Supposedly, "rare" doesn't mean "less", but it somehow does here.

mathematic proof of why (E) is correct by chatgpt:

🧠 Definitions

Let:

K₀ = Korva’s initial Ditrama population

M₀ = Mitro’s initial Ditrama population

G₀ = Guadar’s initial Ditrama population

T₀ = total initial Ditrama population = K₀ + M₀ + G₀

Growth rates (positive real numbers):

rK = Korva’s population growth rate

rM = Mitro’s population growth rate

rG = Guadar’s population growth rate

Then after 1 year:

K₁ = K₀(1 + rK)

M₁ = M₀(1 + rM)

G₁ = G₀(1 + rG)

T₁ = K₁ + M₁ + G₁ = K₀(1 + rK) + M₀(1 + rM) + G₀(1 + rG)

Let’s define:

s₀ = Korva’s initial share = K₀ / T₀

s₁ = Korva’s new share = K₁ / T₁

attempt a contradiction:

Assume:

rK > rM and rK > rG

and assume that Korva’s share declined:

K₁ / T₁ < K₀ / T₀

So:

K₀(1 + rK) / (K₀(1 + rK) + M₀(1 + rM) + G₀(1 + rG)) < K₀ / (K₀ + M₀ + G₀)

Multiply both sides by denominators:

K₀(1 + rK)(K₀ + M₀ + G₀) 0 from both sides:

(1 + rK)(K₀ + M₀ + G₀) < K₀(1 + rK) + M₀(1 + rM) + G₀(1 + rG)

Rewriting LHS:

(1 + rK)(K₀ + M₀ + G₀) = K₀(1 + rK) + M₀(1 + rK) + G₀(1 + rK)

Subtract K₀(1 + rK) from both sides:

M₀(1 + rK) + G₀(1 + rK) < M₀(1 + rM) + G₀(1 + rG)

Rewriting:

M₀[(1 + rK) – (1 + rM)] + G₀[(1 + rK) – (1 + rG)] < 0

⟺ M₀(rK – rM) + G₀(rK – rG) rM and rK > rG, then both (rK – rM) > 0 and (rK – rG) > 0, and M₀, G₀ > 0.

So the sum M₀(rK – rM) + G₀(rK – rG) > 0

∴ Contradiction.

✅ Therefore: It is mathematically impossible for Korva to have the highest percentage population growth among the three regions and yet have its revenue share (i.e., its share of total Ditrama population) decrease.

I ask chatgpt for

1. what does "population" in the stimulus, question, and answer choices mean?

🟩 From the prompt:

“Under the federal revenue-sharing plan, each region receives a share of federal revenues equal to the share of the total population of Ditrama residing in that region as shown by a yearly population survey.”

Here, “population of Ditrama” refers to Ditrama people only — i.e., citizens of Ditrama, not total inhabitants. This is what the revenue-sharing is based on.

“Last year the percentage of federal revenues Korva received for its share decreased somewhat even though the population survey on which the revenue-sharing was based showed that Korva’s population had increased.”

🟨 Here's the key ambiguity:

In this second sentence, when it says “Korva’s population had increased,” it does not explicitly repeat “population of Ditrama people.” So the word “population” here could, in ordinary English, refer to either:

Korva’s total population (including non-Ditrama people), or

Korva’s Ditrama population specifically.

However, given that the population survey referenced is the one used for revenue-sharing, and revenue-sharing is based on Ditrama population specifically, the most natural and logically consistent reading is this:

✅ Throughout the question and the answer choices, “population” refers to the Ditrama population only.

🧾 Therefore, in all five answer choices — (A) through (E) — when they say “population,” we should interpret that as meaning “Ditrama population,” not total residents (which could include non-Ditrama people).

Your question: Also, if histamines play no role in the process by which colds produce their symptoms, then doesn’t that mean that colds will inevitably produce their symptoms if you take an antihistamine alone?

The stimulus has:

1. H doesn't cause colds' symptoms.

so taking ~H, ie removing the cause, doesn't remove the effect, ie colds' symptoms.

2. Taking ~H can have other effects.

Other effects may or may not help with cold symptoms, we don't know.

back to C, taking ~H might not remove cold congestion totally but could reduce it, we don't know. And other effects it has may be effective with cold congestion, again also possible

yes this is a reasonable assumption to make. In the premises, it also states that "the pollutants are known to impair marine mammals' ability to fight off viral infection", so should be fine making that assumpiton

it's been 2 years but I believe correlation does strengthen a causal relationship??

spot-on!

yeah D requires the assumption that attribution shaping perception on certain features would cause wrong attribution

yeah these are the times that would speed you up so much if you see that.

You're assuming being interested in one thing equals having a demand on one thing

yeah agreed with this for why B is wrong

1958 was when urban homicide rates began increasing, and 1962 for rural areas. It's not too late if there were violent tv programs in 1959, as long as the number of homicides continue to grow since 1958?? The trend of homicide rates will still be increasing since 1958.

Would be a problem if violent tv programs didn't exist before 1962, since it couldn't have affected the homicide rates before it existed.

good explanation on (B)

many=some though

nice explanation

yup sufficient. since Only if introduces necessary

as always hahaha

no help at all LOL

a problem not addressed is that diverting the the sewage doesn't necessarily makes it less likely that lobsters eaten by human would contract gill diseases.

Even if (E) human does get ill, the proposal is still pointless.

Unless we made the assumption that removing sewage would make it less likely for lobsters to contract gill diseases.

You tackled this weaken question as it's a cause and effect one, so would you do this to all weaken questions?

A meant they can't go elsewhere instead of the one closing down, so it strengthens.

I'd say it's the same reason why it doesn't strengthen because it's unknown what may cause the decrease. Oftentimes answer that doesn't seem to directly affect the argument, don't work as the strenghtheners or weakeners.

LMAO who comes up with the name of the planet?

Ur anus? seriously?

(D) allows the possibility that they exist but doesn't want to contact us, and thus contradict the conclusion that they don't exist.

where'd you got the 1st question from? It's nowhere in the PTs!!!