Q30 / 60 · KVPY 2014 (SA) · Mathematics

Suppose $a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}$ are are integers such that $$ \frac{5}{7}=\frac{a_{2}}{2 !}+\frac{a_{3}}{3 !}+\frac{a_{4}}{4 !}+\frac{a_{5}}{5 !}+\frac{a_{6}}{6 !}+\frac{a_{7}}{7 !} $$ where $0 \leq a < j$ for $j=2,4,5,6,7$. The sum $a_{2}+a_{3}+a_{4}+a_{5}+a_{6}+a_{7}$ is

  • A
    8
  • Correct answer
    B
    9
  • C
    10
  • D
    11

Solution

$\frac{5}{7}=\frac{2520 a_{2}+840 a_{3}+210 a_{4}+42 a_{5}+7 a_{6}+a_{7}}{L 7}$ $2520 a_{2}+840 a_{3}+210 a_{4}+42 a_{5}+7 a_{6}+a_{7}=3600$ Let $a_{2}=a_{3}=a_{4}=1 a_{5}=0 \quad a_{6}=4 \quad a_{7}=2$

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

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