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.

Q102. For exactly how many of the six mobile phones is it possible to determine exactly which option each one has?

• A. Two
• B. Three
• C. Four
• D. Five

Hint:

Work out Y first from the no-overlap rule with W, then use the three-option ceiling to pin down W, X and V.

Answer 1

The Correct Option is C

Each of the six phones carries a non-empty mix of three options: camera, music, and document viewer. Work through the six phones one at a time and see which ones have no wiggle room left once every rule is applied.

1. Y: W is already guaranteed a camera and a music player. Since W and Y cannot share any option, Y is locked out of both, leaving only the document viewer. Y is fully fixed at one option.
2. W: If W carried all three options, no phone could ever have "more options than W," since three is the maximum, and that breaks the rule that X has more than W. So W is stuck at exactly two options, camera and music, nothing else.
3. X: X needs more options than W's two, and three is the highest count possible, so X is pinned at exactly three, all of camera, music, and document viewer.
4. V: V starts with camera and document viewer guaranteed. If V also had music (all three options), then Z, which shares exactly one option with V, would be capped at one option, and T (with fewer options than Z) would need zero, which is not allowed. So V cannot take the music option; V stays at exactly two, camera and document viewer.
5. Z: Z must share exactly one option with V's set of {camera, document viewer}, so Z gets either camera or document viewer, never both. If that were Z's only option, T would again need zero options, which fails. So Z must also carry music alongside its one shared option, landing on two options, but which one it shares with V (camera or document viewer) is never pinned down by the rules; both stay valid.
6. T: T only needs fewer options than Z's two, which just means exactly one option, but the rules never say which one, so camera alone, music alone, and document viewer alone all remain valid choices for T.

Four phones, V, W, X and Y, always land on one exact answer no matter how you fill in the rest of the puzzle. Z and T both keep multiple valid identities open.

Let's summarize:

• Y, W and X get pinned down through direct option-sharing and count comparisons.
• V gets pinned down because letting it hold all three options would leave T with zero options, which is not allowed.
• Z and T each keep more than one valid answer, so they don't count toward the "exactly determined" total.

That gives four phones with a fully determined option set, so the answer is "Four."