# Quantitative Aptitude – Algebra – Functions – If f1(x) = x^2 + 11x + n

December 30th, 2019 by

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 – 4n > 0 On solving the inequality, we get, n

# Quantitative Aptitude – Algebra – Inequalities – For how many integers n

December 30th, 2019 by

Quantitative Aptitude - Algebra - Inequalities - For how many integers n Quantitative Aptitude - Algebra - Inequalities Question For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 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 – 18n + 56 ≤ 0 Factorize and we get, (n-4)(n-14) ≤ 0 4 ≤ n ≤ 14 No of values of n =11 Answer: 11 Download CAT 2017 Question Paper with answers and detai

# Quantitative Aptitude – Algebra – Inequalities – The number of solutions (x, y, z)

December 30th, 2019 by

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 – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 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

# Quantitative Aptitude – Algebra – Polynomials – If 9^(2x – 1) – 81^(x-1) = 1944

December 30th, 2019 by

Quantitative Aptitude - Algebra - Polynomials - If 9^(2x – 1) – 81^(x-1) = 1944 Quantitative Aptitude - Algebra - Polynomials Question If 9^(2x – 1) – 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) – 9^(2x-2) = 1944 It can be written as 3^(4x)/9 – 3^(4x)/81 = 1944 8(3^(4x)/81) = 1944 x =9/4 Option (B) Download CAT 2017 Question Paper with answers and detailed solutions in PDF C

# Quantitative Aptitude – Algebra – Quadratic Equation – If x + 1 = x^2

December 30th, 2019 by

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 + 4√5 B) 3 + 5√5 C) 5 + 3√5 D) 7 + 3√5 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 +/- √5]/2 X4 = [7 +/-3√5]/2 2x4 = 7 +/- 3√5 As the only option is 7 + 3√5 So, we go with that. Option (D) Down

# Quantitative Aptitude – Algebra – Logarithms – If G is the geometric mean

December 30th, 2019 by

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) √a 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 = √(3^a * 12^a) = 6^a Log (base 6) 6^a = a Option (D) Logarithm Concepts Questions and Answers for

# Quantitative Aptitude – Algebra – Functions – The area of the closed region

December 30th, 2019 by

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) 4π B) 4 C) 8 D) 2π 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) Download CAT 2017 Question Paper

# Quantitative Aptitude – Algebra – Simple Equations – If a and b are integers

December 30th, 2019 by

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 ‘ 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

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

December 29th, 2019 by

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 + …….. + 57 = 630 Remaining sum of weights = 630 – 53 – 57 = 520