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.

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?

Show 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.
Updated On: Jul 13, 2026
  • T has digital camera.
  • Z has document viewer.
  • Exactly four of the six mobile phones have digital camera.
  • Exactly four of the six mobile phones have music player.
Show Solution

The Correct Option is D

Solution and Explanation

The extra condition in this question, Z shares nothing with T but shares something with every other phone, is strong enough to pin every single phone down to one exact option set. Build that table directly instead of working option by option.

  1. Start from Z: Z was already narrowed to two possibilities, {camera, music} or {document viewer, music}. Test {camera, music} against Y = {document viewer}: zero overlap, which fails the new "shares something with every phone" rule. So Z must be {document viewer, music}.
  2. Check Z against the rest: Z = {document viewer, music} shares the document viewer with V, shares music with W, and shares both with X. Every other phone is covered, so this identity for Z is fully consistent.
  3. Pin down T: Z carries document viewer and music, so T (which must share nothing with Z) cannot hold either of those. T only ever has one option to begin with, so the only option left for T is the camera.
  4. Write out the full table: V = camera + document viewer, W = camera + music, X = camera + music + document viewer, Y = document viewer, Z = document viewer + music, T = camera.
  5. Count each option across all six phones: Camera appears in V, W, X, T (4 phones). Music appears in W, X, Z (3 phones). Document viewer appears in V, X, Y, Z (4 phones).

Now check each answer choice against this table: T does have a camera (true), Z does have a document viewer (true), exactly four phones have a camera (true, matches the count), exactly four phones have a document viewer (true, matches the count), and exactly four phones have a music player (false, only 3 phones have it).

Let's summarize:

  • The "shares something with everyone" rule rules out Z = {camera, music}, since that would leave Y with nothing in common with Z.
  • Once Z is fixed, T is squeezed down to just the camera, since it cannot overlap with Z's two options.
  • Counting the final table gives camera = 4, music = 3, document viewer = 4.

The one statement that does not match reality is "Exactly four of the six mobile phones have music player," since the true count is three, so that is the statement that must be false.

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