CAT 2017 Question Paper | Quants Slot 1

The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for Free) head out here: CAT Official Question Mocks. In CAT 2017 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: CAT Question Bank

Question 31 : If the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms, then the ratio of the first term to the common difference is :

1. 2 : 3
2. 3 : 2
3. 3 : 4
4. 4 : 3

Video Explanation

Explanatory Answer

Method of solving this CAT Question from Progressions

Given that the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms
(a + 6d)² = (a + 2d)(a + 16d)
We have to find the ratio of the first term to the common difference
⟹ (a + 6d)² = (a + 2d)(a + 16d)
⟹ a² + 12d + 36 = a² + 2ad + 16ad + 32d²
⟹ 4d² + 12 ad – 18 ad = 0
⟹ 4d² = 6ad
⟹ 4d = 6a
⟹ \\frac{a}{d}) = \\frac{4}{6}) = \\frac{2}{3})
The ratio of first term to the common difference is 2 : 3

The question is "If the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms, then the ratio of the first term to the common difference is :"

Hence, the answer is 2 : 3

Choice A is the correct answer