# Quantitative Aptitude – Modern Maths – Progressions – Let a(base1), a(base2) ## Slot -2 – Quantitative Aptitude – Modern Maths – Progressions – Let a(base1), a(base2), …a(base52)

Let a(base1), a(base2), … , a(base52) be positive integers such that a(base1) < a(base2) < … < a(base52). Suppose, their arithmetic mean is one less than the arithmetic mean of a(base2), a(base3), …, a(base52). If a(base52) = 100, then the largest possible value of a(base1) is?

a) 45
b) 20
c) 48
d) 23

Solution:
We want to maximize the value of a1, subject to the condition that
(a2+ a3 +⋯….+ a52 )/51 -(a1+ a2 +⋯….+ a52 )/52 = 1
Since a(base52) = 100 and all the numbers are positive integers, maximizing a1 entails maximizing a2, a3 ….a51. The only way to do this is to assume that a2, a3…. A52 are in an AP with a common difference of 1.
Let the average of a2, a3, …, a52 i.e.
(a2+ a3 +⋯….+ a52 )/51= a27 =A ( using the average of an odd number of terms in an Arithmetic Progression is equal to the value of the middle-most term)
So a52  = a27 + 25*1 = a27 + 25  and
given a52 = 100
=>  a27 = A = 100 – 25 = 75
a2 + a3 + … + a52 = 75×51 = 3825
Given a1 + a2 +… + a52  = 52(A – 1) = 3848
Hence a1 = 3848 – 3825 = 23
Ans : 23

## Other posts related to Quantitative Aptitude – Modern Maths

Permutation and Combination – Fundamental Principle of Counting
Permutation and Combination – Distribution of Objects
How to find Rank of a Word in Dictionary (With or Without Repetition)
Set Theory- Maximum and Minimum Values
How to solve questions based on At least n in Set Theory for CAT Exam?
Sequence and Series Problems and Concepts for CAT 2019 Exam Preparation
Basic Probability Concepts for CAT Preparation

## Online Coaching Course for CAT 2021 + Test Series

a) 1000+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video