Self-study
Support In the past decade, a decreasing percentage of money spent on treating disease X went to pay for standard methods of treatment, Support which are known to be effective though they are expensive and painful. ██ ██████████ ██████████ ██ █████ █████ ██ ███████████ ███████████ █████ █████ ██████ ███████████ ██████████████ ███ ███████████ ██████████ ████ ██████ ██ ██ ████████████ ██████████ ████ █████ ██ █████ █████ ███ ██ █████████ ██████████ ██ ███████ █ ████ ███ █████ ███ █████ ████
Percentage ≠ Amount
Over the past decade, the share of disease X spending going to standard treatments (which are effective) has been shrinking. Meanwhile, the share going to nonstandard treatments (which are not effective) has been growing. The author concludes that less money is being spent on effective treatments now than ten years ago.
The key move in this argument is a jump from percentage to amount. The premises tell us that the percentage going to standard treatments has decreased. The conclusion claims that the amount going to standard treatments has decreased.
Proving that the Amount Decreased
Does a smaller percentage necessarily mean a smaller amount? No, because the whole pie (the total amount spent on treating disease X) might have gone up!
It helps to see the point with concrete examples. In all three scenarios below, the percentage going to standard treatments drops from 50% to 25%. But whether the dollar amount drops depends on what happened to total spending on disease X. Total spending could have stayed the same, gone down, or gone up.
Scenario 1: Total spending stayed the same ($100)
10 yrs ago
50% standard = $50
Now
25% standard = $25
Amount dropped: $50 to $25 ✓
Scenario 2: Total spending went down ($100 to $80)
10 yrs ago
50% of $100 = $50
Now
25% of $80 = $20
Amount dropped: $50 to $20 ✓
Scenario 3: Total spending tripled ($100 to $300)
10 yrs ago
50% of $100 = $50
Now
25% of $300 = $75
Amount rose: $50 to $75 ✗
The dollar amounts above are just illustrations, but the underlying point would hold no matter what example numbers we choose: a decreasing percentage guarantees a decreasing amount if and only if total spending didn't increase enough to offset the shrinking percentage. Scenario 3 is the problem the argument fails to address. If total disease X spending grew enough, the amount going to standard treatments could have increased even though its share decreased.
Since this is a Sufficient Assumption question, the correct answer, if true, should guarantee the conclusion. So the correct answer should establish that total spending on disease X didn't increase enough to offset the shrinking percentage. For example, if we learn that total spending on disease X stayed the same or decreased, that would guarantee the conclusion.
18.
Which one of the following, ██ ████████ ██████ ███ ██████████ █████ ██ ██ ████████ ██████
a
Varieties of disease █ █████████ █████████ ███████ █████████ ████ ██████ ████ ██████ ██████ ███ ████ ███████
Although these varieties have become less common, that doesn't guarantee total spending on disease X hasn't increased. Maybe fewer people need the expensive special treatment, but more people are seeking treatment for disease X overall. Without knowing what happened to total spending, we can't bridge the percentage-to-amount gap.
b
Nonstandard methods of ████████ ███████ █ ███ ████ █████████ ███ ████ ████ ████ █ ██████ ████
Knowing that nonstandard treatments cost more now doesn't tell us whether total disease X spending increased. (B) allows for total spending to have gone up over the past 10 years. This means the argument is still vulnerable to the possibility that the amount spent on standard treatments has not gone down, even if the percentage spent on standard treatments has gone down.
c
Of total medical █████████████ ███ ██████████ ████ ██ ███ ██ █████████ ██ ███████ █ █████████ ██████ ███ ████ ███████
This tells us that disease X spending grew as a proportion of all medical spending (including heart surgery, cancer, etc.). But that's perfectly compatible with total disease X spending growing too.
For example, imagine that 10 years ago, $100 was spent on disease X out of $1,000 in total medical spending (10%). Now, $300 is spent on disease X out of $1,000 in total medical spending (30%). Disease X's share of all medical spending tripled, and the actual dollar amount spent on disease X also tripled. That puts us right back in Scenario 3 (from the stimulus explanation), where the amount going to standard treatments rises despite its shrinking percentage. We need to know what happened to the total dollar amount spent on disease X, and (C) doesn't tell us that.
d
Most of the █████ █████ ██ ████████ ███████ █ ██████ ███ ████ ██████ ████ ██ ███ ███ ███████████ ███████████
(D) tells us that most disease X money went to nonstandard treatments. But knowing how the pie is divided between standard and nonstandard doesn't tell us whether the pie has gotten bigger. To see why, let's use 40% as the starting share for standard and 60% for nonstandard. Let's say the share going to standard dropped from 40% to 25%, meaning the share spent on nonstandard increased to 75%. So far, this example satisfies (D): most (over half) of the money spent on disease X over the last decade went to nonstandard. Despite this, the dollar amount spent on standard can still rise if total spending grew enough:
10 yrs ago
40% of $100 = $40
60% is nonstandard, i.e. "most"
Now
25% of $300 = $75
75% is nonstandard, i.e. "most"
Amount still rose: $40 to $75
Even with most of the money going to nonstandard treatments in both time periods, the total could have grown so much that the smaller standard slice still represents more dollars than before. So (D) doesn't guarantee the conclusion.
e
The total amount ██ █████ █████ ██ ████████ ███████ █ ██████ ████████ ██████ ███ ████ ███████
(E) establishes that total spending on disease X has been declining. If the total amount shrank, then a smaller percentage of a smaller total guarantees a smaller amount spent on standard treatment for disease X. Think back to the visuals (under the stimulus explanation): (E) ensures we're in something like Scenario 2, where the whole pie got smaller. Combined with the premise that the percentage going to standard treatments shrank, we can validly conclude that the dollar amount going to standard treatments is less than it was ten years ago.