Question

Directions for Questions 102 to 107: A retail electronics showroom chain has six new mobile phone models, T, V, W, X, Y and Z, each equipped with at least one of three options: digital camera, music player and office document viewer. No phone has any other option. The following conditions apply:

• V features both a digital camera and an office document viewer.
• W has a digital camera and a music player.
• W and Y have no options in common.
• X has more options than W.
• V and Z have exactly one option in common.
• T has fewer options than Z.

Q104. If Z has no option in common with T but has at least one option in common with every other mobile phone, then which one of the following must be false?

• A. T has digital camera.
• B. Z has document viewer.
• C. Exactly four of the six mobile phones have digital camera.
• D. Exactly four of the six mobile phones have music player.

Hint:

Test both of Z's possible option sets against Y first; only one avoids a zero-overlap conflict. Then see what is left over for T.

Answer 1

The Correct Option is D

Step 1: Recall Z's two possible identities.
From the base rules, Z is either {camera, music} or {document viewer, music}, and it always shares exactly one option with V = {camera, document viewer}.

Step 2: Apply "Z shares at least one option with every other phone."
Check Z = {camera, music} against Y = {document viewer}: there is no overlap at all, which breaks the new rule that Z must share something with every other phone. So Z cannot be {camera, music} here.
Check Z = {document viewer, music} against Y = {document viewer}: they share the document viewer, which works. Against W = {camera, music}: they share music, which works. Against X = {camera, music, document viewer}: they share both music and document viewer, which works. Against V: they share the document viewer, exactly one option, consistent with the base rule. So Z = {document viewer, music} is the only identity that survives.

Step 3: Apply "Z shares nothing with T."
T has exactly one option. Since Z = {document viewer, music}, T cannot be document viewer or music, or it would overlap with Z. That leaves only one choice: T = {camera}.

Step 4: Compute the final option set for all six phones and count each option.
V = {camera, document viewer}, W = {camera, music}, X = {camera, music, document viewer}, Y = {document viewer}, Z = {document viewer, music}, T = {camera}.
Camera holders: V, W, X, T, that is 4 phones.
Music holders: W, X, Z, that is 3 phones.
Document viewer holders: V, X, Y, Z, that is 4 phones.

Step 5: Check each option.
Option 1, T has a digital camera: true, since T = {camera}.
Option 2, Z has a document viewer: true, since Z = {document viewer, music}.
Option 3, exactly four have a digital camera: true, matches the count above.
Exactly four have a document viewer: true, matches the count above (this was original option 4, dropped in the fold).
Option 4 (originally option 5), exactly four have a music player: false, since only 3 phones (W, X, Z) carry music, not 4.

Final Answer:
The extra condition pins every phone down to one exact answer, and checking the counts shows the music-player count is 3, not 4.
\[ \boxed{\text{"Exactly four of the six mobile phones have music player" must be false.}} \]