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Let 'n' be the number of jelly beans given to first sibling. Thus, sum of all jelly beans (i.e. the sum of all consecutive seven integers) = 7n + 21.

It is also given that –
Sum of all jelly beans = 72 (given to three siblings) + Amount given to Esther (let E) + 73 (given to other three siblings)
S = E + 145

So, 7n + 21 = E + 145
7(n + 3) = E + 145

Hence, E + 145 should be a multiple of 7. Checking all options:
A. 21 + 145 = 166 (Not divisible by 7)
B. 22 + 145 = 167 (Not divisible by 7)
C. 23 + 145 = 168 (Multiple of 7)...

C is the answer.
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