CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about common difference of an Arithmetic Progression. Sum of the first 'n' terms and next 'n' terms are given and we need to find out the common difference. 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 3: Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?

1. \\frac{8}{25}\\)
2. \\frac{4}{25}\\)
3. \\frac{6}{25}\\)
4. \\frac{1}{25}\\)

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: How you would relate the first 25 terms and the next 25 terms?

The sum of the first 25 terms, S₂₅ = 525
The sum of the next 25 terms, K₂₅ = sum of next 25 terms = 725
a₂₆ = a₁ + 25d
a₂₇ = a₂ + 25d

K₂₅ = a₂₆ + a₂₇ + ...... + a₅₀
Or K₂₅ = a₁ + 25d + a₂ + 25d + ...... + a₂₅ + 25d
Or K₂₅ = a₁ + a₂ + ...... + a₂₅ + 25(25d)

Or K₂₅ = S₂₅ + 25(25d)
i.e., 725 = 525 + 25 * 25d
200 = 25 * 25d
8 = 25d
d = \\frac{8}{25}\\)

The question is "what is the common difference?"

Hence the answer is "\\frac{8}{25}\\)"

Choice A is the correct answer.