT worry about "fast" methods. do not EVER think about this. just do the work.

there is absolutely NO benefit—none whatsoever—to be had in worrying about 'short cuts' or 'quick' methods.
the problems are already short, and they NEVER involve tons and tons of 'busy work'. even if there is some sort of short cut, you'll be saving at most 10 or 15 seconds—and usually not even that much.
so, very little benefit.

but, the situation is worse than just 'minimal benefit'. it's worse, because people who are looking for short cuts all the time will tend to HAVE perfectly workable solution methods in mind, but then NOT DO THEM.
they'll sit there and wonder "is there some faster way?" ...and then they'll DO NOTHING AT ALL. do not let this happen to you.

[NinaP494]

As sagacious as always Ron! I agree thats a real danger - I will work on not falling for that trap. But finding ever more efficient, elegant almost poetic solutions is what keeps me motivated to study for the gmat. Thanks

[RonPurewal]

if you are even the slightest bit concerned with "elegant" and "poetic" solutions, then you are WAY past the point of being prepared to take this test, and, frankly, you're just wasting your time by continuing to study for it.
go take the exam!

in fact, if you've gotten to that point, then the most likely effect of more studying will be to make you LESS efficient at solving the problems, for the reason already explained above.