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.

Q103. Which one of the following must be false?

• A. Exactly five mobile phones feature a music player.
• B. Exactly five mobile phones feature a document viewer.
• C. Exactly four mobile phones feature a music player.
• D. Exactly four mobile phones feature a digital camera.

Hint:

Work out which phones can ever carry a music player at all before checking whether five of them is even possible.

Answer 1

The Correct Option is A

Step 1: Recall the fixed and semi-fixed phones.
From the earlier deductions, V = {camera, document viewer}, W = {camera, music}, X = {camera, music, document viewer}, and Y = {document viewer}. Z is either {camera, music} or {document viewer, music}, always carrying music. T has exactly one option, which could be camera, music, or document viewer.

Step 2: Count how many phones can ever carry a music player.
Music comes only from W, X, Z (all guaranteed to have music) and possibly T if T's single option happens to be music. V and Y never carry music at all.
That gives a guaranteed base of 3 music-players (W, X, Z), with T adding at most 1 more if T = music. So the music-player count can only ever be 3 or 4, never 5, since only 4 phones (W, X, Z, T) could ever possibly carry it.

Step 3: Check the music player options against this.
Option 1 says exactly five phones feature a music player. Since only 4 phones (W, X, Z, T) can ever carry music, and even that requires T = music, five is never reachable. This must be false.
Option 3 says exactly four feature a music player; this happens whenever T = music (W, X, Z, T all have it). Achievable, not always false.

Step 4: Check the camera and document viewer options.
Camera comes from V, W, X always, plus Z if Z = {camera, music}, plus T if T = camera; maximum reachable is 5, and 4 is reachable (for example Z = {document viewer, music}, T = camera). So option 4 ("exactly four have digital camera") is achievable, not always false.
Document viewer comes from V, X, Y always, plus Z if Z = {document viewer, music}, plus T if T = document viewer; maximum reachable is 5 (both extra sources active) and 4 is also reachable. So the document viewer counts of five and four are both achievable, not always false.

Final Answer:
Only the music-player count can never reach five, since just four phones (W, X, Z, T) can ever carry it, and T only sometimes does.
\[ \boxed{\text{Option 1: "Exactly five mobile phones feature a music player" must be false.}} \]