Quantitative Aptitude – Modern Maths – Progressions – Let a(base1), a(base2)

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

Answer: 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 Exam Preparation

a) 750+ 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

Know More about Online CAT Course

Quantitative Aptitude – Modern Maths – Progressions – The arithmetic mean of x, y

Quantitative Aptitude – Modern Maths - Progressions – The arithmetic mean of x, y

Slot -2 – Quantitative Aptitude – Modern Maths – Progressions – The arithmetic mean of x, y

The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u=(x+y)/2 and v=(y+z)/2. If x ≥ z, then the minimum possible value of x is?

Answer: 105

Solution:
Given, (x+y+z)/3=80

x+y+z=240——1)

And (x+y+z+u+v)/4=75

x+y+z+u+v =375——2)

From eq 1) & eq 2) u+v =135

And from question , u+v =(x+2y+z)/2

Or 270=x+2y+z

y = 30 and x+z = 210

as x ≥ z
so x will be minimum if x =z

minimum value of x =210/2 = 105

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 2017 Exam Preparation
Basic Probability Concepts for CAT Preparation

Online Coaching Course for CAT Exam Preparation

a) 750+ 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

Know More about Online CAT Course

Quantitative Aptitude – Modern Maths – Progressions – Let x, y, z be three positive real

Quantitative Aptitude – Modern Maths - Progressions – Let x, y, z be three positive real

Slot -1 – Quantitative Aptitude – Modern Maths – Progressions – Let x, y, z be three positive real numbers

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is?

a) 5/2

b) 1/6

c) 3/2

d) 3/6

Solution:
Given x,y, z are in GP . let common ratio of this GP is r so y=xr & z=xr^2

Now 5x, 16y and 12z are in A.P. So

12z-16y=16y-5x
32y=12z+5x
32xr=12xr^2+5x

12r^2-32r+5=0
(6r-1)(2r-5)=0

So r=1/6 or 5/2
As given x < y < z so r >1

Thus r = 5/2
Option a) 5/2 is correct

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 2017 Exam Preparation
Basic Probability Concepts for CAT Preparation

Online Coaching Course for CAT Exam Preparation

a) 750+ 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

Know More about Online CAT Course