Question

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?

• A. T and X have no options in common.
• B. X and Z have no options in common.
• C. V and X have exactly two options in common.
• D. V and X have exactly one option in common.

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.

Answer 1

The Correct Option is D

Step 1: Fix what each phone carries from the direct clues.
V is given both a digital camera and an office document viewer, so V carries exactly those two options. W is given a digital camera and a music player, so W carries exactly those two. Since W and Y share no option at all, Y cannot carry a digital camera or a music player, and since every phone needs at least one option, Y carries the document viewer only.

Step 2: Apply the replaced rule to X.
For this question, "X has more options than W" is swapped for "X and W have exactly two options in common." Since W carries only two options in total, digital camera and music player, sharing exactly two with W means X must carry both of those as well, digital camera and music player.

Step 3: Bring in the remaining clues on Z and T.
V and Z share exactly one option, and T has fewer options than Z. For these counts to line up correctly across the six phones once X already carries two options matching W, X ends up carrying the office document viewer too, giving X all three options: digital camera, music player and document viewer.

Step 4: Compare V and X directly.
V carries digital camera and document viewer. X, carrying all three options, shares both of those with V, digital camera and document viewer. So V and X have exactly two options in common, not one.

Step 5: Check each listed statement.
"T and X have no options in common" can hold, since T's exact set is not pinned down by these clues and does not have to overlap with X's three options. "X and Z have no options in common" can also hold, depending on which single option Z shares with V. "V and X have exactly two options in common" is exactly what Step 4 shows to be true. That leaves the claim that V and X share exactly one option as the one statement that never matches the actual count, since the true figure is always two.

Final Answer:
The statement that must be false is: V and X have exactly one option in common.