#12 - A nationwide poll of students, parents, and teachers

[Administrator]

Complete Question Explanation

Flaw in the Reasoning—#%. The correct answer choice is (B)

The author of this stimulus presents an argument which is inherently contradictory:
Premise: Poll results: 90% say the percentage spent on their counseling is appropriate.
Conclusion: Significant budget increases should be spent elsewhere.

The problem with this argument can be clearly seen through the use of a hypothetical:
If the existing total budget is $100, and the school is spending $10 on counseling programs, the survey consensus is that this is an appropriate portion, in this case 10%.
Today, there is an announcement that all budgets will be doubled (significant increase).
The author argues that the extra money should go elsewhere, in spite of the fact that the survey would suggest doubling the counseling budget to $20—this would allow the school to maintain the same 10% portion spent on counseling programs.

Correct answer choice (B) is the only one which explains the problem with the author’s argument: the author confuses a percentage (that of the budget being spent on counseling programs) with an overall amount. If, for example, the survey showed that most believed 100 dollars to be an appropriate amount spent on school counseling, then it would make sense to recommend spending additional budgetary dollars elsewhere.

Answer choices (A) and (C) are both incorrect, because the author neither asserts a causal argument nor presumes any correlation between part of the budget and the overall budget, and neither of the points presented in answer choices (D) and (E) are considerations necessary in making or assessing the author’s argument.

[sa3334]

Hi,
Despite reading the explanation, I'm still confused about the flaw in the reasoning. Yes if 10% of $100 is being spent, which amounts to $10, and doubling it would then increase the funding to $20--isn't there still a $10 increase in the budget being spent to student counseling program? So I thought the poll of student, parents, and teachers were suggesting this extra $10 be spent elsewhere.

Thank you in advance for the help!

[James Finch]

Hi SA,

The stimulus's conclusion is that the amount (raw number) spent on student counseling shouldn't increase in the case of a significant budgetary increase (raw number). Why? Because 90+% of students, parents and teachers polled believe that the correct percentage of the current budget is being spent on the counseling programs, not raw amount. So if the budget increased, the raw number spent on the programs would have to increase to keep the percentage the same. That is the flaw in the stimulus, that it confuses raw numbers and percentages; keeping the percentage the same would necessitate increasing the number.

Hope this helps!

[massavenue]

Hi,
Despite reading the explanation, I'm still confused about the flaw in the reasoning. Yes if 10% of $100 is being spent, which amounts to $10, and doubling it would then increase the funding to $20--isn't there still a $10 increase in the budget being spent to student counseling program? So I thought the poll of student, parents, and teachers were suggesting this extra $10 be spent elsewhere.

Thank you in advance for the help!

The way I looked at this problem was more of a "pie chart" scenario. Forget the dollar amounts for a quick second.

If you're the president and you're in charge of allocating the total national budget to different areas of the nation, how would you allocate it? Let's say you and the senate agree that allocating 30% of the total national budget to healthcare is approriate. That's lovely, 30% sounds like a decent number.

Now let me ask you this, does 30% mean that there is an appropriate amount of actual dollars going into healthcare? Absolutely not. You and the senate only agreed that 30% of the nation's budget should be allocated to healthcare and thar does not say whether or not there was enough actual dollars.

It's like getting married and you and your spouse agree that you should deposit 10% of your weekly income into a savings account for your children's education. 10% may sound appropriate but it tells us nothing about whether there is an appropriate amount being funded into that account. For all we know, you could be making $10 weekly and only depositng $1.

This was where B was getting at in terms of percetange NOT equaling actual amount.

[Jeff Wren]

Hi massavenue,

Thinking of these numbers/percentages questions in terms of a pie chart can be a useful way to conceptualize the ideas.

The "total pie" would correspond to the total amount, and the size of a "slice" of the pie would correspond to the percentage within the total.

Using pizza as an example, a 10% sized slice of a small pizza would be less pizza than a 10% sized slice of an extra large pizza.