Q167 / 270 · NDA 2016 (Phase 2) · Mathematics

Paragraph: Let $\mathrm{a}, \mathrm{x}, \mathrm{y}, \mathrm{z}, \mathrm{b}$ be in AP , where $\mathrm{x}+\mathrm{y}+\mathrm{z}=15$. Let $\mathrm{a}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{b}$ be in HP , where $\mathrm{p}^{-1}+\mathrm{q}^{-1}+\mathrm{r}^{-1}=\frac{5}{3}$
Question: What is the value of $x y z$ ?

  • A
    $120$
  • Correct answer
    B
    $105$
  • C
    $90$
  • D
    Cannot be determined

Solution

On solving eq (1) \& (2), we get (i) $a=1 \& b=9 \Rightarrow a+4 d=9 \Rightarrow d=2$ (ii) $\mathrm{a}=9 \& \mathrm{~b}=1 \Rightarrow \mathrm{a}+4 \mathrm{~d}=1 \Rightarrow \mathrm{~d}=-2$. For $\mathrm{a}=1 \& \mathrm{~d}=2$, $x=3, y=5 \& z=7$ For $\mathrm{a}=9 \& \mathrm{~d}=-2$, $x=7, \mathrm{y}=5 \& \mathrm{z}=3$ $\Rightarrow \quad x y z=7 \times 5 \times 3=105$

Hence, the correct answer is option: 'B'.

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