Question

Eight sets A, B, C, D, E, F, G and H are such that:

A is a superset of B, but subset of C.
B is a subset of D, but superset of E.
F is a subset of A, but superset of B.
G is a superset of D, but subset of F.
H is a subset of B.

N(A), N(B), N(C), N(D), N(E), N(F), N(G) and N(H) are the number of elements in the sets A, B, C, D, E, F, G and H respectively.

Which of the following could be TRUE, but not necessarily TRUE?

• A. N(A) is the greatest of all
• B. N(G) is greater than N(D)
• C. N(H) is the least of all
• D. N(F) is less than or equal to N(H)

Hint:

Check whether each statement is forced by the chain, contradicted by it, or genuinely open; H versus E is never compared, so H being the smallest is a real toss-up.

Answer 1

The Correct Option is C

This question wants the one statement that the passage neither forces to be true nor rules out entirely, a genuine toss-up. Start from the size chain: N(H) and N(E) both sit at or below N(B), and N(B) sits at or below N(D), which sits at or below N(G), which sits at or below N(F), which sits at or below N(A), which sits at or below N(C).

1. N(A) is the greatest of all: impossible, since the passage directly says A is a subset of C, so C is always at least as large as A. A can never beat C, so this option is simply false, not a toss-up.
2. N(G) is greater than N(D): this is really just the passage's own statement that G is a superset of D, restated as a size comparison. It is not new or uncertain information, so it does not fit what the question is after.
3. N(H) is the least of all: both H and E sit at the bottom of the chain, below everything else, but they were never measured against each other. It is entirely possible for H to be the smaller of the two, making this statement true, and equally possible for E to be the smaller one instead, making it false. Nothing in the passage settles this either way.
4. N(F) is less than or equal to N(H): the chain runs H at most B at most D at most G at most F, so F is always at least as big as H. For F to actually equal H, every one of those in-between sets would need to squeeze down to the exact same size too, which is not a natural reading of the passage and is not the kind of balanced uncertainty being asked about here.

So the first option is flatly impossible, the second is just a repeat of given information, and the fourth needs an unreasonable pile-up of coincidences. Only the third option, about H being the smallest, hinges on a genuinely open question, whether H or E is smaller, that the passage leaves unanswered.

Let's summarize:

• A can never be the greatest since C always contains it.
• H versus E is the one true unknown in this whole passage, which is exactly why "N(H) is the least of all" is a real toss-up.

So the statement that could be true, without being necessarily true, is that N(H) is the least of all. The answer is option (C).