Discussion
For how many days, is it possible to determine the exact number of apples plucked by Shakuntala ?
Answer: D
The charts fix the apples of all ten days, so none of the options 0, 5 or 3 is right and the answer is None of the above.
Let the days be d1 to d10. The first question found d6 = 35 from d4 + d5 + d6 = 145 and the two sums that give d7 + d8 = 125. The rest follows step by step:
\[ \begin{aligned} d_4 + d_5 &= 145 - 35 = 110 \\ d_3 &= 165 - 110 = 55 \\ d_3 + \dots + d_7 = 265 &\Rightarrow d_7 = 265 - 55 - 110 - 35 = 65 \\ d_5 &= 140 - 35 - 65 = 40, \quad d_4 = 70 \\ d_8 &= 125 - 65 = 60 \\ d_9 &= 175 - 65 - 60 = 50 \\ d_{10} &= 155 - 60 - 50 = 45 \\ d_2 &= 150 - 55 - 70 = 25, \quad d_1 = 130 - 25 - 55 = 50 \end{aligned} \]
So the ten days are 50, 25, 55, 70, 40, 35, 65, 60, 50 and 45, and every one of the eight three-day sums and six five-day sums in the charts is reproduced by them. Solving all fourteen equations leaves no free unknown, so the exact count is determined for all 10 days. Zero, 5 and 3 are all too few.
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