Question

If the entire group of six people ordered a total of exactly 11 slices of pizza, which one of the following must be true? (A) Exactly two people ordered exactly one slice. (B) Exactly one person ordered exactly two slices. (C) Exactly two people ordered exactly two slices. (D) Exactly three people ordered exactly two slices. (E) Exactly one person ordered exactly three slices.

Short answer

Option (D) must be true: Exactly three people ordered exactly two slices.

Step-by-step solution

Define Variables

Let each person in the group be represented by variables: A, B, C, D, E, and F. The sum of the slices of pizza each person ordered (a + b + c + d + e + f) is given as 11.

Consider Logical Possibilities

Evaluate each option to see how they fit with the given conditions (six people, total 11 slices). Consider that six people must share these slices, and any configuration must total to 11.

Analyze Option (A)

For exactly two people to have ordered exactly one slice, we're left with 9 slices for the remaining four people. This configuration doesn't easily align with a total of 11 in a way that is specified clearly.

Analyze Option (B)

If one person ordered exactly two slices, the remaining five people must share 9 slices. Again, it's not clear how this fulfills the requirement with exact values.

Analyze Option (C)

With two people ordering exactly two slices each, that uses 4 slices, leaving 7 slices for the remaining four people. Arriving at exact numbers here without further split consideration is troublesome.

Analyze Option (D)

Exactly three people ordering two slices each uses up 6 slices, leaving the remaining three people to share 5 slices. This is feasible if one person orders two slices, and the other orders distribute among them appropriately.

Analyze Option (E)

If one person gets exactly three slices, the remaining slices divide among 5 others without clarity on the specific number per person, making configuration complex.

Confirm Most Feasible Option

Among all possibilities, calculating and logically analyzing the splits tells us that the most balanced division occurs when three people ordered exactly two slices each.

Key concepts

logical reasoning

In LSAT logic games, logical reasoning is foundational. It involves breaking down problems step-by-step to arrive at a logical conclusion. For our problem involving six people and 11 slices of pizza, we need to evaluate each option methodically.
Logical reasoning in this context means:
* Analyzing each choice (A to E) carefully.
* Assessing whether a given configuration can be true given the conditions.
Each option represents a different pizza slice distribution among six people. Our task is to see which distribution aligns best with the requirement (totaling 11 slices while adhering to the specific conditions). This requires clear, structured thinking to filter out unsuitable options, leading us to the correct answer.

variable definition

Defining variables simplifies complex problems, making them more manageable. For our exercise, we represent each of the six people by variables: A, B, C, D, E, and F.
* Let each person’s pizza slices be represented as: a, b, c, d, e, and f.
* The sum of a + b + c + d + e + f must equal 11 slices (total ordered).
This approach ensures we can methodically check if the sum matches the total slices when examining different configurations. By having clear variables, it’s easier to track different slices each person gets and see if the overall sum matches 11 slices. Without variable definition, it would be cumbersome to keep track of all possibilities.

analytical problem solving

Analytical problem solving is about breaking the problem into smaller, more manageable parts. Here, we do this by:
* Evaluating each option (A to E) separately.
* Understanding what each option implies about the distribution of pizza slices.
For example, consider Option D: If three people order exactly two slices each, we use up 6 slices. This leaves 5 slices for the remaining three people. We analyze if this remaining configuration can still sum up to 11. By confirming through simple arithmetic that such a distribution is feasible, we validate this option. This step-by-step analysis helps ensure we don’t overlook any possibilities while ruling out infeasible ones efficiently.

mathematical distribution

Mathematical distribution involves understanding how quantities can be divided among a set of elements. In our problem, we need to distribute 11 pizza slices among six people.
Let’s illustrate this using the correct option (D):
* Three people ordering 2 slices each totals 6 slices (2 + 2 + 2 = 6).
* This leaves 5 slices to be distributed among the remaining three people.
If these three people respectively order varying slices but the sum remains 11, we ensure each combination adheres to the problem's constraints.
This properly checks the rule of distribution and helps confirm that three people getting exactly two slices each is mathematically feasible (in alignment with the problem's restraints).