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

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Quantitative Aptitude â€“ Algebra - Polynomials â€“ If u^2 + (u-2v-1)^2
Slot -1 â€“Â Quantitative Aptitude â€“ Algebra - Polynomials â€“ 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) Â½
c) 0
d) Â¼
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 = Â½
So u + 3v = -1/4
Option a) -1/4 is correct.
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Quantitative Aptitude â€“ Algebra - Polynomials â€“ Given that x^2018 y^2017
Slot -1 â€“Â Quantitative Aptitude â€“ Algebra - Polynomials â€“ 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------

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