CAT Exam Model Paper 6 with solutions for free online practice

Question : 28 of 60

Marks: +1, -0

The question given below is followed by two statements, A and B. Mark the answer using the following instructions:
Mark (a) if the question can be answered by using Statement A alone, but cannot be answered by using Statement B alone.
Mark (b) if the question can be answered by using Statement B alone, but cannot be answered by using Statement A alone.
Mark (c) if the question cannot be answered even by using both the statements together.
Mark (d) if the question can be answered by using either statement alone.
Q. A man has 57 pens. He wants to distribute these pens among his 3 sons such that his eldest son receives the highest number of pens. What will be the number of pens received by the eldest son?
A. The number of pens received by the sons are in Arithmetic Progression.
B. The number of pens received by the sons are in Geometric Progression.

Validate

Solution:

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 =

3/2

, 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.

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