# Quantitative Aptitude – Algebra – Functions – If f(ab) = f(a)f(b) for all positive

January 1st, 2020 by

Quantitative Aptitude - Algebra - Functions - If f(ab) = f(a)f(b) for all positive Quantitative Aptitude - Algebra - Functions Question If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is Answer 1 Solution From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that, Let us take the case when a=b=1 So, f(1) = f(1) f(1) f(1) = [f(1)]^2 f(1)[f(1)-1] = 0 f(1) = 1 So, the maximum value of f(1) = 1 Answer: 1 Download CAT 2017 Question Paper with answers and detailed

# Quantitative Aptitude – Algebra – Number of integer solutions – 1/a + 1/b = 1/9

January 1st, 2020 by

Quantitative Aptitude - Algebra - Number of integer solutions - 1/a + 1/b = 1/9 Quantitative Aptitude - Algebra - Number of integer solutions Question How many different pairs (a, b) of positive integers are there such that a ≤ b and 1/a + 1/b = 1/9 Answer 3 Solution From CAT 2017 - Quantitative Aptitude - Algebra - Number of integer solutions, we can see that, 9(a + b) = ab ab – 9a – 9b + 81 = 81 (a – 9) (b – 9) = 81 = 34 As a, b > 0 and a ≤ b, there are only 3 ordered pairs, given by a – 9 = 1, 3 or 9 and corr

# Quantitative Aptitude – Algebra – Logarithms – If log (2^a × 3^b × 5^c)

January 1st, 2020 by

Quantitative Aptitude - Algebra - Logarithms - If log (2^a × 3^b × 5^c) Quantitative Aptitude - Algebra - Logarithms Question If log (2^a × 3^b × 5^c) is the arithmetic mean of log (2^2 × 3^3 × 5), log (2^6 × 3 × 5^7), and log(2 × 3^2 × 5^4), then a equals Answer 3 Solution From CAT 2017 - Quantitative Aptitude - Algebra - Logarithms, we can see that, log (2^a. 3^b. 5^c) = [log (2^2.3^3.5) + log (2^6.3.5^7) + log (2.3^2.5^4)]/3 3 * log (2^a. 3^b. 5^c) = log (2^9.3^6.5^12) log (2^a. 3^b. 5^c)^3 = log (2^9.3^6.5^12) log (2^3a.

# Quantitative Aptitude – Algebra – If 9^(x-1/2) – 2^(2x-2) = 4^x

January 1st, 2020 by

Quantitative Aptitude - Algebra - If 9^(x-1/2) – 2^(2x-2) = 4^x Quantitative Aptitude - Algebra Question If 9^(x-1/2) – 2^(2x-2) = 4^x – 3^(2x-3) , then x is A) 3/2 B) 2/5 C) 3/4 D) 4/9 Answer Option (A) Solution From CAT 2017 - Quantitative Aptitude - Algebra, we can see that, You can solve the question easily by putting in values from the options given. When we put the value of x as 3/2, it satisfies the equation. So, 3/2 is the correct answer. Option (A) Download CAT 2017 Question Paper with answers and

# Quantitative Aptitude – Algebra – Quadratic Equations – The minimum possible value

January 1st, 2020 by

Quantitative Aptitude - Algebra - Quadratic Equations - The minimum possible value Quantitative Aptitude - Algebra - Quadratic Equations Question The minimum possible value of the sum of the squares of the roots of the equation x^2 + (a + 3)x - (a + 5) = 0 is A) 1 B) 2 C) 3 D) 4 Answer Option (C) Solution From CAT 2017 - Quantitative Aptitude - Algebra - Quadratic Equations, we can see that, b and c can be the roots of the given equation. We have to find, b^2 + c^2 = (b+c)^2 – 2bc b+c = -(a+3) and bc = -(a+5) b^2 +

# Quantitative Aptitude – Algebra – Functions – Let f(x) = x^2 and g(x) = 2^x

January 1st, 2020 by

Quantitative Aptitude - Algebra - Functions - Let f(x) = x^2 and g(x) = 2^x Quantitative Aptitude - Algebra - Functions Question Let f(x) = x^2 and g(x) = 2^x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is A) 16 B) 18 C) 36 D) 40 Answer Option (C) Solution From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that, f(g(x)) = 2^(2x) g(f(x)) = 2^((x)^2) f(f(g(x)) + g(f(x)) = (2^(2x) + 2^(x^2))^2 at x = 1, we get 36 Option (C) Download CAT 2017 Question Paper with answers an

# Quantitative Aptitude – Algebra – Logarithms – If x is a real number

January 1st, 2020 by

Quantitative Aptitude - Algebra - Logarithms - If x is a real number Quantitative Aptitude - Algebra - Logarithms Question If x is a real number such that log(base 3)5 = log(base 5)(2 + x), then which of the following is true? A) 0 < x < 3 B) 23 < x < 30 C) x > 30 D) 3 < x < 23 Answer Option (D) Solution From CAT 2017 - Quantitative Aptitude - Algebra - Logarithms, we can see that, Log(base 3)5 lies between 1 and 2 because Log(base 3)3 = 1 and Log(base 3)9 = 2 1 < Log(base 3)5 < 2 So, log(base 5)(2+x

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

January 1st, 2020 by

Quantitative Aptitude - Algebra - Maxima Minima - If three sides of a rectangular Quantitative Aptitude - Algebra - Maxima Minima Question 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 ar

# Quantitative Aptitude – Algebra – Functions – If f(x) = (5x+2)/(3x-5)

December 30th, 2019 by

Quantitative Aptitude - Algebra - Functions - If f(x) = (5x+2)/(3x-5) Quantitative Aptitude - Algebra - Functions Question If f(x) = (5x+2)/(3x-5) and g(x) = x^2 - 2x - 1, then the value of g(f(f(3))) is A) 2 B) 1/3 C) 6 D) 2/3 Answer Option (A) Solution From CAT 2017 - Quantitative Aptitude - Algebra - Functions, we can see that, f(3) = 17/4 f(17/4) = 3 g(3) = 2 Option (A) Download CAT 2017 Question Paper with answers and detailed solutions in PDF CAT 2017 Questions from Quantitative Aptitude - Algebra - Fun