Let the number of pens distributed be a, b and c with 'a' being the number of pens received by the eldest son.
Hence, a + b + c = 57.
From Statement A:2b = a + c ⇒ b + 2b = 57 ⇒ b = 19 but ‘a’ and ’c’ can assume many values. So Statement ‘A’ alone is not sufficient.
From Statement B:If we assume that b = ar and c = ar
2, where ‘r’ is the common ratio of the GP. then a + ar + ar
2 = 57.
⇒ a(1 + r + r
2) = 57
This is satisfied for more than one set of values of‘a’ and 'r'. e.g.
If a = 1, r = 7, then a, b, c are 1,7, 49 respectively.
If a = 12, r =
, then a, b, c are 12, 18, 27 respectively.
So Statement 'B' alone is not sufficient.
Combining Statement A and Statement B:This results in a = b = c. Hence, ‘a’ won’t be the highest number anymore and the condition given in the question is violated.
Hence the question cannot be answered by using both the statements together.