CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about CAT Geometric Progressions. A question on possible values. We need to find out the possible values of 'n' which is related to the common ratio of a GP. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 1: Second term of a GP is 1000 and the common ratio is r = \\frac{1}{n}\\) where n is a natural number. P_n is the product of n terms of this GP. P₆ > P₅ and P₆ > P₇, what is the sum of all possible values of n?

1. 4
2. 9
3. 5
4. 13

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: This question is almost a puzzle. You have to carefully consider the implications for the common ratio, and then extrapolate to the Product of n terms.

Common ratio is positive, and one of the terms is positive => All terms are positive
P₆ = P₅ * t₆ => If P₆ > P₅, t₆ > 1
P₇ = P₆ * t₇ => If P₆ > P₇, t₇ < 1
t₆ = t₂ * r⁴ = 1000r⁴;
t₇ = t₂ * r⁵ = 1000r⁵
1000r⁴ > 1 and 1000r⁵ < 1
\\frac{1}{r^{4}}\\) < 1000 and \\frac{1}{r^{5}}\\) > 1000.
\\frac{1}{r}\\) = n.
n⁴ < 1000 and n⁵ > 1000, where n is a natural number
n⁴ < 1000 => n < 6
n⁵ > 1000 => n ≥ 4
n could be 4 or 5. Sum of possible values = 9

The question is "what is the sum of all possible values of n?"

Hence the answer is "9"

Choice B is the correct answer.