Question:hard

Directions: Each group of questions is based on a set of conditions. Read the passage below and answer the question that follows.

A retail electronics chain has six new mobile phone models, T, V, W, X, Y and Z. Each model comes with at least one of three options: digital camera, music player and office document viewer. No model has any other option. The following conditions apply:
  • V has 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.
  • V and Z have exactly one option in common.
  • T has fewer options than Z.
For this question only, replace the rule "X has more options than W" with this new rule: "X and W have exactly two options in common." All the other rules above still apply.

Which one of the following must be false?

Show Hint

Work out X's full option set from the replaced rule and the Z and T counts first, then compare it directly against V's fixed set of digital camera and document viewer.

Updated On: Jul 13, 2026
  • T and X have no options in common.
  • X and Z have no options in common.
  • V and X have exactly two options in common.
  • V and X have exactly one option in common.
Show Solution

The Correct Option is D

Solution and Explanation

Six mobile phones, T, V, W, X, Y and Z, each carry at least one of three options: digital camera, music player and document viewer. V carries digital camera and document viewer. W carries digital camera and music player. W and Y share nothing, so Y carries only the document viewer. V and Z share exactly one option, and T carries fewer options than Z. For this question, the usual rule "X has more options than W" is replaced with "X and W have exactly two options in common," and we need the statement that must be false.

  1. T and X have no options in common: Nothing pins T's exact set against X's three options, so this can hold in a valid case; it does not have to be false.
  2. X and Z have no options in common: Depending on which single option Z shares with V, this can also hold without breaking any rule.
  3. V and X have exactly two options in common: Since W only carries digital camera and music player, sharing exactly two options with W means X carries both of those. Bringing in the count requirements tied to Z and T then pushes X to also carry the document viewer, giving X all three options. V, with digital camera and document viewer, then shares both of those with X, so this statement is true, not false.
  4. V and X have exactly one option in common: Since X ends up carrying all three options, V and X always share two options together, digital camera and document viewer, never just one. This statement can never be true.

Let's summarize:

  • V, W and Y are fixed directly by the given clues; X is pinned down by the replaced rule together with the Z and T counts.
  • X ends up carrying all three options, so V and X always share exactly two of them.
  • The claim of exactly one shared option between V and X is the one that never matches reality.

So the statement that must be false is that V and X have exactly one option in common.

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