Among people A, B, C, D, E and F, each having a different height, who is the second shortest? Statement I: Only two people are taller than A. E is taller than both B and C. F is shorter than E. F is taller than C. Statement II: Only two people are shorter than D. A is taller than D but shorter than E. F is neither the tallest nor the shortest. B is taller than C.

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Step 1 — notation and immediate deductions: - Label positions from tallest to shortest as $1,2,3,4,5,6$. - From Statement I: “Only two people are taller than A” ⇒ $A$ is at position $3$. Also $E>B,\;E> C,\;FC$, so among $E,F,C$ we have $E>F>C$ and $E>B$ (relative order of $B$ vs $F$ not fixed). - From Statement II: “Only two people are shorter than D” ⇒ $D$ is at position $4$. Also $E>A>D$ and $B>C$, and $F$ is neither tallest nor shortest (so $F ot=1,6$). Step 2 — combine I and II: - From both statements: positions $1,2$ are taller than $A(3)$; $D$ is $4$; remaining people $E,B,C,F$ occupy positions $1,2,5,6$ with constraints $E>F>C$ and $E>B$ and $B>C$, and $F eq1,6$. Step 3 — produce two distinct valid full orders (both satisfy all constraints) that give different second-shortest persons (position $5$): Example 1: - Order (tallest→shortest): $E(1),\;B(2),\;A(3),\;D(4),\;F(5),\;C(6)$. - Checks: $A$ has two taller ($E,B$); $E>B,C$; $FC$; $D$ has two shorter ($F,C$); $A$ between $E$ and $D$; $F$ not tallest/shortest; $B>C$. Second shortest (pos $5$) = $F$. Example 2: - Order (tallest→shortest): $E(1),\;F(2),\;A(3),\;D(4),\;B(5),\;C(6)$. - Checks: all constraints still satisfied ($E>F>C$, $E>B$, $A$ at $3$, $D$ at $4$, $F ot=1,6$, $B>C$). Second shortest (pos $5$) = $B$. Conclusion: - Even using both statements together we obtain at least two valid arrangements with different second-shortest persons ($F$ in Example 1 and $B$ in Example 2). Therefore the data in both statements I and II together are not sufficient to determine the second shortest. FINAL_ANSWER: a

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