Question:hard

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?

Show Hint

Work out which phones can ever carry a music player at all before checking whether five of them is even possible.
Updated On: Jul 13, 2026
  • Exactly five mobile phones feature a music player.
  • Exactly five mobile phones feature a document viewer.
  • Exactly four mobile phones feature a music player.
  • Exactly four mobile phones feature a digital camera.
Show Solution

The Correct Option is A

Solution and Explanation

This question asks which statement can never happen under the base rules (before any extra condition is added). Rather than listing every possible arrangement, focus on which phones are even capable of carrying each option, since that caps the maximum possible count.

  1. Exactly five feature a music player: Only four phones can ever possibly carry a music player: W and X always have it, Z always has it (both of Z's two possible sets include music), and T carries it only if T's single option happens to be music. V is fixed with no music, and Y is fixed with only a document viewer. With just four eligible phones, and one of them (T) only sometimes qualifying, the count can be at most 4, so it can never reach five.
  2. Exactly five feature a document viewer: V, X and Y always have it. Z adds a fourth if Z is chosen as {document viewer, music}, and T adds a fifth if T's single option is document viewer. Setting both of those at once (Z = {document viewer, music}, T = document viewer) gives five phones with a document viewer, a genuinely valid scenario. So this count of five is reachable.
  3. Exactly four feature a music player: This happens whenever T's single option is music, giving W, X, Z and T all with music, four total. Reachable.
  4. Exactly four feature a digital camera: V, W and X always have a camera. Choosing Z = {document viewer, music} and T = camera adds a fourth camera-holder without a fifth. Reachable.
  5. Exactly four feature a document viewer: V, X and Y always have it; choosing either Z = {document viewer, music} or T = document viewer (but not both) gives exactly four. Reachable.

Every option except the music-player count of five can be matched to a real, rule-following scenario.

Let's summarize:

  • Only four phones, W, X, Z and T, can ever carry a music player, and T only sometimes does, so five music-player phones is out of reach.
  • Camera and document viewer counts of four or five are all reachable by picking the right version of Z and T.

The statement that must be false is "Exactly five mobile phones feature a music player."

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