Quantitative Aptitude – Algebra - Quadratic Equations – If a and b are integers such that 2x^2 Slot -2 – Quantitative Aptitude – Algebra - Quadratic Equations – If a and b are integers such that 2x^2 If a and b are integers such that 2x^2 −ax + 2 > 0 and x^2 −bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a−6b is? Answer: 36 Solution: Given, 2x^2 −ax + 2 > 0 2{ (x-a/4)^2 - a^2/16+1} > 0 ∀ x ∈R -a^2/16+1 > 0 a ∈{ -3,-2,-1,0,1,2,3} x^2 −bx + 8 ≥ 0 (
Quantitative Aptitude – Algebra - Logarithms – 1/log(base2)100 -1/log(base4)100 +1/log(base5)100 Slot -2 – Quantitative Aptitude – Algebra - Logarithms – 1/log(base2)100 -1/log(base4)100 +1/log(base5)100 1/log(base2)100 -1/log(base4)100 +1/log(base5)100 -1/log(base10)100 +1/log(base20)100 -1/log(base25)100 +1/log(base50)100 ---? a) ½ b) 10 c) -4 d) 0 Answer: a) ½ Solution: Using log(basea)b = 1/log(baseb)a 1/log(base2)100 -1/log(base4)100 +1/log(base
Quantitative Aptitude – Algebra - Logarithms – If p^3 = q^4 = r^5 = s^6 Slot -2 – Quantitative Aptitude – Algebra - Logarithms – If p^3 = q^4 = r^5 = s^6 If p^3 = q^4 = r^5 = s^6, then the value of log_spqr is equal to? a) 24/5 b) 16/5 c) 47/10 d) 1 Answer: c) 47/10 Solution: Let p^3 = q^4 = r^5 = s^6=k So p=k^(1/3), q=k^(1/4), r=k^(1/5) and s=k^(1/6) Thus log(base s)pqr = log(base(k^(1/6) )) k^(1/3+1/4+1/5) =6 log(base k) k^((20+15+12)/60)=6×47/60 log(base k) k=47/10 Other p
Quantitative Aptitude – Algebra - Inequalities – If N and x are positive integers Slot -2 – Quantitative Aptitude – Algebra - Inequalities – If N and x are positive integers If N and x are positive integers such that N^N = 2^160 and N^2 + 2^N is an integral multiple of 2^x, then the largest possible x is? Answer: 10 Solution: N^N = (2^5)^32 N^N = 32^32 N=32 32^2 + 2^32 = (2^5)^2 + 2^32 32^2 + 2^32 = 2^10 + 2^32 32^2 + 2^32 = 2^10(1 + 2^22) Hence, Largest possible value of x is 10. Other posts related to Quan
Quantitative Aptitude – Algebra - Functions – Let f(x)=max{5x, 52-2x^2} Slot -2 – Quantitative Aptitude – Algebra - Functions – Let f(x)=max{5x, 52-2x^2} Let f(x)=max{5x, 52-2x^2}, where x is any positive real number. Then the minimum possible value of f(x) is? Answer: 20 Solution: For f(x) to be minimum , 5 = 52 − 2^2 2^2+5 −52 =0 −42+13=0 = 4 Thus minimum value of f(x) = 5x = 5*4 = 20 Other posts related to Quantitative Aptitude – Modern Maths Permutation and Combination – Fundamental Principle
Quantitative Aptitude – Algebra - Inequalities – The smallest integer n such that n^3 Slot -2 – Quantitative Aptitude – Algebra - Inequalities – The smallest integer n such that n^3 The smallest integer n such that n^3 - 11n^2 + 32n - 28 > 0 is? Answer: 8 Solution: Given, n^3 - 11n^2 + 32n - 28 > 0 (n-7) (n-2)^2>0 Therefore n must be greater than 7. So smallest integral value of n = 8 Other posts related to Quantitative Aptitude – Modern Maths Permutation and Combination – Fundamental Principle of
Quantitative Aptitude – Algebra - Logarithms – If x is a positive quantity such that 2^x Slot -1 – Quantitative Aptitude – Algebra - Logarithms – If x is a positive quantity such that 2^x If x is a positive quantity such that 2^x = 3^log(base5)^2 , then x is equal to? a) log(base5)^9 b) 1 + log(base5) 3/5 c) log(base5)^8 d) 1 + log(base3) 5/3 Answer: b) 1 + log(base5) 3/5 Solution: Given , 2^x = 3^log(base5)2 taking log of both sides , x log2 = log(base5) 2 log 3 = (log 2
Quantitative Aptitude – Algebra - Polynomials – If u^2 + (u-2v-1)^2 Slot -1 – Quantitative Aptitude – Algebra - Polynomials – If u^2 + (u-2v-1)^2 If u^2 + (u-2v-1)^2 = -4v(u + v), then what is the value of u + 3v? a) -1/4 b) ½ c) 0 d) ¼ Solution: Given, u^2 + (u-2v-1)^2 = -4v(u + v) Or u^2+4vu+4 v^2 +(u-2v-1)^2 = 0 (u+2v)^2+ (u-2v-1)^2= 0 This will be zero only if u = -2v = 2v + 1 Or v = -1/4 & u = ½ So u + 3v = -1/4 Option a) -1/4 is correct. Other posts related to Quantitat
Quantitative Aptitude – Algebra - Polynomials – Given that x^2018 y^2017 Slot -1 – Quantitative Aptitude – Algebra - Polynomials – Given that x^2018 y^2017 Given that x^2018 y^2017 =1/2 and x^2016 y^2019= 8,the value of x^2 + y^3 is?a) 33/4 b) 35/4 c) 31/4 d) 37/4 Answer: a) 33/4 Solution: Given, x^2018 y^2017 =1/2------------------1) x^2016 y^2019= 8-------------------2) By dividing eq 1) with eq 2) x^2/y^2 =1/16--------3) By multiplying eq 1) with eq 2) x^4034 y^4036=(xy)^4034 y^2= 4------
Quantitative Aptitude – Algebra - Functions – If f(x + 2) = f(x) + f(x + 1) Slot -1 – Quantitative Aptitude – Algebra - Functions – If f(x + 2) = f(x) + f(x + 1) If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals? Answer: 54 Solution: Given , f(x + 2) = f(x) + f(x + 1) f(15) = f(13) + f(14) f(13) + f(14) = 617 ---------------1) f(12) + f(13) = f(14) -------------2) f(11) + f(12) = f(13)-------------3) from eq 1) , 2) & 3) 2f(11) + 3f(12) =