Quantitative Aptitude - Algebra - Functions - If f1(x) = x^2 + 11x + n
Quantitative Aptitude - Algebra - Functions
Question
If f1(x) = x^2 + 11x + n and f2(x) = x, then the largest positive integer n for which the equation f1(x) = f2(x) has two distinct real roots, is
Answer
24
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that,
f1(x) = f2(x)
x^2 + 11x +n = x
x^2 + 10x + n =0
To have distinct and real roots, D>0
D = b^2-4ac = 100 â€“ 4n > 0
On solving the inequality, we get, n

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Quantitative Aptitude - Algebra - Inequalities - For how many integers n
Quantitative Aptitude - Algebra - Inequalities
Question
For how many integers n, will the inequality (n â€“ 5) (n â€“ 10) â€“ 3(n â€“ 2) â‰¤ 0 be satisfied?
Answer
11
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Inequalities, we can see that,
On solving the equation, we get n^2 â€“ 18n + 56 â‰¤ 0
Factorize and we get, (n-4)(n-14) â‰¤ 0
4 â‰¤ n â‰¤ 14
No of values of n =11
Answer: 11
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Quantitative Aptitude - Algebra - Inequalities - The number of solutions (x, y, z)
Quantitative Aptitude - Algebra - Inequalities
Question
The number of solutions (x, y, z) to the equation x â€“ y â€“ z = 25, where x, y, and z are positive integers such that x â‰¤ 40, y â‰¤ 12, and z â‰¤ 12 is
A) 101
B) 99
C) 87
D) 105
Answer
Option (B)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Inequalities, we can see that,
x = 25 + y + z. The possible values of x, y, z and the corresponding number of values of y, z are

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Quantitative Aptitude - Algebra - Polynomials - If 9^(2x â€“ 1) â€“ 81^(x-1) = 1944
Quantitative Aptitude - Algebra - Polynomials
Question
If 9^(2x â€“ 1) â€“ 81^(x-1) = 1944, then x is
A) 3
B) 9/4
C) 4/9
D) 1/3
Answer
Option (B)
Solution
From CAT 2017 - Quantitative Aptitude - Algebra - Polynomials, we can see that,
9^(2x-1) â€“ 9^(2x-2) = 1944
It can be written as 3^(4x)/9 â€“ 3^(4x)/81 = 1944
8(3^(4x)/81) = 1944
x =9/4
Option (B)
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C

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Quantitative Aptitude - Algebra - Quadratic Equation - If x + 1 = x^2
Quantitative Aptitude - Algebra - Quadratic Equation
Question
If x + 1 = x^2 and x > 0, then 2x^4 is
A) 6 + 4âˆš5
B) 3 + 5âˆš5
C) 5 + 3âˆš5
D) 7 + 3âˆš5
Answer
Option (D)
Solution
As per CAT 2017 - Quantitative Aptitude - Algebra - Quadratic Equation, we can see that
x+1=x^2
Find out the roots of x = [1+/- root(5)]/2
X2 = [3 +/- âˆš5]/2
X4 = [7 +/-3âˆš5]/2
2x4 = 7 +/- 3âˆš5
As the only option is 7 + 3âˆš5 So, we go with that.
Option (D)
Down

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Quantitative Aptitude - Algebra - Logarithms - If G is the geometric mean
Quantitative Aptitude - Algebra - Logarithms
Question
Suppose, log(base3)x = log(base12)y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log(base6)G is equal to
A) âˆša
B) 2a
C) a/2
D) a
Answer
Option (D)
Solution
As per CAT 2017 - Quantitative Aptitude - Algebra - Logarithms, we can see that
x=3^a and y=12^a
G = âˆš(3^a * 12^a) = 6^a
Log (base 6) 6^a = a
Option (D)
Logarithm Concepts Questions and Answers for

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Quantitative Aptitude - Algebra - Functions - The area of the closed region
Quantitative Aptitude - Algebra - Functions
Question
The area of the closed region bounded by the equation | x | + | y | = 2 in the two-dimensional plane is
A) 4Ï€
B) 4
C) 8
D) 2Ï€
Answer
Option (C)
Solution
As per the question from CAT 2017 - Quantitative Aptitude - Algebra - Functions,
Remember the formula |x| + |y| = n
Here, area bounded by the region = 2n^2
In the question, n=2
So, area = 8
Option (C)
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Quantitative Aptitude - Algebra - Simple Equations - If a and b are integers
Quantitative Aptitude - Algebra - Simple Equations
Question
If a and b are integers of opposite signs such that (a + 3)^2 : b^2 = 9 : 1 and (a - 1)^2 : (b - 1)^2 = 4 : 1, then the ratio a^2 : b^2 is
A) 9:4 â€˜
B) 81:4
C) 1: 4
D) 25: 4
Answer
Option (D)
Solution
As per the question from CAT 2017 - Quantitative Aptitude - Algebra - Simple Equations,
We get 4 cases
CASE - 1
a+3 = 3b
a-1 = 2b-2
CASE - 2
a+3 = 3b
a-1 = 2b + 2
C

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Quantitative Aptitude - Algebra - Maxima Minima - An elevator has a weight
Quantitative Aptitude - Algebra - Maxima Minima
Question
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 + â€¦â€¦.. + 57 = 630
Remaining sum of weights = 630 â€“ 53 â€“ 57 = 520

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Quantitative Aptitude - Algebra - Arun's present age in years
Quantitative Aptitude - Algebra - Linear Equations
Question
Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?
Answer
20
Solution
After going through CAT 2017 - Quantitative Aptitude - Algebra - Linear Equation, we can assume that
Age of Arun = A and age of Barun = B
Let us assume, A=0.4 B ----- (1)
After a few years, A+x = 0.5(B+x) ----- (2)
On putt

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