Question

If a car has both tinted glass and leather seats, what is the greatest number of additional options that the car could have?

• A. 1
• B. 2
• C. 3
• D. 4
• A. air-conditioning, cassette deck, leather seats, power windows
• B. air-conditioning, cassette deck, leather seats, sunroof
• C. cassette deck, leather seats, sunroof, tinted glass
• D. cassette deck, power windows, sunroof, tinted glass
• A. 2
• B. 3
• C. 4
• D. 5
• A. air-conditioning and cassette deck
• B. tinted glass and sunroof
• C. cassette deck and leather seats
• D. power windows and sunroof
• A. The car has 3 options.
• B. The car has 4 options.
• C. The car has power windows and a sunroof.
• D. The car does not have both leather seats and a cassette deck.

Answer 1

The Correct Option is C

From the rules: 1. **Leather seats** ⇒ cassette deck. 2. **Cassette deck** ⇒ power windows. 3. **Tinted glass** ⇒ sunroof, but no air-conditioning. 4. **Air-conditioning** ⇒ at most two other options (irrelevant here because no AC is allowed with tinted glass). If the car has tinted glass + leather seats: - Tinted glass ⇒ sunroof (and no AC). - Leather seats ⇒ cassette deck ⇒ power windows. So these fixed options are already present: \[ \{\text{tinted glass}, \text{leather seats}, \text{sunroof}, \text{cassette deck}, \text{power windows}\} \] That’s 5 features fixed. Other possible options from the list might still be chosen provided they don’t violate rules — and without AC restriction applying, we can add up to **3** more from whatever remains in the full set of available options. Thus, the **greatest number** of *additional* options possible = \(\boxed{3}\).

Answer 2

Option (D) fits rules: - Tinted glass ⇒ sunroof, no AC — satisfied.
- Cassette deck ⇒ power windows — satisfied.
- No contradictions with leather seat/cassette rule.
Other options break rules:
(A) AC with 7gt; 2 others not possible.
(B) Tinted glass missing for sunroof rule.
(C) Leather seats ⇒ cassette deck ⇒ power windows — missing PW here.
Thus only (D) works.

Answer 3

Power windows ⇒ cassette deck.
Sunroof can come with tinted glass (no AC) or independently.
We list possibilities adding extra allowed items (respecting AC restriction if AC present). The maximum distinct sets possible = 4 by combining allowed options without breaking constraints.

Answer 4

Tinted glass ⇒ sunroof (rule), so both can exist without forcing other items. Other options fail: (A) AC + cassette deck implies power windows (breaks “exactly two”).
(C) Leather seats ⇒ cassette deck ⇒ power windows (more than 2).
(D) Power windows ⇒ cassette deck (more than 2).
Thus only (B) possible.

Answer 5

Tinted glass ⇒ sunroof, no AC. Minimum set: tinted glass + sunroof (2 options). Adding any other obeying rules pushes count to ≥ 4. Thus exactly 3 options is impossible.