Quantitative Aptitude – Algebra – Maxima Minima – If three sides of a rectangular

Quantitative Aptitude – Algebra – Maxima Minima

Question

CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Maxima Minima - If three sides of a rectangular
If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is

Answer

200

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Maxima Minima, we can see that,
Let a and b be the two sides of a rectangle.
a + 2b = 400
Area of rectangle = ab (We have to maximize it)
b = (400-a)/2
Put the value of b in area of rectangle.

a(400-a)/2 = (400a-a^2)/2
On differentiating the above equation, we get
400-2a = 0 => a=200
b = 100
Area will be max when length of longer side = 200.
Answer: 200

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Maxima Minima – Q1: If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is
Quantitative Aptitude – Algebra – Maxima Minima – Q2: An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?
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Quantitative Aptitude – Algebra – Maxima Minima – If three sides of a rectangular
5 (100%) 51 votes

Quantitative Aptitude – Algebra – Maxima Minima – If a, b, c, and d are integers

Quantitative Aptitude – Algebra – Maxima Minima

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Maxima Minima - If a, b, c, and d are integers
If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is

Answer

2

Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Maxima Minima, we can see that,
a + b + c + d = 30
a, b, c, d are integers. (a – b)^2 + (a – c)^2 + (a – d)^2 would have its minimum value when each bracket has the least possible value. Let (a, b, c, d) = (8, 8, 7, 7) The given expression would be 2. It cannot have a smaller value.
Answer: 2

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Maxima Minima – Q1: If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
Quantitative Aptitude – Algebra – Maxima Minima – Q2: An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?
Quantitative Aptitude – Algebra – Functions
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

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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 – Algebra – Maxima Minima – If a, b, c, and d are integers
5 (100%) 59 votes

Quantitative Aptitude – Algebra – Maxima Minima – An elevator has a weight

Quantitative Aptitude – Algebra – Maxima Minima

Question

CAT 2017 - Forenoon slot - Quantitative Aptitude - Algebra - Maxima Minima - An elevator has a weight
An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg.
What is the maximum possible number of people in the group?

Answer

11

Solution

As per the question from CAT 2017 – Quantitative Aptitude – Algebra – Maxima and Minima, we can see that,
53 + …….. + 57 = 630
Remaining sum of weights = 630 – 53 – 57 = 520
Now, the minimum weight can be 53. So, to find maximum number of people
N(max) = 520/53 = 9.81
So, maximum number of people possible = 9+2 = 11
Answer: 11

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Maxima Minima – Q1: If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is
Quantitative Aptitude – Algebra – Maxima Minima – Q2: If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)^2 + (a – c)^2 + (a – d)^2 is
Quantitative Aptitude – Algebra – Functions
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Quadratic Equations
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

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An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam

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 – Algebra – Maxima Minima – An elevator has a weight
5 (100%) 56 votes