Who's Taller?

Logic Level 2

There are six girls, and they decided that they'll measure each other.

•Jenna is taller than Molly, but shorter than Katelyn

•Abby is taller than Molly, but shorter than Teagan

•Teagan is taller than Katelyn

Gretchen is taller than Jenna

  Who's the tallest? Who's the shortest?

Gretchen, Teagan Teagan, Molly Katelyn, Jenna Abby, Jenna

2 solutions

Jordan Cahn
Dec 10, 2018

Let the heights of the six girls be $J, M, K, A, T, G$ , corresponding to the first letters in their names. We know the following: $\begin{aligned} M < J < K && \color{#3D99F6}(1) \\ M < A < T && \color{#3D99F6}(2) \\ K < T && \color{#3D99F6}(3) \\ J < G && \color{#3D99F6}(4) \end{aligned}$

We can conclude from $\color{#3D99F6}(1)$ and $\color{#3D99F6}(4)$ that $M<G$ and, therefore, Molly is the shortest girl. There is only one answer option for which Molly is the shortest: Teagan, Molly

There is not enough information to determine who the tallest girl is, but it must be either Teagan or Gretchen. Fortunately, Gretchen, Molly is not presented as an option.

Iasia Norris
Dec 8, 2018

No solution yet.

Who's Taller?

2 solutions

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